1
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Winer M, Baldwin CL, Barney R, Galitski V, Swingle B. Glass transition of quantum hard spheres in high dimensions. Phys Rev E 2024; 109:044112. [PMID: 38755820 DOI: 10.1103/physreve.109.044112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Accepted: 03/12/2024] [Indexed: 05/18/2024]
Abstract
We study the equilibrium thermodynamics of quantum hard spheres in the infinite-dimensional limit, determining the boundary between liquid and glass phases in the temperature-density plane by means of the Franz-Parisi potential. We find that as the temperature decreases from high values, the effective radius of the spheres is enhanced by a multiple of the thermal de Broglie wavelength, thus increasing the effective filling fraction and decreasing the critical density for the glass phase. Numerical calculations show that the critical density continues to decrease monotonically as the temperature decreases further, suggesting that the system will form a glass at sufficiently low temperatures for any density. The methods used in this paper can be extended to more general potentials, and also to other transitions such as the Kauzman/Replica Symmetry Breaking (RSB) transition, the Gardner transition, and potentially even jamming.
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Affiliation(s)
- Michael Winer
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Christopher L Baldwin
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Richard Barney
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Victor Galitski
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Brian Swingle
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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2
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Martirosyan G, Ho CJ, Etrych J, Zhang Y, Cao A, Hadzibabic Z, Eigen C. Observation of Subdiffusive Dynamic Scaling in a Driven and Disordered Bose Gas. PHYSICAL REVIEW LETTERS 2024; 132:113401. [PMID: 38563934 DOI: 10.1103/physrevlett.132.113401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 01/05/2024] [Indexed: 04/04/2024]
Abstract
We explore the dynamics of a tuneable box-trapped Bose gas under strong periodic forcing in the presence of weak disorder. In absence of interparticle interactions, the interplay of the drive and disorder results in an isotropic nonthermal momentum distribution that shows subdiffusive dynamic scaling, with sublinear energy growth and the universal scaling function captured well by a compressed exponential. We explain that this subdiffusion in momentum space can naturally be understood as a random walk in energy space. We also experimentally show that for increasing interaction strength, the gas behavior smoothly crosses over to wave turbulence characterized by a power-law momentum distribution, which opens new possibilities for systematic studies of the interplay of disorder and interactions in driven quantum systems.
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Affiliation(s)
- Gevorg Martirosyan
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Christopher J Ho
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Jiří Etrych
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Yansheng Zhang
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Alec Cao
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Zoran Hadzibabic
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Christoph Eigen
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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3
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Garcia ER, Hofmann J. Fluctuation corrections to Lifshitz tails in disordered systems. Phys Rev E 2024; 109:L032103. [PMID: 38632721 DOI: 10.1103/physreve.109.l032103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Accepted: 02/13/2024] [Indexed: 04/19/2024]
Abstract
Quenched disorder in semiconductors induces localized electronic states at the band edge, which manifest as an exponential tail in the density of states. For large impurity densities, this tail takes a universal Lifshitz form that is characterized by short-ranged potential fluctuations. We provide both analytical expressions and numerical values for the Lifshitz tail of a parabolic conduction band including its exact fluctuation prefactor. Our analysis is based on a replica field integral approach, where the leading exponential scaling of the tail is determined by an instanton profile and fluctuations around the instanton determine the subleading preexponential factor. This factor contains the determinant of a fluctuation operator, and we avoid a full computation of its spectrum by using a Gel'fand-Yaglom formalism, which provides a concise general derivation of fluctuation corrections in disorder problems. We provide a revised result for the disorder band tail in two dimensions.
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Affiliation(s)
| | - Johannes Hofmann
- Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden
- Nordita, Stockholm University and KTH Royal Institute of Technology, 10691 Stockholm, Sweden
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4
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Ren M, Yu Y, Wu B, Qi X, Wang Y, Yao X, Ren J, Guo Z, Jiang H, Chen H, Liu XJ, Chen Z, Sun Y. Realization of Gapped and Ungapped Photonic Topological Anderson Insulators. PHYSICAL REVIEW LETTERS 2024; 132:066602. [PMID: 38394559 DOI: 10.1103/physrevlett.132.066602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 01/03/2024] [Indexed: 02/25/2024]
Abstract
It is commonly believed that topologically nontrivial one-dimensional systems support edge states rather than bulk states at zero energy. In this work, we find an unanticipated case of topological Anderson insulator (TAI) phase where two bulk modes are degenerate at zero energy, in addition to degenerate edge modes. We term this "ungapped TAI" to distinguish it from the previously known gapped TAIs. Our experimental realization of both gapped and ungapped TAIs relies on coupled photonic resonators, in which the disorder in coupling is judiciously engineered by adjusting the spacing between the resonators. By measuring the local density of states both in the bulk and at the edges, we demonstrate the existence of these two types of TAIs, together forming a TAI plateau in the phase diagram. Our experimental findings are well supported by theoretical analysis. In the ungapped TAI phase, we observe stable coexistence of topological edge states and localized bulk states at zero energy, highlighting the distinction between TAIs and traditional topological insulators.
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Affiliation(s)
- Mina Ren
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Ye Yu
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Bintao Wu
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xin Qi
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Yiwei Wang
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xiaogang Yao
- Information Materials and Devices Research Center, Shanghai Institute of Ceramics, Chinese Academy of Science, Shanghai 201800, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Zhiwei Guo
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Haitao Jiang
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Hong Chen
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- International Quantum Academy, Shenzhen 518048, China
| | - Zhigang Chen
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Yong Sun
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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5
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Lin L, Wei Y, He D. Disorder-induced spiky phonon transmission of harmonic lattices. Phys Rev E 2024; 109:024129. [PMID: 38491675 DOI: 10.1103/physreve.109.024129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2023] [Accepted: 02/05/2024] [Indexed: 03/18/2024]
Abstract
In this article, we find that impurity in a one-dimensional harmonic chain leads to spikes in the phonon transmission. Using the Langevin equations and Green's function method (LEGF), we find the underlying mechanism of spikes, which comes from the fact that the wave energy can be transferred through uniform subchains laid between impurities without loss. Both the position and magnitude of spikes can be analytically obtained. By employing these results, we provide an analytical approach to transmission in the thermodynamic limit, thereby compensating for the limitation of LEGF that are practically confined to finite system size. Finally, we determine an expression for the localization length based on LEGF, demonstrating the equivalence between mass disorder and spatial disorder in low impurity concentration.
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Affiliation(s)
- Lu Lin
- Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China
| | - Yuhang Wei
- Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China
| | - Dahai He
- Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China
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6
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Mu S, Gong J, Lemarié G. Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets. PHYSICAL REVIEW LETTERS 2024; 132:046301. [PMID: 38335351 DOI: 10.1103/physrevlett.132.046301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 09/08/2023] [Accepted: 12/14/2023] [Indexed: 02/12/2024]
Abstract
We identify the key features of Kardar-Parisi-Zhang (KPZ) universality class in the fluctuations of the wave density logarithm in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of 1/3, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent 2/3. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched exponential correction to its well-known exponential localization.
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Affiliation(s)
- Sen Mu
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China
| | - Gabriel Lemarié
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, France
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7
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Sinha S, Ray S, Sinha S. Classical route to ergodicity and scarring in collective quantum systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:163001. [PMID: 38190726 DOI: 10.1088/1361-648x/ad1bf5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Accepted: 01/08/2024] [Indexed: 01/10/2024]
Abstract
Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.
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Affiliation(s)
- Sudip Sinha
- Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741246, India
| | - Sayak Ray
- Physikalisches Institut, Universität Bonn, Nußallee 12, 53115 Bonn, Germany
| | - Subhasis Sinha
- Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741246, India
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8
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Cheng Z. Accurate Thermodynamic Properties of Ideal Bosons in a Highly Anisotropic 2D Harmonic Potential. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1513. [PMID: 37998205 PMCID: PMC10670444 DOI: 10.3390/e25111513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Revised: 08/01/2023] [Accepted: 08/15/2023] [Indexed: 11/25/2023]
Abstract
One can derive an analytic result for the issue of Bose-Einstein condensation (BEC) in anisotropic 2D harmonic traps. We find that the number of uncondensed bosons is represented by an analytic function, which includes a series expansion of q-digamma functions in mathematics. One can utilize this analytic result to evaluate various thermodynamic functions of ideal bosons in 2D anisotropic harmonic traps. The first major discovery is that the internal energy of a finite number of ideal bosons is a monotonically increasing function of anisotropy parameter p. The second major discovery is that, when p≥0.5, the changing with temperature of the heat capacity of a finite number of ideal bosons possesses the maximum value, which happens at critical temperature Tc. The third major discovery is that, when 0.1≤p<0.5, the changing with temperature of the heat capacity of a finite number of ideal bosons possesses an inflection point, but when p<0.1, the inflection point disappears. The fourth major discovery is that, in the thermodynamic limit, at Tc and when p≥0.5, the heat capacity at constant number reveals a cusp singularity, which resembles the λ-transition of liquid helium-4. The fifth major discovery is that, in comparison to 2D isotropic harmonic traps (p=1), the singular peak of the specific heat becomes very gentle when p is lowered.
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Affiliation(s)
- Ze Cheng
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
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9
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Gonçalves M, Amorim B, Castro EV, Ribeiro P. Critical Phase Dualities in 1D Exactly Solvable Quasiperiodic Models. PHYSICAL REVIEW LETTERS 2023; 131:186303. [PMID: 37977623 DOI: 10.1103/physrevlett.131.186303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 09/25/2023] [Indexed: 11/19/2023]
Abstract
We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-André model and the models of Sriram Ganeshan, J. H. Pixley, and S. Das Sarma [Phys. Rev. Lett. 114, 146601 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.146601] and J. Biddle and S. Das Sarma [Phys. Rev. Lett. 104, 070601 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.070601]. The analytical treatment follows from recognizing these models as a novel type of fixed points of the renormalization group procedure recently proposed in Phys. Rev. B 108, L100201 (2023)10.1103/PhysRevB.108.L100201 for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and nontrivial mobility edges in an undriven system without the need for the unbounded potentials required by previous proposals.
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Affiliation(s)
- Miguel Gonçalves
- CeFEMA-LaPMET, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
- Centro de Física das Universidades do Minho e Porto, LaPMET, Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
| | - Bruno Amorim
- Centro de Física das Universidades do Minho e Porto, LaPMET, University of Minho, Campus of Gualtar, 4710-057 Braga, Portugal
| | - Eduardo V Castro
- Centro de Física das Universidades do Minho e Porto, LaPMET, Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Pedro Ribeiro
- CeFEMA-LaPMET, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
- Beijing Computational Science Research Center, Beijing 100193, China
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10
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Zhou XC, Wang Y, Poon TFJ, Zhou Q, Liu XJ. Exact New Mobility Edges between Critical and Localized States. PHYSICAL REVIEW LETTERS 2023; 131:176401. [PMID: 37955469 DOI: 10.1103/physrevlett.131.176401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 08/25/2023] [Accepted: 09/29/2023] [Indexed: 11/14/2023]
Abstract
The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one-dimensional models are featured by a quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This Letter may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.
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Affiliation(s)
- Xin-Chi Zhou
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
| | - Yongjian Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
- School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China
| | - Ting-Fung Jeffrey Poon
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
| | - Qi Zhou
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Hefei National Laboratory, Hefei 230088, China
- International Quantum Academy, Shenzhen 518048, China
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11
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Li L, Zhou C, Xiong W, Huang M, Fang S, Xu X, Ji J, Gao M, Song T, Hong Y, Liang Z, Chen D, Hou X, Zhou X, Chen X, Chen W, Wang B, Li T, Liu L. All-fiber laser system for all-optical 87Rb Bose Einstein condensate to space application. APPLIED OPTICS 2023; 62:7844-7851. [PMID: 37855495 DOI: 10.1364/ao.497749] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 09/21/2023] [Indexed: 10/20/2023]
Abstract
In the development of the Cold Atom Physics Research Rack (CAPR) on board the Chinese Space Station, the laser system plays a critical role in preparing the all-optical 87 R b Bose-Einstein condensates (BECs). An all-fiber laser system has been developed for CAPR to provide the required optical fields for atom interaction and to maintain the beam pointing in long-term operation. The laser system integrates a 780 nm fiber laser system and an all-fiber optical control module for sub-Doppler cooling, as well as an all-fiber 1064 nm laser system for evaporative cooling. The high-power, single-frequency 780 nm lasers are achieved through rare-Earth doped fiber amplification, fiber frequency-doubling, and frequency stabilization technology. The all-fiber optical control module divides the output of the 780 nm laser system into 15 channels and regulates them for cooling, trapping, and probing atoms. Moreover, the power consistency of each pair of cooling beams is ensured by three power tracking modules, which is a prerequisite for maintaining stable MOT and molasses. A high-power, compact, controlled-flexible, and highly stable l064 nm all-fiber laser system employing two-stage ytterbium-doped fiber amplifier (YDFA) technology has been designed for evaporative cooling in the optical dipole trap (ODT). Finally, an all-optical 87 R b BEC is realized with this all-fiber laser system, which provides an alternative solution for trapping and manipulating ultra-cold atoms in challenging environmental conditions.
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12
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Hopjan M, Vidmar L. Scale-Invariant Survival Probability at Eigenstate Transitions. PHYSICAL REVIEW LETTERS 2023; 131:060404. [PMID: 37625072 DOI: 10.1103/physrevlett.131.060404] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 04/21/2023] [Accepted: 07/20/2023] [Indexed: 08/27/2023]
Abstract
Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here, we argue that a scaled survival probability, where time is measured in units of a typical Heisenberg time, exhibits a scale-invariant behavior at eigenstate transitions. We first demonstrate this property in two paradigmatic quadratic models, the one-dimensional Aubry-Andre model and three-dimensional Anderson model. Surprisingly, we then show that similar phenomenology emerges in the interacting avalanche model of ergodicity breaking phase transitions. This establishes an intriguing similarity between localization transition in quadratic systems and ergodicity breaking phase transition in interacting systems.
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Affiliation(s)
- Miroslav Hopjan
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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13
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Yao LH, Wald S. Coined quantum walks on the line: Disorder, entanglement, and localization. Phys Rev E 2023; 108:024139. [PMID: 37723699 DOI: 10.1103/physreve.108.024139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 07/25/2023] [Indexed: 09/20/2023]
Abstract
Disorder in coined quantum walks generally leads to localization. We investigate the influence of the localization on the entanglement properties of coined quantum walks. Specifically, we consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. After confirming that our choice of disorder localizes the walker, we study how the localization affects the properties of the coined quantum walk. We find that the mixing properties of the walk are altered nontrivially with mixing being improved at short time scales. Special focus is given to the influence of coin disorder on the properties of the quantum state and the coin-walker entanglement. We find that disorder alters the quantum state significantly even when the walker probability distribution is still close to the nondisordered case. We observe that, generically, coin disorder decreases the coin-walker entanglement and that the localization leaves distinct traces in the entanglement entropy and the entanglement negativity of the coined quantum walk.
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Affiliation(s)
- Louie Hong Yao
- Department of Physics & Center for Soft Matter and Biological Physics, MC 0435, Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Sascha Wald
- Statistical Physics Group, Centre for Fluid and Complex Systems, Coventry University, United Kingdom
- 𝕃4 Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, European Union
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14
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Qin D, Chen J, Lu N. A Novel Density of States (DOS) for Disordered Organic Semiconductors. MICROMACHINES 2023; 14:1361. [PMID: 37512673 PMCID: PMC10383803 DOI: 10.3390/mi14071361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Revised: 06/27/2023] [Accepted: 06/30/2023] [Indexed: 07/30/2023]
Abstract
In this work, we proposed a novel theory of DOS for disordered organic semiconductors based on the frontier orbital theory and probability statistics. The proposed DOS has been verified by comparing with other DOS alternatives and experimental data, and the mobility calculated by the proposed DOS is closer to experimental data than traditional DOS. Moreover, we also provide a detailed method to choose the DOS parameter for better use of the proposed DOS. This paper also contains a prediction for the DOS parameters, and it has been verified by the experimental data. More importantly, the physical meaning of the proposed DOS parameter has been explained by equilibrium energy theory and transport energy theory to make this proposed model more rational. Compared with the improved DOS based on Gaussian and exponential DOS, this work is a new attempt to combine probabilistic theory with physical theory related to DOS in disordered organic semiconductors, showing great significance for the further investigation of the properties of DOS.
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Affiliation(s)
- Dong Qin
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Jiezhi Chen
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Nianduan Lu
- State Key Lab of Fabrication Technologies for Integrated Circuits & Laboratory of Microelectronics Devices and Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China
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15
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Zhu Z, Yao H, Sanchez-Palencia L. Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential. PHYSICAL REVIEW LETTERS 2023; 130:220402. [PMID: 37327407 DOI: 10.1103/physrevlett.130.220402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 05/10/2023] [Indexed: 06/18/2023]
Abstract
Quantum simulation of quasicrystals in synthetic bosonic matter now paves the way for the exploration of these intriguing systems in wide parameter ranges. Yet thermal fluctuations in such systems compete with quantum coherence and significantly affect the zero-temperature quantum phases. Here we determine the thermodynamic phase diagram of interacting bosons in a two-dimensional, homogeneous quasicrystal potential. We find our results using quantum Monte Carlo simulations. Finite-size effects are carefully taken into account and the quantum phases are systematically distinguished from thermal phases. In particular, we demonstrate stabilization of a genuine Bose glass phase against the normal fluid in sizable parameter ranges. We interpret our results for strong interactions using a fermionization picture and discuss experimental relevance.
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Affiliation(s)
- Zhaoxuan Zhu
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
| | - Hepeng Yao
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
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16
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Sauerwein N, Orsi F, Uhrich P, Bandyopadhyay S, Mattiotti F, Cantat-Moltrecht T, Pupillo G, Hauke P, Brantut JP. Engineering random spin models with atoms in a high-finesse cavity. NATURE PHYSICS 2023; 19:1128-1134. [PMID: 37575364 PMCID: PMC10415180 DOI: 10.1038/s41567-023-02033-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 03/23/2023] [Indexed: 08/15/2023]
Abstract
All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics over holographic duality in high-energy physics to annealing algorithms in quantum computing. Typically, these models are abstractions that do not find unambiguous physical realizations in nature. Here we realize an all-to-all interacting, disordered spin system by subjecting an atomic cloud in a cavity to a controllable light shift. Adjusting the detuning between atom resonance and cavity mode, we can tune between disordered versions of a central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically probing the low-energy excitations of the system, we explore the competition of interactions with disorder across a broad parameter range. We show how disorder in the central-mode model breaks the strong collective coupling, making the dark-state manifold cross over to a random distribution of weakly mixed light-matter, 'grey', states. In the Lipkin-Meshkov-Glick model, the ferromagnetic finite-sized ground state evolves towards a paramagnet as disorder is increased. In that regime, semi-localized eigenstates emerge, as we observe by extracting bounds on the participation ratio. These results present substantial steps towards freely programmable cavity-mediated interactions for the design of arbitrary spin Hamiltonians.
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Affiliation(s)
- Nick Sauerwein
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Francesca Orsi
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Philipp Uhrich
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Soumik Bandyopadhyay
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Francesco Mattiotti
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, Strasbourg, France
| | - Tigrane Cantat-Moltrecht
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Guido Pupillo
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, Strasbourg, France
| | - Philipp Hauke
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Jean-Philippe Brantut
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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17
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Cai X, Yu YC. Exact mobility edges in quasiperiodic systems without self-duality. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:035602. [PMID: 36347043 DOI: 10.1088/1361-648x/aca136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 11/08/2022] [Indexed: 06/16/2023]
Abstract
Mobility edge (ME), a critical energy separating localized and extended states in spectrum, is a central concept in understanding localization physics. However, there are few models with exact MEs, and their presences are fragile against perturbations. In the paper, we generalize the Aubry-André-Harper model proposed in (Ganeshanet al2015Phys. Rev. Lett.114146601) and recently realized in (Anet al2021Phys. Rev. Lett.126040603), by introducing a relative phase in the quasiperiodic potential. Applying Avila's global theory, we analytically compute localization lengths of all single-particle states and determine the exact expression of ME, which both significantly depend on the relative phase. They are verified by numerical simulations, and physical perception of the exact expression is also provided. We show that old exact MEs, guaranteed by the delicate self-duality which is broken by the relative phase, are special ones in a series controlled by the phase. Furthermore, we demonstrate that out of expectation, exact MEs are invariant against a shift in the quasiperiodic potential, although the shift changes the spectrum and localization properties. Finally, we show that the exact ME is related to the one in the dual model which has long-range hoppings.
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Affiliation(s)
- Xiaoming Cai
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
| | - Yi-Cong Yu
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
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18
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Lecoutre B, Guo Y, Yu X, Niranjan M, Mukhtar M, Volchkov VV, Aspect A, Josse V. Bichromatic state-dependent disordered potential for Anderson localization of ultracold atoms. THE EUROPEAN PHYSICAL JOURNAL. D, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 2022; 76:218. [PMID: 36588589 PMCID: PMC9799246 DOI: 10.1140/epjd/s10053-022-00549-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 10/27/2022] [Indexed: 06/17/2023]
Abstract
ABSTRACT The ability to load ultracold atoms at a well-defined energy in a disordered potential is a crucial tool to study quantum transport, and in particular Anderson localization. In this paper, we present a new method for achieving that goal by rf transfer of atoms in an atomic Bose-Einstein condensate from a disorder-insensitive state to a disorder-sensitive state. It is based on a bichromatic laser speckle pattern, produced by two lasers whose frequencies are chosen so that their light-shifts cancel each other in the first state and add up in the second state. Moreover, the spontaneous scattering rate in the disorder-sensitive state is low enough to allow for long observation times of quantum transport in that state. We theoretically and experimentally study the characteristics of the resulting potential.
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Affiliation(s)
- Baptiste Lecoutre
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Yukun Guo
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Xudong Yu
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - M. Niranjan
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Musawwadah Mukhtar
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Valentin V. Volchkov
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Alain Aspect
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Vincent Josse
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
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19
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Takayoshi S, Giamarchi T. Dynamical conductivity of disordered quantum chains. THE EUROPEAN PHYSICAL JOURNAL. D, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 2022; 76:213. [PMID: 36397821 PMCID: PMC9640472 DOI: 10.1140/epjd/s10053-022-00524-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 10/07/2022] [Indexed: 06/16/2023]
Abstract
ABSTRACT We study the transport properties of a one-dimensional quantum system with disorder. We numerically compute the frequency dependence of the conductivity of a fermionic chain with nearest-neighbor interaction and a random chemical potential by using the Chebyshev matrix product state (CheMPS) method. As a benchmark, we investigate the noninteracting case first. Comparison with exact diagonalization and analytical solutions demonstrates that the results of CheMPS are reliable over a wide range of frequencies. We then calculate the dynamical conductivity spectra of the interacting system for various values of the interaction and disorder strengths. In the high-frequency regime, the conductivity decays as a power law, with an interaction-dependent exponent. This behavior is qualitatively consistent with the bosonized field theory predictions, although the numerical evaluation of the exponent shows deviations from the analytically expected values. We also compute the characteristic pinning frequency at which a peak in the conductivity appears. We confirm that it is directly related to the inverse of the localization length, even in the interacting case. We demonstrate that the localization length follows a power law of the disorder strength with an exponent dependent on the interaction, and find good quantitative agreement with the field theory predictions. In the low-frequency regime, we find a behavior consistent with the one of the noninteracting system ω 2 ( ln ω ) 2 independently of the interaction. We discuss the consequences of our finding for experiments in cold atomic gases.
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Affiliation(s)
| | - Thierry Giamarchi
- Department of Quantum Matter Physics, University of Geneva, 1211 Geneva, Switzerland
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20
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Costa E, Scriva G, Fazio R, Pilati S. Deep-learning density functionals for gradient descent optimization. Phys Rev E 2022; 106:045309. [PMID: 36397567 DOI: 10.1103/physreve.106.045309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 09/27/2022] [Indexed: 06/16/2023]
Abstract
Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily be trained to accurately map ground-state density profiles to the corresponding energies, their functional derivatives often turn out to be too noisy, leading to instabilities in self-consistent iterations and in gradient-based searches of the ground-state density profile. We investigate how these instabilities occur when standard deep neural networks are adopted as regression models, and we show how to avoid them by using an ad hoc convolutional architecture featuring an interchannel averaging layer. The main testbed we consider is a realistic model for noninteracting atoms in optical speckle disorder. With the interchannel average, accurate and systematically improvable ground-state energies and density profiles are obtained via gradient-descent optimization, without instabilities nor violations of the variational principle.
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Affiliation(s)
- E Costa
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
| | - G Scriva
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
| | - R Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Dipartimento di Fisica, Università di Napoli "Federico II," Monte S. Angelo, I-80126 Napoli, Italy
| | - S Pilati
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
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21
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Lin Q, Li T, Xiao L, Wang K, Yi W, Xue P. Topological Phase Transitions and Mobility Edges in Non-Hermitian Quasicrystals. PHYSICAL REVIEW LETTERS 2022; 129:113601. [PMID: 36154424 DOI: 10.1103/physrevlett.129.113601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 08/19/2022] [Indexed: 06/16/2023]
Abstract
Non-Hermiticity significantly enriches the properties of topological models, leading to exotic features such as the non-Hermitian skin effects and non-Bloch bulk-boundary correspondence that have no counterparts in Hermitian settings. Its impact is particularly illustrating in non-Hermitian quasicrystals where the interplay between non-Hermiticity and quasiperiodicity results in the concurrence of the delocalization-localization transition, the parity-time (PT)-symmetry breaking, and the onset of the non-Hermitian skin effects. Here, we experimentally simulate non-Hermitian quasicrystals using photonic quantum walks. Using dynamic observables, we demonstrate that the system can transit from a delocalized, PT-symmetry broken phase that features non-Hermitian skin effects, to a localized, PT-symmetry unbroken phase with no non-Hermitian skin effects. The measured critical point is consistent with the theoretical prediction through a spectral winding number, confirming the topological origin of the phase transition. More interestingly, we also provide the first experimental evidence for mobility edges which are induced by non-Hermiticity. Our Letter opens the avenue of investigating the interplay of non-Hermiticity, quasiperiodicity, and spectral topology in open quantum systems.
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Affiliation(s)
- Quan Lin
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Tianyu Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Lei Xiao
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Kunkun Wang
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Peng Xue
- Beijing Computational Science Research Center, Beijing 100084, China
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22
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Wang Y, Zhang JH, Li Y, Wu J, Liu W, Mei F, Hu Y, Xiao L, Ma J, Chin C, Jia S. Observation of Interaction-Induced Mobility Edge in an Atomic Aubry-André Wire. PHYSICAL REVIEW LETTERS 2022; 129:103401. [PMID: 36112456 DOI: 10.1103/physrevlett.129.103401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
A mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. The Aubry-André (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for a mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of a mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our Letter also offers new possibilities to engineer quantum transport and phase transitions in disordered systems.
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Affiliation(s)
- Yunfei Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
| | - Jia-Hui Zhang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
| | - Yuqing Li
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jizhou Wu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Wenliang Liu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Ying Hu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jie Ma
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Cheng Chin
- James Franck Institute, Enrico Fermi Institute, Department of Physics, University of Chicago, Illinois 60637, USA
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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23
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Molina MI. A fractional Anderson model. PHYSICS LETTERS A 2022; 442:128190. [DOI: 10.1016/j.physleta.2022.128190] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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24
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Nagler B, Will M, Hiebel S, Barbosa S, Koch J, Fleischhauer M, Widera A. Ultracold Bose Gases in Dynamic Disorder with Tunable Correlation Time. PHYSICAL REVIEW LETTERS 2022; 128:233601. [PMID: 35749186 DOI: 10.1103/physrevlett.128.233601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Revised: 12/25/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
We study experimentally the dissipative dynamics of ultracold bosonic gases in a dynamic disorder potential with tunable correlation time. First, we measure the heating rate of thermal clouds exposed to the dynamic potential and present a model of the heating process, revealing the microscopic origin of dissipation from a thermal, trapped cloud of bosons. Second, for Bose-Einstein condensates, we measure the particle loss rate induced by the dynamic environment. Depending on the correlation time, the losses are either dominated by heating of residual thermal particles or the creation of excitations in the superfluid, a notion we substantiate with a rate model. Our results illuminate the interplay between superfluidity and time-dependent disorder and on more general grounds establish ultracold atoms as a platform for studying spatiotemporal noise and time-dependent disorder.
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Affiliation(s)
- Benjamin Nagler
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Martin Will
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Silvia Hiebel
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Sian Barbosa
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Jennifer Koch
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Michael Fleischhauer
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Artur Widera
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
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25
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Dikopoltsev A, Weidemann S, Kremer M, Steinfurth A, Sheinfux HH, Szameit A, Segev M. Observation of Anderson localization beyond the spectrum of the disorder. SCIENCE ADVANCES 2022; 8:eabn7769. [PMID: 35613273 DOI: 10.1126/sciadv.abn7769] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Anderson localization predicts that transport in one-dimensional uncorrelated disordered systems comes to a complete halt, experiencing no transport whatsoever. However, in reality, a disordered physical system is always correlated because it must have a finite spectrum. Common wisdom in the field states that localization is dominant only for wave packets whose spectral extent resides within the region of the wave number span of the disorder. Here, we show experimentally that Anderson localization can occur and even be dominant for wave packets residing entirely outside the spectral extent of the disorder. We study the evolution of wave packets in synthetic photonic lattices containing bandwidth-limited (correlated) disorder and observe strong localization for wave packets centered at twice the mean wave number of the disorder spectral extent and at low wave numbers, both far beyond the spectrum of the disorder. Our results shed light on fundamental aspects of disordered systems and offer avenues for using spectrally shaped disorder for controlling transport.
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Affiliation(s)
| | | | - Mark Kremer
- Institute for Physics, University of Rostock, 18059 Rostock, Germany
| | - Andrea Steinfurth
- Institute for Physics, University of Rostock, 18059 Rostock, Germany
| | - Hanan Herzig Sheinfux
- Physics Department, Technion, 32000 Haifa, Israel
- ICFO-Institute of Photonic Sciences, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
| | - Alexander Szameit
- Institute for Physics, University of Rostock, 18059 Rostock, Germany
| | - Mordechai Segev
- Physics Department, Technion, 32000 Haifa, Israel
- Electrical Engineering Department, Technion, 32000 Haifa, Israel
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26
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Ngapasare A, Theocharis G, Richoux O, Skokos C, Achilleos V. Wave-packet spreading in disordered soft architected structures. CHAOS (WOODBURY, N.Y.) 2022; 32:053116. [PMID: 35649992 DOI: 10.1063/5.0089055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 04/20/2022] [Indexed: 06/15/2023]
Abstract
We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice, which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of Deng et al. [Nat. Commun. 9, 1 (2018)]. This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site), which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered, and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media.
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Affiliation(s)
- A Ngapasare
- Nonlinear Dynamics and Chaos Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
| | - G Theocharis
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique-Graduate School (IA-GS), CNRS, Le Mans Université, Le Mans, France
| | - O Richoux
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique-Graduate School (IA-GS), CNRS, Le Mans Université, Le Mans, France
| | - Ch Skokos
- Nonlinear Dynamics and Chaos Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
| | - V Achilleos
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique-Graduate School (IA-GS), CNRS, Le Mans Université, Le Mans, France
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27
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Topological Superconducting Transition Characterized by a Modified Real-Space-Pfaffian Method and Mobility Edges in a One-Dimensional Quasiperiodic Lattice. Symmetry (Basel) 2022. [DOI: 10.3390/sym14020371] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
A modified real-space-Pfaffian method is applied to characterize the topological superconducting transition of a one-dimensional p-wave superconductor with quasiperiodic potentials. We found that the Majorana zero-energy mode exists in the topological non-trivial phase, and its spatial distribution is localized at ends of the system, whereas in the topological trivial phase, there is no Majorana zero mode. Furthermore, we numerically found that due to the competition between the localized quasi-disorder and the extended p-wave pairing, there are mobility edges in the energy spectra. Our theoretical work enriches the research on the quasiperiodic p-wave superconducting models.
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28
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Quantum Reservoir Computing for Speckle Disorder Potentials. CONDENSED MATTER 2022. [DOI: 10.3390/condmat7010017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Quantum reservoir computing is a machine learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and fast training strategy. In this work, this technique is introduced with a quantum reservoir of spins and it is applied to find the ground state energy of an additional quantum system. The quantum reservoir computer is trained with a linear model to predict the lowest energy of a particle in the presence of different speckle disorder potentials. The performance of the task is analyzed with a focus on the observable quantities extracted from the reservoir and it is shown to be enhanced when two-qubit correlations are employed.
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29
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Topological triple phase transition in non-Hermitian Floquet quasicrystals. Nature 2022; 601:354-359. [PMID: 35046602 PMCID: PMC8770143 DOI: 10.1038/s41586-021-04253-0] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2021] [Accepted: 11/09/2021] [Indexed: 11/08/2022]
Abstract
Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among which is the well known Anderson localization1, where increasing the randomness induces a metal–insulator transition. The introduction of topology in condensed-matter physics2–4 lead to the discovery of topological phase transitions and materials as topological insulators5. Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy6 and new topological phases7–9. Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition10. Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal–insulator), a topological and parity–time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops11. Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled. A triple phase transition, where changing a single parameter simultaneously gives rise to metal–insulator, topological and a parity–time symmetry-breaking phase transitions, is observed in non-Hermitian Floquet quasicrystals.
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Localization Properties of a Quasiperiodic Ladder under Physical Gain and Loss: Tuning of Critical Points, Mixed-Phase Zone and Mobility Edge. MATERIALS 2022; 15:ma15020597. [PMID: 35057314 PMCID: PMC8779531 DOI: 10.3390/ma15020597] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Revised: 01/04/2022] [Accepted: 01/07/2022] [Indexed: 12/10/2022]
Abstract
We explore the localization properties of a double-stranded ladder within a tight-binding framework where the site energies of different lattice sites are distributed in the cosine form following the Aubry-André-Harper (AAH) model. An imaginary site energy, which can be positive or negative, referred to as physical gain or loss, is included in each of these lattice sites which makes the system a non-Hermitian (NH) one. Depending on the distribution of imaginary site energies, we obtain balanced and imbalanced NH ladders of different types, and for all these cases, we critically investigate localization phenomena. Each ladder can be decoupled into two effective one-dimensional (1D) chains which exhibit two distinct critical points of transition from metallic to insulating (MI) phase. Because of the existence of two distinct critical points, a mixed-phase (MP) zone emerges which yields the possibility of getting a mobility edge (ME). The conducting behaviors of different energy eigenstates are investigated in terms of inverse participation ratio (IPR). The critical points and thus the MP window can be selectively controlled by tuning the strength of the imaginary site energies which brings a new insight into the localization aspect. A brief discussion on phase transition considering a multi-stranded ladder was also given as a general case, to make the present communication a self-contained one. Our theoretical analysis can be utilized to investigate the localization phenomena in different kinds of simple and complex quasicrystals in the presence of physical gain and/or loss.
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31
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Abbas K, Boudjemâa A. Binary Bose-Einstein condensates in a disordered time-dependent potential. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:125102. [PMID: 34929676 DOI: 10.1088/1361-648x/ac44d3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2021] [Accepted: 12/20/2021] [Indexed: 06/14/2023]
Abstract
We study the non-equilibrium evolution of binary Bose-Einstein condensates in the presence of a weak random potential with Gaussian correlation function using the time-dependent perturbation theory. We apply this theory to construct a closed set of equations that highlight the role of the spectacular interplay between the disorder and the interspecies interactions in the time evolution of the density induced by disorder in each component. It is found that this latter increases with time favoring localization of both species. The time scale at which the theory remains valid depends on the respective system parameters. We show analytically and numerically that such a system supports a steady state that periodically changing during its time propagation. The obtained dynamical corrections indicate that disorder may transform the system into a stationary out-of-equilibrium states. Understanding this time evolution is pivotal for the realization of Floquet condensates.
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Affiliation(s)
- Karima Abbas
- Department of Physics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, PO Box 78, 02000, Ouled-Fares, Chlef, Algeria
- Laboratory of Mechanics and Energy, Hassiba Benbouali University of Chlef, PO Box 78, 02000, Ouled-Fares, Chlef, Algeria
| | - Abdelâali Boudjemâa
- Department of Physics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, PO Box 78, 02000, Ouled-Fares, Chlef, Algeria
- Laboratory of Mechanics and Energy, Hassiba Benbouali University of Chlef, PO Box 78, 02000, Ouled-Fares, Chlef, Algeria
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32
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One-Dimensional Disordered Bosonic Systems. ATOMS 2021. [DOI: 10.3390/atoms9040112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.
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33
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Observation of topological phase with critical localization in a quasi-periodic lattice. Sci Bull (Beijing) 2021; 66:2175-2180. [PMID: 36654108 DOI: 10.1016/j.scib.2021.07.025] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2021] [Revised: 07/01/2021] [Accepted: 07/14/2021] [Indexed: 01/20/2023]
Abstract
Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce topology from trivial band structures, wherein topological invariants are shared by completely localized states. Here we experimentally investigate a fundamentally distinct scenario where topology is identified in a critically localized regime, with eigenstates neither fully extended nor completely localized. Adopting the technique of momentum-lattice engineering for ultracold atoms, we implement a one-dimensional, generalized Aubry-André model with both diagonal and off-diagonal quasi-periodic disorder in momentum space, and characterize its localization and topological properties through dynamic observables. We then demonstrate the impact of interactions on the critically localized topological state, as a first experimental endeavor toward the clarification of many-body critical phase, the critical analogue of the many-body localized state.
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34
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Fujimoto K, Hamazaki R, Kawaguchi Y. Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models. PHYSICAL REVIEW LETTERS 2021; 127:090601. [PMID: 34506194 DOI: 10.1103/physrevlett.127.090601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Revised: 06/10/2021] [Accepted: 07/08/2021] [Indexed: 06/13/2023]
Abstract
Localization is one of the most fundamental interference phenomena caused by randomness, and its universal aspects have been extensively explored from the perspective of one-parameter scaling mainly for static properties. We numerically study dynamics of fermions on disordered one-dimensional potentials exhibiting localization and find dynamical one-parameter scaling for surface roughness, which represents particle-number fluctuations at a given length scale, and for entanglement entropy when the system is in delocalized phases. This dynamical scaling corresponds to the Family-Vicsek scaling originally developed in classical surface growth, and the associated scaling exponents depend on the type of disorder. Notably, we find that partially localized states in the delocalized phase of the random-dimer model lead to anomalous scaling, where destructive interference unique to quantum systems leads to exponents unknown for classical systems and clean systems.
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Affiliation(s)
- Kazuya Fujimoto
- Institute for Advanced Research, Nagoya University, Nagoya 464-8601, Japan
- Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
| | - Ryusuke Hamazaki
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
| | - Yuki Kawaguchi
- Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
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35
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Zeng J, Hu Y, Zhang X, Fu S, Yin H, Li Z, Chen Z. Localization-to-delocalization transition of light in frequency-tuned photonic moiré lattices. OPTICS EXPRESS 2021; 29:25388-25398. [PMID: 34614871 DOI: 10.1364/oe.434281] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 07/19/2021] [Indexed: 06/13/2023]
Abstract
We demonstrate in a numerical manner the intriguing localization-to-delocalization transition of light in frequency-tuned photonic moiré lattices, both in the zero-order and the higher-order regimes of light waves. We present a different technique to realize the composite photonic lattices, by means of two relatively twisted sublattices with different modulated lattice constants. Even though various kinds of photonic patterns including the commensurable and the incommensurable lattices can be well constructed, the observed transition between the localization and the delocalization of light field is moiré angle-independent. This angle-insensitive property was not reported before, and cannot be achieved by those photonic moiré lattices that are all moiré angle-dependent. We reveal that the obtained phase transition of light is robust to the changes of refractive index modulation of the photonic lattices. Moreover, we reveal that the effect of moiré angle-independent transition of light can be extended to the higher-order vortex light field, hence allowing prediction, for the first time to our knowledge, of both the localization and the delocalization of the vortex light field in the photonic lattices.
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36
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Wang R, Yang XM, Song Z. Localization transitions and mobility edges in quasiperiodic ladder. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:365403. [PMID: 34157686 DOI: 10.1088/1361-648x/ac0d86] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2021] [Accepted: 06/22/2021] [Indexed: 06/13/2023]
Abstract
We investigate localization properties of two-coupled uniform chains (ladder) with quasiperiodic modulation on interchain coupling strength. We demonstrate that this ladder is equivalent to two Aubry-André chains when two legs are symmetric. Analytical and numerical results indicate the appearance of mobility edges in asymmetric ladder systems. We propose an easy-to-engineer quasiperiodic Moiré superlattice ladder system comprising two-coupled uniform chains. An irrational lattice constant difference results in a quasiperiodic structure. Numerical simulations indicate that such a system supports the existence of mobility edges. Furthermore, we demonstrate that the mobility edges can be detected through a dynamical method, that is based on the measurement of survival probability in the presence of a single imaginary negative potential. The results provide insights into localization transitions and mobility edges in experiments.
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Affiliation(s)
- R Wang
- School of Physics, Nankai University, Tianjin 300071, People's Republic of China
| | - X M Yang
- School of Physics, Nankai University, Tianjin 300071, People's Republic of China
| | - Z Song
- School of Physics, Nankai University, Tianjin 300071, People's Republic of China
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37
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Roy N, Sharma A. Entanglement entropy and out-of-time-order correlator in the long-range Aubry-André-Harper model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:334001. [PMID: 34062514 DOI: 10.1088/1361-648x/ac06e9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Accepted: 06/01/2021] [Indexed: 06/12/2023]
Abstract
We investigate the nonequilibrium dynamics of entanglement entropy and out-of-time-order correlator (OTOC) of noninteracting fermions at half-filling starting from a product state to distinguish the delocalized, multifractal (in the limit of nearest neighbor hopping), localized and mixed phases hosted by the quasiperiodic Aubry-André-Harper (AAH) model in the presence of long-range hopping. For sufficiently long-range hopping strength a secondary logarithmic behavior in the entanglement entropy is found in the mixed phases whereas the primary behavior is a power-law the exponent of which is different in different phases. The saturation value of entanglement entropy in the delocalized, multifractal and mixed phases depends linearly on system size whereas in the localized phase (in the short-range regime) it is independent of system size. The early-time growth of OTOC shows very different power-law behaviors in the presence of nearest neighbor hopping and long-range hopping. The late time decay of OTOC leads to noticeably different power-law exponents in different phases. The spatial profile of OTOC and its system-size dependence also provide distinct features to distinguish phases. In the mixed phases the spatial profile of OTOC shows two different dependences on space for small and large distances respectively. Interestingly the spatial profile contains large fluctuations at the special locations related to the quasiperiodicity parameter in the presence of multifractal states.
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Affiliation(s)
- Nilanjan Roy
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462066, India
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Auditya Sharma
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462066, India
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38
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Dos Santos MCP, Cardoso WB. Anderson localization induced by interaction in linearly coupled binary Bose-Einstein condensates. Phys Rev E 2021; 103:052210. [PMID: 34134255 DOI: 10.1103/physreve.103.052210] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
In this paper we investigate the existence of Anderson localization induced by one specific component of a binary Bose-Einstein condensate (BEC). We use a mean-field approach, in which each type of particle of the BEC is considered as a specific field, and we consider that only one kind of particle is subject to a quasiperiodic potential, which induces a localization in the partner field. We assume the system is under a Rabi coupling, i.e., a linear coupling mixing the two-field component, and we investigate the conditions associated with the parameter values of the system for observing the localization. Numerical simulations are performed, confirming the existence of Anderson localization in the partner field.
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Affiliation(s)
- Mateus C P Dos Santos
- Instituto de Física, Universidade Federal de Goiás, 74.690-970 Goiânia, Goiás, Brazil
| | - Wesley B Cardoso
- Instituto de Física, Universidade Federal de Goiás, 74.690-970 Goiânia, Goiás, Brazil
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39
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Zhang R, Yan Y, Zhou Q. Localization on a Synthetic Hall Cylinder. PHYSICAL REVIEW LETTERS 2021; 126:193001. [PMID: 34047582 DOI: 10.1103/physrevlett.126.193001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 04/20/2021] [Indexed: 06/12/2023]
Abstract
By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon into a synthetic Hall cylinder could naturally lead to localization. Unlike a Hall ribbon, a Hall cylinder hosts an intrinsic lattice, which arises due to the periodic boundary condition in the azimuthal direction, in addition to the external periodic potential imposed by extra lasers. When these two lattices are incommensurate, localization may occur on a synthetic Hall cylinder. Near the localization-delocalization transitions, physical observables strongly depend on the axial magnetic flux, providing us a sensitive means to probe either the transition or the axial flux using one another. In the irrational limit, physical observables are no longer affected by the axial flux, signifying a scheme to suppress decoherence induced by fluctuations of the axial flux.
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Affiliation(s)
- Ren Zhang
- School of Physics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Yangqian Yan
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Qi Zhou
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
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40
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Kawabata K, Ryu S. Nonunitary Scaling Theory of Non-Hermitian Localization. PHYSICAL REVIEW LETTERS 2021; 126:166801. [PMID: 33961484 DOI: 10.1103/physrevlett.126.166801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Revised: 01/20/2021] [Accepted: 03/18/2021] [Indexed: 06/12/2023]
Abstract
Non-Hermiticity can destroy Anderson localization and lead to delocalization even in one dimension. However, a unified understanding of non-Hermitian delocalization has yet to be established. Here, we develop a scaling theory of localization in non-Hermitian systems. We reveal that non-Hermiticity introduces a new scale and breaks down the one-parameter scaling, which is the central assumption of the conventional scaling theory of localization. Instead, we identify the origin of unconventional non-Hermitian delocalization as the two-parameter scaling. Furthermore, we establish the threefold universality of non-Hermitian localization based on reciprocity; reciprocity forbids delocalization without internal degrees of freedom, whereas symplectic reciprocity results in a new type of symmetry-protected delocalization.
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Affiliation(s)
- Kohei Kawabata
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Shinsei Ryu
- Department of Physics, Princeton University, Princeton, New Jersey 08540, USA
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41
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Gautier R, Yao H, Sanchez-Palencia L. Strongly Interacting Bosons in a Two-Dimensional Quasicrystal Lattice. PHYSICAL REVIEW LETTERS 2021; 126:110401. [PMID: 33798372 DOI: 10.1103/physrevlett.126.110401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
Quasicrystals exhibit exotic properties inherited from the self-similarity of their long-range ordered, yet aperiodic, structure. The recent realization of optical quasicrystal lattices paves the way to the study of correlated Bose fluids in such structures, but the regime of strong interactions remains largely unexplored, both theoretically and experimentally. Here, we determine the quantum phase diagram of two-dimensional correlated bosons in an eightfold quasicrystal potential. Using large-scale quantum Monte Carlo calculations, we demonstrate a superfluid-to-Bose glass transition and determine the critical line. Moreover, we show that strong interactions stabilize Mott insulator phases, some of which have spontaneously broken eightfold symmetry. Our results are directly relevant to current generation experiments and, in particular, drive prospects to the observation of the still elusive Bose glass phase in two dimensions and exotic Mott phases.
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Affiliation(s)
- Ronan Gautier
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
| | - Hepeng Yao
- CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
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42
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Roy S, Mishra T, Tanatar B, Basu S. Reentrant Localization Transition in a Quasiperiodic Chain. PHYSICAL REVIEW LETTERS 2021; 126:106803. [PMID: 33784113 DOI: 10.1103/physrevlett.126.106803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2020] [Accepted: 02/01/2021] [Indexed: 06/12/2023]
Abstract
Systems with quasiperiodic disorder are known to exhibit a localization transition in low dimensions. After a critical strength of disorder, all the states of the system become localized, thereby ceasing the particle motion in the system. However, in our analysis, we show that in a one-dimensional dimerized lattice with staggered quasiperiodic disorder, after the localization transition, some of the localized eigenstates become extended for a range of intermediate disorder strengths. Eventually, the system undergoes a second localization transition at a higher disorder strength, leading to all states being localized. We also show that the two localization transitions are associated with the mobility regions hosting the single-particle mobility edges. We establish this reentrant localization transition by analyzing the eigenspectra, participation ratios, and the density of states of the system.
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Affiliation(s)
- Shilpi Roy
- Department of Physics, Indian Institute of Technology Guwahati-Guwahati, 781039 Assam, India
| | - Tapan Mishra
- Department of Physics, Indian Institute of Technology Guwahati-Guwahati, 781039 Assam, India
| | - B Tanatar
- Department of Physics, Bilkent University, TR-06800 Bilkent, Ankara, Turkey
| | - Saurabh Basu
- Department of Physics, Indian Institute of Technology Guwahati-Guwahati, 781039 Assam, India
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43
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Xu Y, Wang X, Zhang W, Schäfer L, Reindl J, Vom Bruch F, Zhou Y, Evang V, Wang JJ, Deringer VL, Ma E, Wuttig M, Mazzarello R. Materials Screening for Disorder-Controlled Chalcogenide Crystals for Phase-Change Memory Applications. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2006221. [PMID: 33491816 DOI: 10.1002/adma.202006221] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Revised: 12/14/2020] [Indexed: 06/12/2023]
Abstract
Tailoring the degree of disorder in chalcogenide phase-change materials (PCMs) plays an essential role in nonvolatile memory devices and neuro-inspired computing. Upon rapid crystallization from the amorphous phase, the flagship Ge-Sb-Te PCMs form metastable rocksalt-like structures with an unconventionally high concentration of vacancies, which results in disordered crystals exhibiting Anderson-insulating transport behavior. Here, ab initio simulations and transport experiments are combined to extend these concepts to the parent compound of Ge-Sb-Te alloys, viz., binary Sb2 Te3 , in the metastable rocksalt-type modification. Then a systematic computational screening over a wide range of homologous, binary and ternary chalcogenides, elucidating the critical factors that affect the stability of the rocksalt structure is carried out. The findings vastly expand the family of disorder-controlled main-group chalcogenides toward many more compositions with a tunable bandgap size for demanding phase-change applications, as well as a varying strength of spin-orbit interaction for the exploration of potential topological Anderson insulators.
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Affiliation(s)
- Yazhi Xu
- Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
- Institute for Theoretical Solid-State Physics, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
| | - Xudong Wang
- Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
- Center for Alloy Innovation and Design (CAID), Materials Studio for Neuro-Inspired Computing, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Wei Zhang
- Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
- Center for Alloy Innovation and Design (CAID), Materials Studio for Neuro-Inspired Computing, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Lisa Schäfer
- I. Institute of Physics (IA), JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
| | - Johannes Reindl
- I. Institute of Physics (IA), JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
| | - Felix Vom Bruch
- I. Institute of Physics (IA), JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
| | - Yuxing Zhou
- Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
- Center for Alloy Innovation and Design (CAID), Materials Studio for Neuro-Inspired Computing, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Valentin Evang
- Institute for Theoretical Solid-State Physics, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
| | - Jiang-Jing Wang
- Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
- I. Institute of Physics (IA), JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
| | - Volker L Deringer
- Department of Chemistry, Inorganic Chemistry Laboratory, University of Oxford, Oxford, OX1 3QR, UK
| | - En Ma
- Center for Advancing Materials Performance from the Nanoscale, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, China
- Center for Alloy Innovation and Design (CAID), Materials Studio for Neuro-Inspired Computing, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Matthias Wuttig
- I. Institute of Physics (IA), JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
- Peter Grünberg Institute (PGI 10), Forschungszentrum Jülich GmbH, 52425, Jülich, Germany
| | - Riccardo Mazzarello
- Institute for Theoretical Solid-State Physics, JARA-FIT and JARA-HPC, RWTH Aachen University, 52056, Aachen, Germany
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44
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Wang M, Zhang RY, Zhang L, Wang D, Guo Q, Zhang ZQ, Chan CT. Topological One-Way Large-Area Waveguide States in Magnetic Photonic Crystals. PHYSICAL REVIEW LETTERS 2021; 126:067401. [PMID: 33635715 DOI: 10.1103/physrevlett.126.067401] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2020] [Accepted: 01/14/2021] [Indexed: 06/12/2023]
Abstract
We have theoretically and experimentally achieved large-area one-way transport by using heterostructures consisting of a domain of an ordinary photonic crystal sandwiched between two domains of magnetic photonic crystals. The nonmagnetized domain carries two orthogonal one-way waveguide states which have amplitude uniformly distributed over a large area. We show that such one-way waveguide states can be used to abruptly narrow the beam width of an extended state to concentrate energy, and the transport is robust against different kinds of defects and imperfections. They are also immune to the Anderson-type localization when large randomness is introduced.
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Affiliation(s)
- Mudi Wang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
| | - Ruo-Yang Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
| | - Lei Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Dongyang Wang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
| | - Qinghua Guo
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
- Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
| | - Zhao-Qing Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
| | - C T Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong 999077, China
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45
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Abstract
We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. By changing linear size L and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction and find that a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.
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46
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An FA, Padavić K, Meier EJ, Hegde S, Ganeshan S, Pixley JH, Vishveshwara S, Gadway B. Interactions and Mobility Edges: Observing the Generalized Aubry-André Model. PHYSICAL REVIEW LETTERS 2021; 126:040603. [PMID: 33576679 DOI: 10.1103/physrevlett.126.040603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 12/04/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-André model, with an energy-dependent self-duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing low and high energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model's tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of high energy states due to screening. This study paves the way for quantitative studies of interaction effects on self-duality induced mobility edges.
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Affiliation(s)
- Fangzhao Alex An
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Karmela Padavić
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Eric J Meier
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Suraj Hegde
- Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany
| | - Sriram Ganeshan
- Physics Department, City College of the CUNY, New York, New York 10031, USA
- CUNY Graduate Center, New York, New York 10031, USA
| | - J H Pixley
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Smitha Vishveshwara
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Bryce Gadway
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
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47
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Wang JR, Li W, Wang G, Zhang CJ. Global phase diagram of Coulomb-interacting anisotropic Weyl semimetal with disorder. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:125601. [PMID: 33326939 DOI: 10.1088/1361-648x/abd426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
Taking into account the interplay between the disorder and Coulomb interaction, the phase diagram of three-dimensional anisotropic Weyl semimetal is studied by renormalization group (RG) theory. Weak disorder is irrelevant in anisotropic Weyl semimetal, while the disorder becomes relevant and drives a quantum phase transition (QPT) from semimetal to compressible diffusive metal (CDM) phases if the disorder strength is larger than a critical value. The long-range Coulomb interaction is irrelevant in clean anisotropic Weyl semimetal. However, interestingly, we find that the long-range Coulomb interaction exerts a dramatic influence on the critical disorder strength for phase transition to CDM. Specifically, the critical disorder strength can receive a prominent change even though an arbitrarily weak Coulomb interaction is included. This novel behavior is closely related to the anisotropic screening effect of Coulomb interaction, and essentially results from the specifical energy dispersion of the fermion excitations in anisotropic Weyl semimetal. The theoretical results are helpful for understanding the physical properties of the candidates of anisotropic Weyl semimetal, such as pressured BiTeI, and some other related materials.
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Affiliation(s)
- Jing-Rong Wang
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of Anhui Province, Chinese Academy of Sciences, Hefei 230031, People's Republic of China
| | - Wei Li
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, People's Republic of China
| | - Gang Wang
- College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, People's Republic of China
| | - Chang-Jin Zhang
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of Anhui Province, Chinese Academy of Sciences, Hefei 230031, People's Republic of China
- Institute of Physical Science and Information Technology, Anhui University, Hefei 230601, People's Republic of China
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48
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Agrawal U, Gopalakrishnan S, Vasseur R. Quantum Criticality in the 2D Quasiperiodic Potts Model. PHYSICAL REVIEW LETTERS 2020; 125:265702. [PMID: 33449710 DOI: 10.1103/physrevlett.125.265702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Accepted: 11/19/2020] [Indexed: 06/12/2023]
Abstract
Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic q-state Potts model in 2+1D. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of q, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be ν=1, saturating a modified version of the Harris-Luck criterion.
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Affiliation(s)
- Utkarsh Agrawal
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Sarang Gopalakrishnan
- Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314; Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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49
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Sbroscia M, Viebahn K, Carter E, Yu JC, Gaunt A, Schneider U. Observing Localization in a 2D Quasicrystalline Optical Lattice. PHYSICAL REVIEW LETTERS 2020; 125:200604. [PMID: 33258663 DOI: 10.1103/physrevlett.125.200604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 09/18/2020] [Indexed: 06/12/2023]
Abstract
Quasicrystals are long-range ordered but not periodic, representing an interesting middle ground between order and disorder. We experimentally and numerically study the localization transition in the ground state of noninteracting and weakly interacting bosons in an eightfold symmetric quasicrystalline optical lattice. In contrast to typically used real space in situ techniques, we probe the system in momentum space by recording matter wave diffraction patterns. Shallow lattices lead to extended states whereas we observe a localization transition at a critical lattice depth of V_{0}≈1.78(2)E_{rec} for the noninteracting system. Our measurements and Gross-Pitaevskii simulations demonstrate that in interacting systems the transition is shifted to deeper lattices, as expected from superfluid order counteracting localization. Quasiperiodic potentials, lacking conventional rare regions, provide the ideal testing ground to realize many-body localization in 2D.
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Affiliation(s)
- Matteo Sbroscia
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Konrad Viebahn
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland
| | - Edward Carter
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Jr-Chiun Yu
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | | | - Ulrich Schneider
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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50
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Wang Y, Xia X, Zhang L, Yao H, Chen S, You J, Zhou Q, Liu XJ. One-Dimensional Quasiperiodic Mosaic Lattice with Exact Mobility Edges. PHYSICAL REVIEW LETTERS 2020; 125:196604. [PMID: 33216579 DOI: 10.1103/physrevlett.125.196604] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Revised: 08/30/2020] [Accepted: 10/15/2020] [Indexed: 06/11/2023]
Abstract
The mobility edges (MEs) in energy that separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results that allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived through computing the Lyapunov exponents from Avila's global theory and also numerically verified by calculating the fractal dimension. We further propose a novel scheme with experimental feasibility to realize our model based on an optical Raman lattice, which paves the way for experimental exploration of the predicted exact ME physics.
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Affiliation(s)
- Yucheng Wang
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xu Xia
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Long Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hepeng Yao
- CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay 91128 Palaiseau, France
| | - Shu Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Yangtze River Delta Physics Research Center, Liyang, Jiangsu 213300, China
| | - Jiangong You
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Qi Zhou
- Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
| | - Xiong-Jun Liu
- Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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