1
|
Lysne M, Schüler M, Werner P. Quantum Optics Measurement Scheme for Quantum Geometry and Topological Invariants. PHYSICAL REVIEW LETTERS 2023; 131:156901. [PMID: 37897742 DOI: 10.1103/physrevlett.131.156901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Accepted: 09/07/2023] [Indexed: 10/30/2023]
Abstract
We show how a quantum optical measurement scheme based on heterodyne detection can be used to explore geometrical and topological properties of condensed matter systems. Considering a 2D material placed in a cavity with a coupling to the environment, we compute correlation functions of the photons exiting the cavity and relate them to the hybrid light-matter state within the cavity. Different polarizations of the intracavity field give access to all components of the quantum geometric tensor on contours in the Brillouin zone defined by the transition energy. Combining recent results based on the metric-curvature correspondence with the measured quantum metric allows us to characterize the topological phase of the material. Moreover, in systems where S_{z} is a good quantum number, the procedure also allows us to extract the spin Chern number. As an interesting application, we consider a minimal model for twisted bilayer graphene at the magic angle, and discuss the feasibility of extracting the Euler number.
Collapse
Affiliation(s)
- Markus Lysne
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - Michael Schüler
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
- Laboratory for Materials Simulations, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - Philipp Werner
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| |
Collapse
|
2
|
Baldelli N, Bhattacharya U, González-Cuadra D, Lewenstein M, Graß T. Detecting Majorana Zero Modes via Strong Field Dynamics. ACS OMEGA 2022; 7:47424-47430. [PMID: 36570179 PMCID: PMC9773937 DOI: 10.1021/acsomega.2c07169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 11/24/2022] [Indexed: 06/17/2023]
Abstract
We propose a protocol to detect topological phase transitions of one-dimensional p-wave superconductors from their harmonic emission spectra in strong fields. Specifically, we identify spectral features due to radiating edge modes, which characterize the spectrum and the density of states in the topological phase and are absent in the trivial phase. These features allow us to define a measurable signature, obtained from emission measurements, that unambiguously differentiates between the two phases. Local probing provides insight into the localized and topologically protected nature of the modes. The presented results establish that high-harmonic spectroscopy can be used as an all-optical tool for the detection of Majorana zero modes.
Collapse
Affiliation(s)
- Niccolò Baldelli
- Institut
de Ciencies Fotoniques (ICFO), The Barcelona Institute of Science
and Technology, 08860Castelldefels, Barcelona, Spain
| | - Utso Bhattacharya
- Institut
de Ciencies Fotoniques (ICFO), The Barcelona Institute of Science
and Technology, 08860Castelldefels, Barcelona, Spain
| | - Daniel González-Cuadra
- Institut
de Ciencies Fotoniques (ICFO), The Barcelona Institute of Science
and Technology, 08860Castelldefels, Barcelona, Spain
- Institute
for Theoretical Physics, University of Innsbruck, 6020Innsbruck, Austria
- Institute
for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020Innsbruck, Austria
| | - Maciej Lewenstein
- Institut
de Ciencies Fotoniques (ICFO), The Barcelona Institute of Science
and Technology, 08860Castelldefels, Barcelona, Spain
- Institución
Catalana de Investigación y Esteudios Avanzados (ICREA), Pg. Lluis Companys 23, 08010Barcelona, Barcelona, Spain
| | - Tobias Graß
- Institut
de Ciencies Fotoniques (ICFO), The Barcelona Institute of Science
and Technology, 08860Castelldefels, Barcelona, Spain
- Donostia
International Physics Center (DIPC), Paseo Manuel de Lardizábal 4, 20018San Sebastián, Gipuzkoa, Spain
- Ikerbasque, Maria Diaz de Haro 3, 48013Bilbao, Biscay, Spain
| |
Collapse
|
3
|
Huang GH, Xu ZF, Wu Z. Intrinsic Anomalous Hall Effect in a Bosonic Chiral Superfluid. PHYSICAL REVIEW LETTERS 2022; 129:185301. [PMID: 36374672 DOI: 10.1103/physrevlett.129.185301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 08/25/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a p-orbital Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [Wang et al., Nature (London) 596, 227 (2021)NATUAS0028-083610.1038/s41586-021-03702-0]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real experimental system. We find that in the high frequency limit, the Hall conductivity is determined by finite loop current correlations on the s-orbital residing sublattice, the latter a defining feature of the system's chirality. In the opposite limit, the dc Hall conductivity can trace its origin back to the noninteracting band Berry curvature at the condensation momentum, although the contribution from atomic interactions can be significant. We discuss available experimental probes to observe this intrinsic anomalous Hall effect at both zero and finite frequencies.
Collapse
Affiliation(s)
- Guan-Hua Huang
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhi-Fang Xu
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhigang Wu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| |
Collapse
|
4
|
Käming N, Dawid A, Kottmann K, Lewenstein M, Sengstock K, Dauphin A, Weitenberg C. Unsupervised machine learning of topological phase transitions from experimental data. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abffe7] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Abstract
Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries from noisy and imperfect data without the knowledge of the order parameter. Here, we apply different unsupervised machine learning techniques, including anomaly detection and influence functions, to experimental data from ultracold atoms. In this way, we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion. We show that these methods can successfully be applied to experimental data at finite temperatures and to the data of Floquet systems when post-processing the data to a single micromotion phase. Our work provides a benchmark for the unsupervised detection of new exotic phases in complex many-body systems.
Collapse
|
5
|
Goldman N, Yefsah T. The Weyl side of ultracold matter. Science 2021; 372:234-235. [PMID: 33859019 DOI: 10.1126/science.abg0892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Nathan Goldman
- Interdisciplinary Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Tarik Yefsah
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond 75005 Paris, France.
| |
Collapse
|
6
|
Cian ZP, Dehghani H, Elben A, Vermersch B, Zhu G, Barkeshli M, Zoller P, Hafezi M. Many-Body Chern Number from Statistical Correlations of Randomized Measurements. PHYSICAL REVIEW LETTERS 2021; 126:050501. [PMID: 33605765 DOI: 10.1103/physrevlett.126.050501] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
One of the main topological invariants that characterizes several topologically ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant are conventionally based on the linear-response techniques that require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wave function. Remarkably, our results apply to disklike geometries that are more amenable to current quantum simulator architectures.
Collapse
Affiliation(s)
- Ze-Pei Cian
- Joint Quantum Institute, College Park, Maryland 20742, USA
- The Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Hossein Dehghani
- Joint Quantum Institute, College Park, Maryland 20742, USA
- The Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Andreas Elben
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Benoît Vermersch
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
| | - Guanyu Zhu
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Maissam Barkeshli
- Joint Quantum Institute, College Park, Maryland 20742, USA
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Peter Zoller
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Mohammad Hafezi
- Joint Quantum Institute, College Park, Maryland 20742, USA
- The Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|
7
|
Lu YH, Wang BZ, Liu XJ. Ideal Weyl semimetal with 3D spin-orbit coupled ultracold quantum gas. Sci Bull (Beijing) 2020; 65:2080-2085. [PMID: 36732960 DOI: 10.1016/j.scib.2020.09.036] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Revised: 09/21/2020] [Accepted: 09/24/2020] [Indexed: 02/04/2023]
Abstract
There is an immense effort in search for various types of Weyl semimetals, of which the most fundamental phase consists of the minimal number of i.e. two Weyl points, but is hard to engineer in solids. Here we demonstrate how such fundamental Weyl semimetal can be realized in a maneuverable optical Raman lattice, with which the three-dimensional (3D) spin-orbit (SO) coupling is synthesised for ultracold atoms. In addition, a new novel Weyl phase with coexisting Weyl nodal points and nodal ring is also predicted here, and is shown to be protected by nontrivial linking numbers. We further propose feasible techniques to precisely resolve 3D Weyl band topology through 2D equilibrium and dynamical measurements. This work leads to the first realization of the most fundamental Weyl semimetal band and the 3D SO coupling for ultracold quantum gases, which are respectively the significant issues in the condensed matter and ultracold atom physics.
Collapse
Affiliation(s)
- Yue-Hui Lu
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Bao-Zong Wang
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China; International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials and 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.
| |
Collapse
|
8
|
Julià-Farré S, Müller M, Lewenstein M, Dauphin A. Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator. PHYSICAL REVIEW LETTERS 2020; 125:240601. [PMID: 33412044 DOI: 10.1103/physrevlett.125.240601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 11/05/2020] [Indexed: 06/12/2023]
Abstract
Many-body interactions in topological quantum systems can give rise to new phases of matter, which simultaneously exhibit both rich spatial features and topological properties. In this work, we consider spinless fermions on a checkerboard lattice with nearest and next-to-nearest neighbor interactions. We calculate the phase diagram at half filling, which presents, in particular, an interaction-induced quantum anomalous Hall phase. We study the system at incommensurate fillings using an unrestricted Hartree-Fock ansatz and report a rich zoo of solutions such as self-trapped polarons and domain walls above an interaction-induced topological insulator. We find that, as a consequence of the interplay between the interaction-induced topology and topological defects, these domain walls separate two phases with opposite topological invariants and host topologically protected chiral edge states. Finally, we discuss experimental prospects to observe these novel phenomena in a quantum simulator based on laser-dressed Rydberg atoms in an optical lattice.
Collapse
Affiliation(s)
- Sergi Julià-Farré
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - Markus Müller
- Institute for Quantum Information, RWTH Aachen University, D-52074 Aachen, Germany
- Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52428 Jülich, Germany
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
- ICREA, Passeig Lluís Companys 23, 08010 Barcelona, Spain
| | - Alexandre Dauphin
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| |
Collapse
|
9
|
Marsal Q, Varjas D, Grushin AG. Topological Weaire-Thorpe models of amorphous matter. Proc Natl Acad Sci U S A 2020; 117:30260-30265. [PMID: 33208535 PMCID: PMC7720235 DOI: 10.1073/pnas.2007384117] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Accepted: 10/26/2020] [Indexed: 11/18/2022] Open
Abstract
Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire-Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their short-range properties allow us to analytically predict spectral gaps. Their symmetry under permutation of orbitals allows us to analytically compute topological phase diagrams, which determine quantized observables like circular dichroism, by introducing symmetry indicators in amorphous systems. These models and our procedures to define invariants are generalizable to higher coordination number and dimensions, opening a route toward a complete classification of amorphous topological states in real space using quasilocal properties.
Collapse
Affiliation(s)
- Quentin Marsal
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Dániel Varjas
- QuTech, Delft University of Technology, 2600 GA Delft, The Netherlands
- Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
| | - Adolfo G Grushin
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France;
| |
Collapse
|
10
|
Klees RL, Rastelli G, Cuevas JC, Belzig W. Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter. PHYSICAL REVIEW LETTERS 2020; 124:197002. [PMID: 32469576 DOI: 10.1103/physrevlett.124.197002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 11/13/2019] [Accepted: 04/06/2020] [Indexed: 06/11/2023]
Abstract
Quantization effects due to topological invariants such as Chern numbers have become very relevant in many systems, yet key quantities such as the quantum geometric tensor providing local information about quantum states remain experimentally difficult to access. Recently, it has been shown that multiterminal Josephson junctions constitute an ideal platform to synthesize topological systems in a controlled manner. We theoretically study properties of Andreev states in topological Josephson matter and demonstrate that the quantum geometric tensor of Andreev states can be extracted by synthetically polarized microwaves. The oscillator strength of the absorption rates provides direct evidence of topological quantum properties of the Andreev states.
Collapse
Affiliation(s)
- R L Klees
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - G Rastelli
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
- Zukunftskolleg, Universität Konstanz, D-78457 Konstanz, Germany
| | - J C Cuevas
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - W Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| |
Collapse
|
11
|
Yu M, Yang P, Gong M, Cao Q, Lu Q, Liu H, Zhang S, Plenio MB, Jelezko F, Ozawa T, Goldman N, Cai J. Experimental measurement of the quantum geometric tensor using coupled qubits in diamond. Natl Sci Rev 2020; 7:254-260. [PMID: 34692040 PMCID: PMC8288884 DOI: 10.1093/nsr/nwz193] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Revised: 11/17/2019] [Accepted: 11/18/2019] [Indexed: 12/03/2022] Open
Abstract
Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.
Collapse
Affiliation(s)
- Min Yu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Pengcheng Yang
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Musang Gong
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Qingyun Cao
- Institut für Quantenoptik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Qiuyu Lu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Haibin Liu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Shaoliang Zhang
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Martin B Plenio
- Institut für Theoretische Physik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Fedor Jelezko
- Institut für Quantenoptik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Tomoki Ozawa
- Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, B-1050 Brussels, Belgium
| | - Jianming Cai
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| |
Collapse
|
12
|
Schüler M, De Giovannini U, Hübener H, Rubio A, Sentef MA, Werner P. Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials. SCIENCE ADVANCES 2020; 6:eaay2730. [PMID: 32158939 PMCID: PMC7048418 DOI: 10.1126/sciadv.aay2730] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Accepted: 12/04/2019] [Indexed: 06/07/2023]
Abstract
Topologically nontrivial two-dimensional materials hold great promise for next-generation optoelectronic applications. However, measuring the Hall or spin-Hall response is often a challenge and practically limited to the ground state. An experimental technique for tracing the topological character in a differential fashion would provide useful insights. In this work, we show that circular dichroism angle-resolved photoelectron spectroscopy provides a powerful tool that can resolve the topological and quantum-geometrical character in momentum space. In particular, we investigate how to map out the signatures of the momentum-resolved Berry curvature in two-dimensional materials by exploiting its intimate connection to the orbital polarization. A spin-resolved detection of the photoelectrons allows one to extend the approach to spin-Chern insulators. The present proposal can be extended to address topological properties in materials out of equilibrium in a time-resolved fashion.
Collapse
Affiliation(s)
- Michael Schüler
- Stanford Institute for Materials and Energy Sciences (SIMES), SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
- Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland
| | - Umberto De Giovannini
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Hannes Hübener
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center for Computational Quantum Physics (CCQ), The Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
| | - Michael A. Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Philipp Werner
- Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland
| |
Collapse
|
13
|
Pozo O, Repellin C, Grushin AG. Quantization in Chiral Higher Order Topological Insulators: Circular Dichroism and Local Chern Marker. PHYSICAL REVIEW LETTERS 2019; 123:247401. [PMID: 31922878 DOI: 10.1103/physrevlett.123.247401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Indexed: 06/10/2023]
Abstract
The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the surface Hall conductivity known to be quantized in the infinite slab geometry, is nonuniversal for a finite surface. This is due to a nonuniversal contribution of the hinge states, previously unaccounted for, that distinguishes surfaces of chiral HOTIs from Chern insulators. Our findings are relevant to establish higher order topology in systems such as the axion insulator candidate EuIn_{2}As_{2}, and cold atomic realizations.
Collapse
Affiliation(s)
- Oscar Pozo
- Instituto de Ciencia de Materiales de Madrid, and CSIC, Cantoblanco, 28049 Madrid, Spain
| | - Cécile Repellin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Adolfo G Grushin
- University Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| |
Collapse
|
14
|
Repellin C, Goldman N. Detecting Fractional Chern Insulators through Circular Dichroism. PHYSICAL REVIEW LETTERS 2019; 122:166801. [PMID: 31075039 DOI: 10.1103/physrevlett.122.166801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/09/2023]
Abstract
Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Recent achievements in this direction, together with the possibility of tuning interparticle interactions, suggest that strongly correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. We validate this approach by comparing the circular-dichroic signal to the many-body Chern number and discuss how such measurements could be performed to distinguish FQH-type states from competing states. Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state.
Collapse
Affiliation(s)
- C Repellin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - N Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| |
Collapse
|
15
|
Anderson R, Wang F, Xu P, Venu V, Trotzky S, Chevy F, Thywissen JH. Conductivity Spectrum of Ultracold Atoms in an Optical Lattice. PHYSICAL REVIEW LETTERS 2019; 122:153602. [PMID: 31050527 DOI: 10.1103/physrevlett.122.153602] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2018] [Indexed: 06/09/2023]
Abstract
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analog of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.
Collapse
Affiliation(s)
- Rhys Anderson
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Fudong Wang
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Peihang Xu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Vijin Venu
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Stefan Trotzky
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
| | - Frédéric Chevy
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
| | - Joseph H Thywissen
- Department of Physics, University of Toronto, Ontario M5S 1A7 Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1M1 Canada
| |
Collapse
|
16
|
Cooper NR, Dalibard J, Spielman IB. Topological bands for ultracold atoms. REVIEWS OF MODERN PHYSICS 2019; 91:10.1103/revmodphys.91.015005. [PMID: 32189812 PMCID: PMC7079706 DOI: 10.1103/revmodphys.91.015005] [Citation(s) in RCA: 113] [Impact Index Per Article: 22.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, descriptions are given of the forms of interparticle interactions that emerge when atoms are subjected to these energy bands and of some of the many-body phases that may be sought in future experiments.
Collapse
Affiliation(s)
- N R Cooper
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - J Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 place Marcelin Berthelot, 75005, Paris, France
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
| |
Collapse
|
17
|
Li H, Zhao YY. Thermal transport in topological-insulator-based superconducting hybrid structures with mixed singlet and triplet pairing states. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:465001. [PMID: 28967869 DOI: 10.1088/1361-648x/aa9043] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In the framework of the Bogoliubov-de Gennes equation, we investigate the thermal transport properties in topological-insulator-based superconducting hybrid structures with mixed spin-singlet and spin-triplet pairing states, and emphasize the different manifestations of the spin-singlet and spin-triplet pairing states in the thermal transport signatures. It is revealed that the temperature-dependent differential thermal conductance strongly depends on the components of the pairing state, and the negative differential thermal conductance only occurs in the spin-singlet pairing state dominated regime. It is also found that the thermal conductance is profoundly sensitive to the components of the pairing state. In the spin-singlet pairing state controlled regime, the thermal conductance obviously oscillates with the phase difference and junction length. With increasing the proportion of the spin-triplet pairing state, the oscillating characteristic of the thermal conductance fades out distinctly. These results suggest an alternative route for distinguishing the components of pairing states in topological-insulator-based superconducting hybrid structures.
Collapse
Affiliation(s)
- Hai Li
- Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, TX 77204, United States of America
| | | |
Collapse
|