1
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Goo J, Lim Y, Shin Y. Defect Saturation in a Rapidly Quenched Bose Gas. PHYSICAL REVIEW LETTERS 2021; 127:115701. [PMID: 34558957 DOI: 10.1103/physrevlett.127.115701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Accepted: 07/15/2021] [Indexed: 06/13/2023]
Abstract
We investigate the saturation of defect density in an atomic Bose gas rapidly cooled into a superfluid phase. The number of quantum vortices, which are spontaneously created in the quenched gas, exhibits a Poissonian distribution not only for a slow quench in the Kibble-Zurek (KZ) scaling regime but also for a fast quench, in which case the mean vortex number is saturated. This shows that the saturation is not caused by destructive vortex collisions, but by the early-time coarsening in an emerging condensate, which is further supported by the observation that the condensate growth lags the quenching in the saturation regime. Our results demonstrate that the defect saturation is an effect beyond the KZ mechanism, opening a path for studying critical phase transition dynamics using the defect number distribution.
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Affiliation(s)
- Junhong Goo
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
| | - Younghoon Lim
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
- Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea
| | - Y Shin
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
- Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea
- Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
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2
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Yi CR, Liu S, Jiao RH, Zhang JY, Zhang YS, Chen S. Exploring Inhomogeneous Kibble-Zurek Mechanism in a Spin-Orbit Coupled Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2020; 125:260603. [PMID: 33449755 DOI: 10.1103/physrevlett.125.260603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Revised: 11/10/2020] [Accepted: 12/09/2020] [Indexed: 06/12/2023]
Abstract
The famous Kibble-Zurek mechanism offers us a significant clue to study quantum phase transitions out of equilibrium. Here, we investigate an intriguing phenomenon of a spin-orbit coupled Bose-Einstein condensate by quenching the Raman coupling strength from a high-symmetry phase (nonmagnetic phase) to a low-symmetry phase (magnetic phase). When crossing the critical point, the fluctuation of momentum distribution leads to delayed bifurcation structures. Simultaneously, the domain information emerges in momentum space. Moreover, the universal scalings of spatiotemporal dynamics are extracted from the fluctuations and domains, which manifests homogeneous and inhomogeneous Kibble-Zurek power laws at different timescales. Our work demonstrates a paradigmatic study on the inhomogeneous Kibble-Zurek mechanism.
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Affiliation(s)
- Chang-Rui Yi
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Anhui 230026, China
- Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Sheng Liu
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Anhui 230026, China
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Rui-Heng Jiao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Anhui 230026, China
- Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Jin-Yi Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Anhui 230026, China
- Shanghai Research Center for Quantum Science, Shanghai 201315, China
| | - Yong-Sheng Zhang
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Anhui 230026, China
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Shuai Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Anhui 230026, China
- Shanghai Research Center for Quantum Science, Shanghai 201315, China
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3
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de Souza LC, de Souza AJF, Lyra ML. Hamiltonian short-time critical dynamics of the three-dimensional XY model. Phys Rev E 2019; 99:052104. [PMID: 31212448 DOI: 10.1103/physreve.99.052104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2018] [Indexed: 06/09/2023]
Abstract
The short-time relaxation critical behavior of the XY model on a simple-cubic lattice is investigated within the scope of deterministic Hamiltonian dynamics. The Hamiltonian includes a first-neighbor interaction between planar vectors and a rotational kinetic term from which the motion equations are derived. The dynamical evolution from a fully ordered initial state is followed by employing a symplectic algorithm based on a high-order Trotter-Suzuki decomposition of the time-evolution operator. A finite-time scaling analysis is performed to provide accurate estimates of the critical energy density, the order-parameter relaxation exponent, and the dynamical critical exponent. The estimated critical exponents are consistent with prior theoretical and experimental values reported for the superfluid ^{4}He, extreme type-II superconducting, and Bose-Einstein condensation transitions.
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Affiliation(s)
- Lindiane C de Souza
- Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife PE, Brazil
| | - Adauto J F de Souza
- Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife PE, Brazil
| | - Marcelo L Lyra
- Instituto de Física, Universidade Federal de Alagoas, 57072-970, Maceió AL, Brazil
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4
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You JB, Yang W. Characterizing real-space topology in Rice-Mele model by thermodynamics. Phys Rev E 2018; 97:012136. [PMID: 29448374 DOI: 10.1103/physreve.97.012136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2017] [Indexed: 11/07/2022]
Abstract
The thermodynamic quantities which are related to energy-level statistics are used to characterize the real-space topology of the Rice-Mele model. Through studying the energy spectrum of the model under different boundary conditions, we found that the non-normalizable wave function for the infinite domain is reduced to the edge state adhered to the boundary. For the finite domain with symmetric boundary condition, the critical point for the topological phase transition is equal to the inverse of the domain length. In contrast, the critical point is zero for the semi-infinite domain. Additionally, the symmetry of the energy spectrum is found to be sensitive to the boundary conditions of the Rice-Mele model, and the emergence of the edge states as well as the topological phase transition can be reflected in the thermodynamic properties. A potentially practical scheme is proposed for simulating the Rice-Mele model and detecting the relevant thermodynamic quantities in the context of Bose-Einstein condensate.
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Affiliation(s)
- Jia-Bin You
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China.,Department of Electronics and Photonics, Institute of High Performance Computing, 1 Fusionopolis Way, 16-16 Connexis, Singapore 138632, Singapore
| | - Wanli Yang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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5
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Yang B, Chen YY, Zheng YG, Sun H, Dai HN, Guan XW, Yuan ZS, Pan JW. Quantum criticality and the Tomonaga-Luttinger liquid in one-dimensional Bose gases. PHYSICAL REVIEW LETTERS 2017; 119:165701. [PMID: 29099230 DOI: 10.1103/physrevlett.119.165701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2016] [Indexed: 06/07/2023]
Abstract
We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.
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Affiliation(s)
- Bing Yang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Yang-Yang Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Yong-Guang Zheng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Hui Sun
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Han-Ning Dai
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Xi-Wen Guan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
- Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia
| | - Zhen-Sheng Yuan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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6
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Karl M, Cakir H, Halimeh JC, Oberthaler MK, Kastner M, Gasenzer T. Universal equilibrium scaling functions at short times after a quench. Phys Rev E 2017; 96:022110. [PMID: 28950605 DOI: 10.1103/physreve.96.022110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Indexed: 06/07/2023]
Abstract
By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.
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Affiliation(s)
- Markus Karl
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Halil Cakir
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Jad C Halimeh
- Physics Department and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Michael Kastner
- National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa
- Department of Physics, Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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7
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Damm T, Dung D, Vewinger F, Weitz M, Schmitt J. First-order spatial coherence measurements in a thermalized two-dimensional photonic quantum gas. Nat Commun 2017; 8:158. [PMID: 28761123 PMCID: PMC5537358 DOI: 10.1038/s41467-017-00270-8] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Accepted: 06/16/2017] [Indexed: 11/21/2022] Open
Abstract
Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. Correlations allow the quantification of the degree of order and the classification of different phases. Here we report measurements of first-order spatial correlations in a harmonically trapped two-dimensional photon gas below, at and above the critical particle number for Bose–Einstein condensation, using interferometric measurements of the emission of a dye-filled optical microcavity. For the uncondensed gas, the transverse coherence decays on a length scale determined by the thermal de Broglie wavelength of the photons, which shows the expected scaling with temperature. At the onset of Bose–Einstein condensation, true long-range order emerges, and we observe quantum statistical effects as the thermal wave packets overlap. The excellent agreement with equilibrium Bose gas theory prompts microcavity photons as promising candidates for studies of critical scaling and universality in optical quantum gases. Phase transitions in quantum matter are related to correlation effects and they can change the ordering of material. Here the authors measure the first-order spatial correlation and the de Broglie wavelength for both thermal and condensed form of a photonic Bose gas in a dye-filled optical microcavity.
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Affiliation(s)
- Tobias Damm
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany
| | - David Dung
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany
| | - Frank Vewinger
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany
| | - Martin Weitz
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany.
| | - Julian Schmitt
- Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, Bonn, 53115, Germany.
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8
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Ye Z, Hu Y, He J, Wang J. Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms. Sci Rep 2017; 7:6289. [PMID: 28740216 PMCID: PMC5524852 DOI: 10.1038/s41598-017-06615-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2017] [Accepted: 06/14/2017] [Indexed: 12/04/2022] Open
Abstract
We study the performance of a cyclic heat engine which uses a small system with a finite number of ultracold atoms as its working substance and works between two heat reservoirs at constant temperatures T h and T c (
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Affiliation(s)
- Zhuolin Ye
- Department of Physics, Nanchang University, Nanchang, 330031, China
| | - Yingying Hu
- Department of Physics, Nanchang University, Nanchang, 330031, China
| | - Jizhou He
- Department of Physics, Nanchang University, Nanchang, 330031, China
| | - Jianhui Wang
- Department of Physics, Nanchang University, Nanchang, 330031, China.
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, 20742, USA.
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China.
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9
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Anquez M, Robbins BA, Bharath HM, Boguslawski M, Hoang TM, Chapman MS. Quantum Kibble-Zurek Mechanism in a Spin-1 Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2016; 116:155301. [PMID: 27127974 DOI: 10.1103/physrevlett.116.155301] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2015] [Indexed: 06/05/2023]
Abstract
The dynamics of a quantum phase transition are explored using slow quenches from the polar to the broken-axisymmetry phases in a small spin-1 ferromagnetic Bose-Einstein condensate. Measurements of the evolution of the spin populations reveal a power-law scaling of the temporal onset of excitations versus quench speed as predicted from quantum extensions of the Kibble-Zurek mechanism. The satisfactory agreement of the measured scaling exponent with the analytical theory and numerical simulations provides experimental confirmation of the quantum Kibble-Zurek model.
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Affiliation(s)
- M Anquez
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - B A Robbins
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - H M Bharath
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - M Boguslawski
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - T M Hoang
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - M S Chapman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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10
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Nicklas E, Karl M, Höfer M, Johnson A, Muessel W, Strobel H, Tomkovič J, Gasenzer T, Oberthaler MK. Observation of Scaling in the Dynamics of a Strongly Quenched Quantum Gas. PHYSICAL REVIEW LETTERS 2015; 115:245301. [PMID: 26705638 DOI: 10.1103/physrevlett.115.245301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2015] [Indexed: 06/05/2023]
Abstract
We report on the experimental observation of scaling in the time evolution following a sudden quench into the vicinity of a quantum critical point. The experimental system, a two-component Bose gas with coherent exchange between the constituents, allows for the necessary high level of control of parameters as well as the access to time-resolved spatial correlation functions. The theoretical analysis reveals that when quenching the system close to the critical point, the energy introduced by the quench leads to a short-time evolution exhibiting crossover reminiscent of the finite-temperature critical properties in the system's universality class. Observing the time evolution after a quench represents a paradigm shift in accessing and probing experimentally universal properties close to a quantum critical point and allows in a new way benchmarking of quantum many-body theory with experiments.
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Affiliation(s)
- E Nicklas
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - M Karl
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - M Höfer
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - A Johnson
- Laboratoire Charles-Fabry, Institut d'Optique Avenue Augustin Fresnel, 91 127 Palaiseau Cedex, France
| | - W Muessel
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - H Strobel
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - J Tomkovič
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - T Gasenzer
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - M K Oberthaler
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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11
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Affiliation(s)
- Cheng Chin
- James Franck Institute, Enrico Fermi Institute, University of Chicago, USA
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12
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Campostrini M, Nespolo J, Pelissetto A, Vicari E. Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022108. [PMID: 25768459 DOI: 10.1103/physreve.91.022108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Indexed: 06/04/2023]
Abstract
We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQTs), such as those arising in the presence of a space-dependent external field, which smooths out the discontinuities of the low-energy properties at the transition. We argue that a universal scaling behavior emerges in the space transition region close to the point in which the external field takes the value for which the homogeneous system undergoes the FOQT. We verify the general theory in two model systems. We consider the quantum Ising chain in the ferromagnetic phase and the q-state Potts chain for q=10, investigating the scaling behavior which arises in the presence of an additional inhomogeneous parallel and transverse magnetic field, respectively. Numerical results are in full agreement with the general theory.
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Affiliation(s)
- Massimo Campostrini
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Jacopo Nespolo
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma "La Sapienza" and INFN, Sezione di Roma I, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
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13
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Affiliation(s)
- Gabriele Ferrari
- Istituto Nazionale di Ottica-Consiglio Nazionale delle Ricerche, BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
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14
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Navon N, Gaunt AL, Smith RP, Hadzibabic Z. Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas. Science 2015; 347:167-70. [DOI: 10.1126/science.1258676] [Citation(s) in RCA: 199] [Impact Index Per Article: 22.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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15
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Bernier JS, Citro R, Kollath C, Orignac E. Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas. PHYSICAL REVIEW LETTERS 2014; 112:065301. [PMID: 24580691 DOI: 10.1103/physrevlett.112.065301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2013] [Indexed: 06/03/2023]
Abstract
We investigate the response of a one-dimensional Bose gas to a slow increase of its interaction strength. We focus on the rich dynamics of equal-time single-particle correlations treating the Lieb-Liniger model within a bosonization approach and the Bose-Hubbard model using the time-dependent density-matrix renormalization group method. For short distances, correlations follow a power law with distance with an exponent given by the adiabatic approximation. In contrast, for long distances, correlations decay algebraically with an exponent understood within the sudden quench approximation. This long distance regime is separated from an intermediate distance one by a generalized Lieb-Robinson criterion. At long times, in this intermediate regime, bosonization predicts that single-particle correlations decay following a stretched exponential, an unconventional behavior. We develop here an intuitive understanding for the propagation of correlations, in terms of a generalized light cone, applicable to a large variety of systems and quench forms.
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Affiliation(s)
- Jean-Sébastien Bernier
- Department of Physics and Astronomy, University of British Columbia, Vancouver V6T 1Z1, Canada
| | - Roberta Citro
- Dipartimento di Fisica "E. R. Caianiello" and CNR-SPIN, Università degli Studi di Salerno, I-84084 Fisciano, Italy
| | - Corinna Kollath
- HISKP, University of Bonn, Nussallee 14-16, D-53115 Bonn, Germany
| | - Edmond Orignac
- Laboratoire de Physique de l'École Normale Supérieure de Lyon, CNRS UMR5672, 46 Allée d'Italie, F-69364 Lyon Cedex 7, France
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16
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Schmidutz TF, Gotlibovych I, Gaunt AL, Smith RP, Navon N, Hadzibabic Z. Quantum Joule-Thomson effect in a saturated homogeneous Bose gas. PHYSICAL REVIEW LETTERS 2014; 112:040403. [PMID: 24580421 DOI: 10.1103/physrevlett.112.040403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2013] [Indexed: 06/03/2023]
Abstract
We study the thermodynamics of Bose-Einstein condensation in a weakly interacting quasihomogeneous atomic gas, prepared in an optical-box trap. We characterize the critical point for condensation and observe saturation of the thermal component in a partially condensed cloud, in agreement with Einstein's textbook picture of a purely statistical phase transition. Finally, we observe the quantum Joule-Thomson effect, namely isoenthalpic cooling of an (essentially) ideal gas. In our experiments this cooling occurs spontaneously, due to energy-independent collisions with the background gas in the vacuum chamber. We extract a Joule-Thomson coefficient μJT>10(9) K/bar, about 10 orders of magnitude larger than observed in classical gases.
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Affiliation(s)
- Tobias F Schmidutz
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Igor Gotlibovych
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Alexander L Gaunt
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Robert P Smith
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Nir Navon
- 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
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17
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del Campo A, Kibble TWB, Zurek WH. Causality and non-equilibrium second-order phase transitions in inhomogeneous systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:404210. [PMID: 24025443 DOI: 10.1088/0953-8984/25/40/404210] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
When a second-order phase transition is crossed at a finite rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: it obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental testing of defect formation theories.
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Affiliation(s)
- A del Campo
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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18
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Gaunt AL, Schmidutz TF, Gotlibovych I, Smith RP, Hadzibabic Z. Bose-Einstein condensation of atoms in a uniform potential. PHYSICAL REVIEW LETTERS 2013; 110:200406. [PMID: 25167389 DOI: 10.1103/physrevlett.110.200406] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2013] [Indexed: 05/16/2023]
Abstract
We have observed the Bose-Einstein condensation of an atomic gas in the (quasi)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of a noncondensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.
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Affiliation(s)
- Alexander L Gaunt
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Tobias F Schmidutz
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Igor Gotlibovych
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Robert P Smith
- 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
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19
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Das A, Sabbatini J, Zurek WH. Winding up superfluid in a torus via Bose Einstein condensation. Sci Rep 2012; 2:352. [PMID: 22500209 PMCID: PMC3324982 DOI: 10.1038/srep00352] [Citation(s) in RCA: 80] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2011] [Accepted: 03/02/2012] [Indexed: 11/09/2022] Open
Abstract
Phase transitions are usually treated as equilibrium phenomena, which yields telltale universality classes with scaling behavior of relaxation time and healing length. However, in second-order phase transitions relaxation time diverges near the critical point ("critical slowing down"). Therefore, every such transition traversed at a finite rate is a non-equilibrium process. Kibble-Zurek mechanism (KZM) captures this basic physics, predicting sizes of domains - fragments of broken symmetry - and the density of topological defects, long-lived relics of symmetry breaking that can survive long after the transition. To test KZM we simulate Bose-Einstein condensation in a ring using stochastic Gross-Pitaevskii equation and show that BEC formation can spontaneously generate quantized circulation of the newborn condensate. The magnitude of the resulting winding numbers and the time-lag of BEC density growth - both experimentally measurable - follow scalings predicted by KZM. Our results may also facilitate measuring the dynamical critical exponent for the BEC transition.
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Affiliation(s)
- Arnab Das
- Theory Division, LANL, MS-B213, Los Alamos, NM 87545, USA
| | - Jacopo Sabbatini
- ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
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20
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Wong CH, van Driel HJ, Kittinaradorn R, Stoof HTC, Duine RA. Spin caloritronics in noncondensed Bose gases. PHYSICAL REVIEW LETTERS 2012; 108:075301. [PMID: 22401219 DOI: 10.1103/physrevlett.108.075301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2011] [Indexed: 05/31/2023]
Abstract
We consider coupled spin and heat transport in a two-component atomic Bose gas in the noncondensed state. We find that the transport coefficients show a temperature dependence reflecting the bosonic enhancement of scattering and discuss experimental signatures of the spin-heat coupling in spin accumulation, spin separation, and total dissipation. Close to the critical temperature for Bose-Einstein condensation, we find that the spin-heat coupling is strongly reduced, which is also reflected in the spin caloritronics figure of merit that determines the thermodynamic efficiency of spin-heat conversion.
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Affiliation(s)
- C H Wong
- Institute for Theoretical Physics, Utrecht University, Utrecht, The Netherlands
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21
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Zhang X, Hung CL, Tung SK, Chin C. Observation of quantum criticality with ultracold atoms in optical lattices. Science 2012; 335:1070-2. [PMID: 22345397 DOI: 10.1126/science.1217990] [Citation(s) in RCA: 92] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Quantum criticality emerges when a many-body system is in the proximity of a continuous phase transition that is driven by quantum fluctuations. In the quantum critical regime, exotic, yet universal properties are anticipated; ultracold atoms provide a clean system to test these predictions. We report the observation of quantum criticality with two-dimensional Bose gases in optical lattices. On the basis of in situ density measurements, we observe scaling behavior of the equation of state at low temperatures, locate the quantum critical point, and constrain the critical exponents. We observe a finite critical entropy per particle that carries a weak dependence on the atomic interaction strength. Our experiment provides a prototypical method to study quantum criticality with ultracold atoms.
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Affiliation(s)
- Xibo Zhang
- The James Franck Institute, The University of Chicago, Chicago, IL 60637, USA.
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22
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Observation of scale invariance and universality in two-dimensional Bose gases. Nature 2011; 470:236-9. [PMID: 21270797 DOI: 10.1038/nature09722] [Citation(s) in RCA: 200] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2010] [Accepted: 12/01/2010] [Indexed: 11/09/2022]
Abstract
The collective behaviour of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics; for example, thermodynamic observables follow generalized scaling laws near the phase transition. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry result in a broad fluctuation regime and an extended range of universal scaling behaviour. Studies of the BKT transition in cold atoms have stimulated great interest in recent years, but a clear demonstration of critical behaviour near the phase transition has remained elusive. Here we report in situ density and density-fluctuation measurements of two-dimensional Bose gases of caesium at different temperatures and interaction strengths, observing scale-invariant, universal behaviours. The extracted thermodynamic functions confirm the existence of a wide universal region near the BKT phase transition, and provide a sensitive test of the universality predicted by classical-field theory and quantum Monte Carlo calculations. Our experimental results provide evidence for growing density-density correlations in the fluctuation region, and call for further explorations of universal phenomena in classical and quantum critical physics.
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23
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Heo MS, Kim Y, Kim K, Moon G, Lee J, Noh HR, Dykman MI, Jhe W. Ideal mean-field transition in a modulated cold atom system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031134. [PMID: 21230052 DOI: 10.1103/physreve.82.031134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2010] [Revised: 03/09/2010] [Indexed: 05/30/2023]
Abstract
We show that an atomic system in a periodically modulated optical trap displays an ideal mean-field symmetry-breaking transition. The symmetry is broken with respect to time translation by the modulation period. We describe experimental observations and develop a full microscopic theory of the observed critical phenomena. The transition is explained as resulting from the interplay of the long-range interatomic interaction and nonequilibrium fluctuations in the strongly modulated system. The observations, including anomalous fluctuations in the symmetry broken phase, are fully described by the theory.
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Affiliation(s)
- Myoung-Sun Heo
- Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
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24
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Damski B, Zurek WH. Soliton creation during a Bose-Einstein condensation. PHYSICAL REVIEW LETTERS 2010; 104:160404. [PMID: 20482032 DOI: 10.1103/physrevlett.104.160404] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2009] [Indexed: 05/29/2023]
Abstract
We use the stochastic Gross-Pitaevskii equation to study dynamics of Bose-Einstein condensation. We show that cooling into a Bose-Einstein condensate (BEC) can create solitons with density given by the cooling rate and by the critical exponents of the transition. Thus, counting solitons left in its wake should allow one to determine the critical exponents z and nu for a BEC phase transition. The same information can be extracted from two-point correlation functions.
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Affiliation(s)
- Bogdan Damski
- Theoretical Division, Los Alamos National Laboratory, MS-B213, Los Alamos, New Mexico 87545, USA
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25
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Diehl S, Baranov M, Daley AJ, Zoller P. Observability of quantum criticality and a continuous supersolid in atomic gases. PHYSICAL REVIEW LETTERS 2010; 104:165301. [PMID: 20482060 DOI: 10.1103/physrevlett.104.165301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2009] [Revised: 02/14/2010] [Indexed: 05/29/2023]
Abstract
We analyze the Bose-Hubbard model with a three-body hard-core constraint by mapping the system to a theory of two coupled bosonic degrees of freedom. We find striking features that could be observable in experiments, including a quantum Ising critical point on the transition from atomic to dimer superfluidity at unit filling, and a continuous supersolid phase for strongly bound dimers.
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Affiliation(s)
- S Diehl
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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26
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Campostrini M, Vicari E. Critical behavior and scaling in trapped systems. PHYSICAL REVIEW LETTERS 2009; 102:240601. [PMID: 19658988 DOI: 10.1103/physrevlett.102.240601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2009] [Revised: 05/21/2009] [Indexed: 05/28/2023]
Abstract
We study the scaling properties of critical particle systems confined by a potential. Using renormalization-group arguments, we show that their critical behavior can be cast in the form of a trap-size scaling, resembling finite-size scaling theory, with a nontrivial trap critical exponent theta, which describes how the correlation length xi scales with the trap size l, i.e., xi approximately l;{theta} at T_{c}. theta depends on the universality class of the transition, the power law of the confining potential, and on the way it is coupled to the critical modes. We present numerical results for two-dimensional lattice gas (Ising) models with various types of harmonic traps, which support the trap-size scaling scenario.
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Affiliation(s)
- Massimo Campostrini
- Dipartimento di Fisica dell'Università di Pisa and INFN, I-56127 Pisa, Italy
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27
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Zurek WH. Causality in condensates: gray solitons as relics of BEC formation. PHYSICAL REVIEW LETTERS 2009; 102:105702. [PMID: 19392126 DOI: 10.1103/physrevlett.102.105702] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2008] [Revised: 02/03/2009] [Indexed: 05/27/2023]
Abstract
Symmetry breaking during phase transitions can lead to the formation of topological defects (such as vortex lines in superfluids). However, the usually studied Bose-Einstein condensates (BECs) have the shape of a cigar, a geometry that impedes vortex formation, survival, and detection. I show that, in elongated traps, one can expect the formation of gray solitons (long-lived, nontopological "phase defects") as a result of the same mechanism. Their number will rise approximately in proportion to the transition rate. This steep rise is due to the increasing size of the region of the BEC cigar where the phase of the condensate wave function is chosen locally (rather than passed on from the already formed BEC).
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Affiliation(s)
- Wojciech H Zurek
- Theory Division, LANL, MS-B213, Los Alamos, New Mexico 87545, USA
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28
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Gangardt DM, Kamenev A. Bloch oscillations in a one-dimensional spinor gas. PHYSICAL REVIEW LETTERS 2009; 102:070402. [PMID: 19257649 DOI: 10.1103/physrevlett.102.070402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2008] [Revised: 01/19/2009] [Indexed: 05/27/2023]
Abstract
A force applied to a spin-flipped particle in a one-dimensional spinor gas may lead to Bloch oscillations of the particle's position and velocity. The existence of Bloch oscillations crucially depends on the viscous friction force exerted by the rest of the gas on the spin excitation. We evaluate the friction in terms of the quantum fluid parameters. In particular, we show that the friction is absent for integrable cases, such as an SU(2) symmetric gas of bosons or fermions. For small deviations from the exact integrability the friction is very weak, opening the possibility to observe Bloch oscillations.
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Affiliation(s)
- D M Gangardt
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom.
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29
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Altman E. Critical Insights. Science 2007; 315:1504-5. [PMID: 17363649 DOI: 10.1126/science.1140809] [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)
- Ehud Altman
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel.
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