1
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Sable H, Gaur D, Angom D. Fine-grained domain counting and percolation analysis in two-dimensional lattice systems with linked lists. Phys Rev E 2023; 108:045307. [PMID: 37978691 DOI: 10.1103/physreve.108.045307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 09/25/2023] [Indexed: 11/19/2023]
Abstract
We present a fine-grained approach to identify clusters and perform percolation analysis in a two-dimensional (2D) lattice system. In our approach, we develop an algorithm based on the linked-list data structure whereby the members of a cluster are nodes of a path. This path is mapped to a linked-list. This approach facilitates unique cluster labeling in a lattice with a single scan. We use the algorithm to determine the critical exponent in the quench dynamics from the Mott insulator to the superfluid phase of bosons in 2D square optical lattices. The results obtained are consistent with the Kibble-Zurek mechanism. We also employ the algorithm to compute the correlation length using definitions based on percolation theory and use it to identify the quantum critical point of the Bose Glass to superfluid transition in the disordered 2D square optical lattices. In addition, we compute the critical exponent ν which quantify the divergence of the correlation length ξ across the phase transition and the fractal dimension of the hulls of the superfluid clusters.
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Affiliation(s)
- Hrushikesh Sable
- Physical Research Laboratory, Ahmedabad 380009, Gujarat, India
- Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar 382355, Gujarat, India
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Deepak Gaur
- Physical Research Laboratory, Ahmedabad 380009, Gujarat, India
- Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar 382355, Gujarat, India
| | - D Angom
- Physical Research Laboratory, Ahmedabad 380009, Gujarat, India
- Department of Physics, Manipur University, Canchipur 795003, Manipur, India
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2
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Dupuis N, Daviet R. Bose-glass phase of a one-dimensional disordered Bose fluid: Metastable states, quantum tunneling, and droplets. Phys Rev E 2020; 101:042139. [PMID: 32422844 DOI: 10.1103/physreve.101.042139] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 03/23/2020] [Indexed: 06/11/2023]
Abstract
We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K_{k}∼k^{θ} that vanishes with an exponent θ=z-1 related to the dynamical critical exponent z. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics, and yields a (dissipative) conductivity vanishing as ω^{2} in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks," or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.
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Affiliation(s)
- Nicolas Dupuis
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| | - Romain Daviet
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
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3
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Dupuis N. Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid. Phys Rev E 2019; 100:030102. [PMID: 31640005 DOI: 10.1103/physreve.100.030102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Indexed: 06/10/2023]
Abstract
We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsible for the ω^{2} behavior of the (dissipative) conductivity in the low-frequency limit. These results can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.
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Affiliation(s)
- Nicolas Dupuis
- Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, Sorbonne Université, CNRS, F-75005 Paris, France
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4
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Ma T, Zhang L, Chang CC, Hung HH, Scalettar RT. Localization of Interacting Dirac Fermions. PHYSICAL REVIEW LETTERS 2018; 120:116601. [PMID: 29601744 DOI: 10.1103/physrevlett.120.116601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Revised: 12/18/2017] [Indexed: 06/08/2023]
Abstract
Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.
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Affiliation(s)
- Tianxing Ma
- Department of Physics, Beijing Normal University, Beijing 100875, China
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Lufeng Zhang
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Chia-Chen Chang
- Department of Physics, University of California, Davis, California 95616, USA
| | - Hsiang-Hsuan Hung
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Richard T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
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Lin F, Maier TA, Scarola VW. Disordered Supersolids in the Extended Bose-Hubbard Model. Sci Rep 2017; 7:12752. [PMID: 28986536 PMCID: PMC5630629 DOI: 10.1038/s41598-017-13040-9] [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: 07/04/2017] [Accepted: 09/12/2017] [Indexed: 11/17/2022] Open
Abstract
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.
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Affiliation(s)
- Fei Lin
- Department of Physics, Virginia Tech, Blacksburg, Virginia, 24061, USA
| | - T A Maier
- Computational Science and Engineering Division and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA
| | - V W Scarola
- Department of Physics, Virginia Tech, Blacksburg, Virginia, 24061, USA.
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6
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Krinner S, Esslinger T, Brantut JP. Two-terminal transport measurements with cold atoms. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:343003. [PMID: 28749788 DOI: 10.1088/1361-648x/aa74a1] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.
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Affiliation(s)
- Sebastian Krinner
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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7
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Angelone A, Mezzacapo F, Pupillo G. Superglass Phase of Interaction-Blockaded Gases on a Triangular Lattice. PHYSICAL REVIEW LETTERS 2016; 116:135303. [PMID: 27081986 DOI: 10.1103/physrevlett.116.135303] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Indexed: 06/05/2023]
Abstract
We investigate the quantum phases of monodispersed bosonic gases confined to a triangular lattice and interacting via a class of soft-shoulder potentials. The latter correspond to soft-core potentials with an additional hard-core onsite interaction. Using exact quantum Monte Carlo simulations, we show that the low temperature phases for weak and strong interactions following a temperature quench are a homogeneous superfluid and a glass, respectively. The latter is an insulating phase characterized by inhomogeneity in the density distribution and structural disorder. Remarkably, we find that for intermediate interaction strengths a superglass occurs in an extended region of the phase diagram, where glassy behavior coexists with a sizable finite superfluid fraction. This glass phase is obtained in the absence of geometrical frustration or external disorder and is a result of the competition of quantum fluctuations and cluster formation in the corresponding classical ground state. For high enough temperature, the glass and superglass turn into a floating stripe solid and a supersolid, respectively. Given the simplicity and generality of the model, these phases should be directly relevant for state-of-the-art experiments with Rydberg-dressed atoms in optical lattices.
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Affiliation(s)
- Adriano Angelone
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Fabio Mezzacapo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Guido Pupillo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
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8
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Wang Y, Guo W, Sandvik AW. Anomalous quantum glass of bosons in a random potential in two dimensions. PHYSICAL REVIEW LETTERS 2015; 114:105303. [PMID: 25815942 DOI: 10.1103/physrevlett.114.105303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Indexed: 06/04/2023]
Abstract
We present a quantum Monte Carlo study of the "quantum glass" phase of the two-dimensional Bose-Hubbard model with random potentials at filling ρ=1. In the narrow region between the Mott and superfluid phases, the compressibility has the form κ∼exp(-b/T^{α})+c with α<1 and c vanishing or very small. Thus, at T=0 the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only 10% changes the low-temperature compressibility by more than 4 orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp crossover.
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Affiliation(s)
- Yancheng Wang
- Department of Physics, Beijing Normal University, Beijing 100875, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wenan Guo
- Department of Physics, Beijing Normal University, Beijing 100875, China
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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9
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D'Errico C, Lucioni E, Tanzi L, Gori L, Roux G, McCulloch IP, Giamarchi T, Inguscio M, Modugno G. Observation of a disordered bosonic insulator from weak to strong interactions. PHYSICAL REVIEW LETTERS 2014; 113:095301. [PMID: 25215990 DOI: 10.1103/physrevlett.113.095301] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Indexed: 06/03/2023]
Abstract
We employ ultracold atoms with controllable disorder and interaction to study the paradigmatic problem of disordered bosons in the full disorder-interaction plane. Combining measurements of coherence, transport and excitation spectra, we get evidence of an insulating regime extending from weak to strong interaction and surrounding a superfluidlike regime, in general agreement with the theory. For strong interaction, we reveal the presence of a strongly correlated Bose glass coexisting with a Mott insulator.
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Affiliation(s)
- Chiara D'Errico
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, 50019 Sesto Fiorentino, Italy and Istituto Nazionale di Ottica, CNR, 50019 Sesto Fiorentino, Italy
| | - Eleonora Lucioni
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, 50019 Sesto Fiorentino, Italy and Istituto Nazionale di Ottica, CNR, 50019 Sesto Fiorentino, Italy
| | - Luca Tanzi
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, 50019 Sesto Fiorentino, Italy
| | - Lorenzo Gori
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, 50019 Sesto Fiorentino, Italy
| | | | - Ian P McCulloch
- Centre for Engineered Quantum Systems, University of Queensland, Brisbane 4072, Australia
| | | | - Massimo Inguscio
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, 50019 Sesto Fiorentino, Italy and INRIM, 10135 Torino, Italy
| | - Giovanni Modugno
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, 50019 Sesto Fiorentino, Italy and Istituto Nazionale di Ottica, CNR, 50019 Sesto Fiorentino, Italy
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10
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Jörder F, Zimmermann K, Rodriguez A, Buchleitner A. Interaction effects on dynamical localization in driven helium. PHYSICAL REVIEW LETTERS 2014; 113:063004. [PMID: 25148324 DOI: 10.1103/physrevlett.113.063004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2013] [Indexed: 06/03/2023]
Abstract
Dynamical localization prevents driven atomic systems from fast fragmentation by hampering the excitation process. We present numerical simulations within a collinear model of microwave-driven helium Rydberg atoms and prove that dynamical localization survives the impact of electron-electron interaction, even for doubly excited states in the presence of fast autoionization. We conclude that the effect of electron-electron repulsion on localization can be described by an appropriate rescaling of the atomic level density and of the external field with the strength of the interaction.
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Affiliation(s)
- Felix Jörder
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| | - Klaus Zimmermann
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| | - Alberto Rodriguez
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| | - Andreas Buchleitner
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
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11
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Yao Z, da Costa KPC, Kiselev M, Prokof'ev N. Critical exponents of the superfluid-Bose-glass transition in three dimensions. PHYSICAL REVIEW LETTERS 2014; 112:225301. [PMID: 24949775 DOI: 10.1103/physrevlett.112.225301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Indexed: 06/03/2023]
Abstract
Recent experimental and numerical studies of the critical-temperature exponent ϕ for the superfluid-Bose-glass universality in three-dimensional systems report strong violations of the key quantum critical relation, ϕ=νz, where z and ν are the dynamic and correlation-length exponents, respectively; these studies question the conventional scaling laws for this quantum critical point. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal-fluid transition-temperature dependence on the chemical potential (or the magnetic field, in spin systems), T_{c}∝(μ-μ_{c})^{ϕ}, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the ϕ=νz law [with ϕ=2.7(2), z=3, and ν=0.88(5)] holds true, resolving the ϕ-exponent "crisis."
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Affiliation(s)
- Zhiyuan Yao
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Karine P C da Costa
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA and Instituto de Física, Universidade de São Paulo, 05508-090 São Paulo, Brazil
| | - Mikhail Kiselev
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy
| | - Nikolay Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA and Russian Research Center "Kurchatov Institute," 123182 Moscow, Russia
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12
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Álvarez Zúñiga JP, Laflorencie N. Bose-glass transition and spin-wave localization for 2D bosons in a random potential. PHYSICAL REVIEW LETTERS 2013; 111:160403. [PMID: 24182237 DOI: 10.1103/physrevlett.111.160403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2013] [Revised: 09/11/2013] [Indexed: 06/02/2023]
Abstract
A spin-wave approach of the zero temperature superfluid-insulator transition for two-dimensional hard-core bosons in a random potential μ=±W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations leads to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass phase emerges over a finite region until the insulator appears. Furthermore, in the strongly disordered SF regime, a mobility edge in the spin-wave excitation spectrum is found at a finite frequency Ω(c) decreasing with W, and presumably vanishing in the Bose-glass phase.
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13
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Krinner S, Stadler D, Meineke J, Brantut JP, Esslinger T. Superfluidity with disorder in a thin film of quantum gas. PHYSICAL REVIEW LETTERS 2013; 110:100601. [PMID: 23521243 DOI: 10.1103/physrevlett.110.100601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2012] [Revised: 01/21/2013] [Indexed: 06/01/2023]
Abstract
We investigate the properties of a strongly interacting superfluid gas of (6)Li(2) Feshbach molecules forming a thin film confined in a quasi-two-dimensional channel with a tunable random potential, creating a microscopic disorder. We measure the atomic current, extract the resistance of the film in a two-terminal configuration, and identify a superfluid state at low disorder strength, which evolves into a normal poorly conducting state for strong disorder. The transition takes place when the chemical potential reaches the percolation threshold of the disorder. The evolution of the conduction properties contrasts with the smooth behavior of the density and compressibility across the transition, measured in situ at equilibrium. These features suggest the emergence of a glasslike phase at strong disorder.
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Habibian H, Winter A, Paganelli S, Rieger H, Morigi G. Bose-Glass phases of ultracold atoms due to cavity backaction. PHYSICAL REVIEW LETTERS 2013; 110:075304. [PMID: 25166381 DOI: 10.1103/physrevlett.110.075304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2012] [Revised: 11/16/2012] [Indexed: 06/03/2023]
Abstract
We determine the quantum ground-state properties of ultracold bosonic atoms interacting with the mode of a high-finesse resonator. The atoms are confined by an external optical lattice, whose period is incommensurate with the cavity mode wavelength, and are driven by a transverse laser, which is resonant with the cavity mode. While for pointlike atoms photon scattering into the cavity is suppressed, for sufficiently strong lasers quantum fluctuations can support the buildup of an intracavity field, which in turn amplifies quantum fluctuations. The dynamics is described by a Bose-Hubbard model where the coefficients due to the cavity field depend on the atomic density at all lattice sites. Quantum Monte Carlo simulations and mean-field calculations show that, for large parameter regions, cavity backaction forces the atoms into clusters with a checkerboard density distribution. Here, the ground state lacks superfluidity and possesses finite compressibility, typical of a Bose glass. This system constitutes a novel setting where quantum fluctuations give rise to effects usually associated with disorder.
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Affiliation(s)
- Hessam Habibian
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany and Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
| | - André Winter
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Simone Paganelli
- Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
| | - Heiko Rieger
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Giovanna Morigi
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
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15
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Larson D, Kao YJ. Tuning the disorder in superglasses. PHYSICAL REVIEW LETTERS 2012; 109:157202. [PMID: 23102360 DOI: 10.1103/physrevlett.109.157202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2012] [Revised: 07/30/2012] [Indexed: 06/01/2023]
Abstract
We study the interplay of superfluidity, glassy, and magnetic orders in the XXZ model with random Ising interactions on a three dimensional cubic lattice. In the classical limit, this model reduces to a ±J Edwards-Anderson Ising model with concentration p of ferromagnetic bonds, which hosts a glassy-ferromagnetic transition at a critical concentration p(c)(cl)~0.77. Our quantum Monte Carlo simulation results show that quantum fluctuations stabilize the coexistence of superfluidity and glassy order (superglass), and shift the (super)glassy-ferromagnetic transition to p(c)>p(c)(cl). In contrast, antiferromagnetic order coexists with superfluidity to form a supersolid, and the transition to the glassy phase occurs at a higher p.
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Affiliation(s)
- Derek Larson
- Department of Physics, National Taiwan University, Taipei 10607, Taiwan
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16
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Söyler SG, Kiselev M, Prokof'ev NV, Svistunov BV. Phase diagram of the commensurate two-dimensional disordered Bose-Hubbard model. PHYSICAL REVIEW LETTERS 2011; 107:185301. [PMID: 22107640 DOI: 10.1103/physrevlett.107.185301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2011] [Indexed: 05/31/2023]
Abstract
We establish the full ground state phase diagram of the disordered Bose-Hubbard model in two dimensions at a unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid-insulator transition of the pure system, we observe an unexpectedly weak--almost not resolvable--sensitivity of the critical interaction to the strength of (weak) disorder.
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Affiliation(s)
- S G Söyler
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy
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17
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Stark C, Pollet L, Imamoğlu A, Renner R. Localization of toric code defects. PHYSICAL REVIEW LETTERS 2011; 107:030504. [PMID: 21838340 DOI: 10.1103/physrevlett.107.030504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2011] [Indexed: 05/31/2023]
Abstract
We explore the possibility of passive error correction in the toric code model. We first show that even coherent dynamics, stemming from spin interactions or the coupling to an external magnetic field, lead to logical errors. We then argue that Anderson localization of the defects, arising from unavoidable fluctuations of the coupling constants, provides a remedy. This protection is demonstrated by using general analytical arguments that are complemented with numerical results which show that self-correcting memory can in principle be achieved in the limit of a nonzero density of identical defects.
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Affiliation(s)
- Cyril Stark
- Theoretische Physik, ETH Zurich, CH-8093 Zurich, Switzerland
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