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White DH, Haase TA, Brown DJ, Hoogerland MD, Najafabadi MS, Helm JL, Gies C, Schumayer D, Hutchinson DAW. Observation of two-dimensional Anderson localisation of ultracold atoms. Nat Commun 2020; 11:4942. [PMID: 33009375 PMCID: PMC7532155 DOI: 10.1038/s41467-020-18652-w] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2019] [Accepted: 09/01/2020] [Indexed: 11/29/2022] Open
Abstract
Anderson localisation -the inhibition of wave propagation in disordered media- is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.
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Affiliation(s)
- Donald H White
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Waseda Research Institute for Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan
| | - Thomas A Haase
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
| | - Dylan J Brown
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Light-Matter Interactions for Quantum Technologies Unit, Okinawa Institute of Science and Technology, Tancha, Onna, Okinawa, Japan
| | - Maarten D Hoogerland
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand.
| | - Mojdeh S Najafabadi
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - John L Helm
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - Christopher Gies
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany
| | - Daniel Schumayer
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - David A W Hutchinson
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Auckland, New Zealand.
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.
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Yao H, Giamarchi T, Sanchez-Palencia L. Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes. PHYSICAL REVIEW LETTERS 2020; 125:060401. [PMID: 32845659 DOI: 10.1103/physrevlett.125.060401] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2020] [Accepted: 07/13/2020] [Indexed: 06/11/2023]
Abstract
The emergence of a compressible insulator phase, known as the Bose glass, is characteristic of the interplay of interactions and disorder in correlated Bose fluids. While widely studied in tight-binding models, its observation remains elusive owing to stringent temperature effects. Here we show that this issue may be overcome by using Lieb-Liniger bosons in shallow quasiperiodic potentials. A Bose glass, surrounded by superfluid and Mott phases, is found above a critical potential and for finite interactions. At finite temperature, we show that the melting of the Mott lobes is characteristic of a fractal structure and find that the Bose glass is robust against thermal fluctuations up to temperatures accessible in quantum gases. Our results raise questions about the universality of the Bose glass transition in such shallow quasiperiodic potentials.
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Affiliation(s)
- Hepeng Yao
- CPHT, CNRS, Institut Polytechnique de Paris, Route de Saclay 91128 Palaiseau, France
| | - Thierry Giamarchi
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
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Localisation of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects. Sci Rep 2019; 9:11049. [PMID: 31363111 PMCID: PMC6667487 DOI: 10.1038/s41598-019-47279-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Accepted: 07/02/2019] [Indexed: 11/24/2022] Open
Abstract
We investigate the effects of disorder and lattice geometry against localisation phenomena in a weakly interacting ultracold bosonic gas confined in a 2D optical lattice. The behaviour of the quantum fluid is studied at the mean-field level performing computational experiments, as a function of disorder strength for lattices of sizes similar to current experiments. Quantification of localisation, away from the Bose glass phase, was obtained directly from the stationary density profiles through a robust statistical analysis of the condensate component, as a function of the disorder amplitude. Our results show a smooth transition, or crossover, to localisation induced by disorder in square and triangular lattices. In contrast, associated to its larger tunneling amplitude, honeycomb lattices show absence of localisation for the same range of disorder strengths and same lattice amplitude, while also exhibiting partial localisation for large disorder amplitudes. We also conclude that the coordination number z have a partial influence on how fast this smooth transition occurs as the system size increases. Signatures of disorder are also found in the ground state energy spectrum, where a continuous distribution emerges instead of a distribution of sharp peaks proper to the system in the absence of disorder.
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Carleo G, Boéris G, Holzmann M, Sanchez-Palencia L. Universal superfluid transition and transport properties of two-dimensional dirty bosons. PHYSICAL REVIEW LETTERS 2013; 111:050406. [PMID: 23952374 DOI: 10.1103/physrevlett.111.050406] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2013] [Indexed: 06/02/2023]
Abstract
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.
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Affiliation(s)
- Giuseppe Carleo
- Laboratoire Charles Fabry, Institut d'Optique, CNRS, Univ Paris Sud 11, 2 avenue Augustin Fresnel, F-91127 Palaiseau cedex, France
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Fontanesi L, Wouters M, Savona V. Superfluid to Bose-Glass transition in a 1D weakly interacting Bose gas. PHYSICAL REVIEW LETTERS 2009; 103:030403. [PMID: 19659256 DOI: 10.1103/physrevlett.103.030403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2009] [Revised: 06/18/2009] [Indexed: 05/28/2023]
Abstract
We study the one-dimensional Bose gas in spatially correlated disorder at zero temperature, using an extended density-phase Bogoliubov method. We analyze, in particular, the decay of the one-body density matrix and the behavior of the Bogoliubov excitations across the phase boundary. We observe that the transition to the Bose-glass phase is marked by a power-law divergence of the density of states at low energy. A measure of the localization length displays a power-law energy dependence in both regions, with the exponent equal to -1 at the boundary. We draw the phase diagram of the superfluid-insulator transition in the limit of small interaction strength.
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Affiliation(s)
- Luca Fontanesi
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne EPFL, CH-1015 Lausanne, Switzerland.
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Gurarie V, Refael G, Chalker JT. Excitations of one-dimensional Bose-Einstein condensates in a random potential. PHYSICAL REVIEW LETTERS 2008; 101:170407. [PMID: 18999729 DOI: 10.1103/physrevlett.101.170407] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2008] [Indexed: 05/27/2023]
Abstract
We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as l(omega) approximately 1/omega(alpha). We show that the well-known result alpha=2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, alpha starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, alpha=1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.
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Affiliation(s)
- V Gurarie
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
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Samelsohn G, Gruzdev E. Dynamics of wave packets in two-dimensional random systems with anisotropic disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:036601. [PMID: 18851174 DOI: 10.1103/physreve.78.036601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2008] [Indexed: 05/26/2023]
Abstract
A theoretical model is proposed to describe narrowband pulse dynamics in two-dimensional systems with arbitrary correlated disorder. In anisotropic systems with elongated cigarlike inhomogeneities, fast propagation is predicted in the direction across the structure where the wave is exponentially localized and tunneling of evanescent modes plays a dominant role in typical realizations. Along the structure, where the wave is channeled as in a waveguide, the motion of the wave energy is relatively slow. Numerical simulations performed for ultra-wide-band pulses show that even at the initial stage of wave evolution, the radiation diffuses predominantly in the direction along the major axis of the correlation ellipse. Spectral analysis of the results relates the long tail of the wave observed in the transverse direction to a number of frequency domain "lucky shots" associated with the long-living resonant modes localized inside the sample.
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Affiliation(s)
- Gregory Samelsohn
- Department of Communication Engineering, Holon Institute of Technology, Holon 58102, Israel.
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Palpacelli S, Succi S. Quantum lattice Boltzmann simulation of expanding Bose-Einstein condensates in random potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:066708. [PMID: 18643398 DOI: 10.1103/physreve.77.066708] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2008] [Indexed: 05/26/2023]
Abstract
The phenomenon of Anderson localization in expanding one-dimensional Bose-Einstein condensates is investigated by numerically solving the Gross-Pitaevskii equation with a random speckle potential. To this purpose, a quantum lattice Boltzmann (QLB) method is used, and compared with a standard Crank-Nicolson scheme. The QLB simulations show evidence of Anderson localization even for relatively low-energy condensates, with a healing length as large as one-tenth of the Thomas-Fermi length. Moreover, very long-time simulations, lasting up to 15 000 optical confinement periods, indicate that the Anderson localization degrades in time, although at a very slow pace. In particular, the inverse localization length is found to decay according to a t;{-1/3} law. This lends support to the idea that localized wave functions, although not strictly ground states, represent extremely long-lived metastable states of the expanding condensate.
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Affiliation(s)
- S Palpacelli
- Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
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Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 2008; 453:891-4. [DOI: 10.1038/nature07000] [Citation(s) in RCA: 1191] [Impact Index Per Article: 74.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2008] [Accepted: 04/09/2008] [Indexed: 11/08/2022]
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Niederberger A, Schulte T, Wehr J, Lewenstein M, Sanchez-Palencia L, Sacha K. Disorder-induced order in two-component Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2008; 100:030403. [PMID: 18232950 DOI: 10.1103/physrevlett.100.030403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2007] [Indexed: 05/25/2023]
Abstract
We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for XY spin models. We show that a random Raman coupling induces a relative phase of pi/2 between the two BECs and that the effect is robust. We demonstrate it in one, two, and three dimensions at T=0 and present evidence that it persists at small T>0. Applications to phase control in ultracold spinor condensates are discussed.
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Affiliation(s)
- A Niederberger
- ICFO-Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, Castelldefels, Barcelona, Spain
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