1
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Lin L, Wei Y, He D. Disorder-induced spiky phonon transmission of harmonic lattices. Phys Rev E 2024; 109:024129. [PMID: 38491675 DOI: 10.1103/physreve.109.024129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2023] [Accepted: 02/05/2024] [Indexed: 03/18/2024]
Abstract
In this article, we find that impurity in a one-dimensional harmonic chain leads to spikes in the phonon transmission. Using the Langevin equations and Green's function method (LEGF), we find the underlying mechanism of spikes, which comes from the fact that the wave energy can be transferred through uniform subchains laid between impurities without loss. Both the position and magnitude of spikes can be analytically obtained. By employing these results, we provide an analytical approach to transmission in the thermodynamic limit, thereby compensating for the limitation of LEGF that are practically confined to finite system size. Finally, we determine an expression for the localization length based on LEGF, demonstrating the equivalence between mass disorder and spatial disorder in low impurity concentration.
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Affiliation(s)
- Lu Lin
- Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China
| | - Yuhang Wei
- Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China
| | - Dahai He
- Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China
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2
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Mu S, Gong J, Lemarié G. Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets. PHYSICAL REVIEW LETTERS 2024; 132:046301. [PMID: 38335351 DOI: 10.1103/physrevlett.132.046301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 09/08/2023] [Accepted: 12/14/2023] [Indexed: 02/12/2024]
Abstract
We identify the key features of Kardar-Parisi-Zhang (KPZ) universality class in the fluctuations of the wave density logarithm in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of 1/3, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent 2/3. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched exponential correction to its well-known exponential localization.
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Affiliation(s)
- Sen Mu
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China
| | - Gabriel Lemarié
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, France
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3
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Tomsovic S, Urbina JD, Richter K. Controlling quantum chaos: Time-dependent kicked rotor. Phys Rev E 2023; 108:044202. [PMID: 37978592 DOI: 10.1103/physreve.108.044202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Accepted: 09/08/2023] [Indexed: 11/19/2023]
Abstract
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent Letter [Phys. Rev. Lett. 130, 020201 (2023)0031-900710.1103/PhysRevLett.130.020201], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the Letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as ℏ→0.
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Affiliation(s)
- Steven Tomsovic
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
- Department of Physics and Astronomy, Washington State University, Pullman 99164-2814, Washington, USA
| | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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4
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Tomsovic S, Urbina JD, Richter K. Controlling Quantum Chaos: Optimal Coherent Targeting. PHYSICAL REVIEW LETTERS 2023; 130:020201. [PMID: 36706382 DOI: 10.1103/physrevlett.130.020201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 12/20/2022] [Indexed: 06/18/2023]
Abstract
One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor, a preeminent quantum chaotic paradigm, to illustrate the method, and investigate its accuracy. The method's error can be made to vanish as ℏ→0.
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Affiliation(s)
- Steven Tomsovic
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
| | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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5
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Wang Y, Zhang JH, Li Y, Wu J, Liu W, Mei F, Hu Y, Xiao L, Ma J, Chin C, Jia S. Observation of Interaction-Induced Mobility Edge in an Atomic Aubry-André Wire. PHYSICAL REVIEW LETTERS 2022; 129:103401. [PMID: 36112456 DOI: 10.1103/physrevlett.129.103401] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
A mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. The Aubry-André (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for a mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of a mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our Letter also offers new possibilities to engineer quantum transport and phase transitions in disordered systems.
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Affiliation(s)
- Yunfei Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
| | - Jia-Hui Zhang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
| | - Yuqing Li
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jizhou Wu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Wenliang Liu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Ying Hu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jie Ma
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Cheng Chin
- James Franck Institute, Enrico Fermi Institute, Department of Physics, University of Chicago, Illinois 60637, USA
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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6
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Zonnios M, Levinsen J, Parish MM, Pollock FA, Modi K. Signatures of Quantum Chaos in an Out-of-Time-Order Tensor. PHYSICAL REVIEW LETTERS 2022; 128:150601. [PMID: 35499886 DOI: 10.1103/physrevlett.128.150601] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 02/26/2022] [Accepted: 03/02/2022] [Indexed: 06/14/2023]
Abstract
Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of interest interacts with a small quantum probe whose dynamical properties identify the chaoticity of the system. Specifically, we propose a fully quantum version of the out-of-time-order correlator-which we term the out-of-time-order tensor-whose correlations offer clear information theoretic meanings about the chaoticity of a process. We illustrate the utility of the out-of-time-order tensor as a signature of chaos using random unitary processes as well as in the quantum kicked rotor, where the chaoticity is tunable.
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Affiliation(s)
- Magdalini Zonnios
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Jesper Levinsen
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Meera M Parish
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Felix A Pollock
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Kavan Modi
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
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7
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Xing Y, Zhao X, Lü Z, Liu S, Zhang S, Wang HF. Observing two-particle Anderson localization in linear disordered photonic lattices. OPTICS EXPRESS 2021; 29:40428-40446. [PMID: 34809384 DOI: 10.1364/oe.446007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Accepted: 11/08/2021] [Indexed: 06/13/2023]
Abstract
We theoretically and systematically investigate Anderson localization of two bosons with nearest-neighbor interaction in one dimension under short- and long-time scales, two types of disorders, and three types of initial states, which can be directly observed in linear disordered photonic lattices via two experimentally measurable physical quantities, participation ratio and spatial correlation. We find that the behavior of localization characterized by the participation ratio depends on the strength of interaction and the type of disorder and initial condition. Two-boson spatial correlation reveals more novel and unique features. In the ordered case, two types of two-boson bindings and bosonic "fermionization" are shown, which are intimately attributed to the band structure of the system. In the disordered case, the impact of interaction on the two-boson Anderson localization is reexamined and the joint effect of disorder and interaction is addressed. We further demonstrate that the independence of the participation ratio or spatial correlation on the sign of interaction can be eliminated by employing an initial state that breaks one of two specific symmetries. Finally, we elucidate the relevant details of the experimental implementation in a two-dimensional linear photonic lattice.
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8
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Wang WY, Zhao WL. Protected quantum coherence by gain and loss in a noisy quantum kicked rotor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:025403. [PMID: 34587610 DOI: 10.1088/1361-648x/ac2b68] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Accepted: 09/29/2021] [Indexed: 06/13/2023]
Abstract
We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.
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Affiliation(s)
- Wen-Yuan Wang
- Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, People's Republic of China
- Beijing Computational Science Research Center, Beijing 100193, People's Republic of China
| | - Wen-Lei Zhao
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, People's Republic of China
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9
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Pizzamiglio A, Chang SY, Bondani M, Montangero S, Gerace D, Benenti G. Dynamical Localization Simulated on Actual Quantum Hardware. ENTROPY 2021; 23:e23060654. [PMID: 34071055 PMCID: PMC8224768 DOI: 10.3390/e23060654] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Revised: 05/10/2021] [Accepted: 05/18/2021] [Indexed: 11/16/2022]
Abstract
Quantum computers are invaluable tools to explore the properties of complex quantum systems. We show that dynamical localization of the quantum sawtooth map, a highly sensitive quantum coherent phenomenon, can be simulated on actual, small-scale quantum processors. Our results demonstrate that quantum computing of dynamical localization may become a convenient tool for evaluating advances in quantum hardware performances.
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Affiliation(s)
- Andrea Pizzamiglio
- Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, Via Valleggio 11, 22100 Como, Italy;
| | - Su Yeon Chang
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland;
- CERN, 1211 Meyrin, Switzerland
| | - Maria Bondani
- Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Via Valleggio 11, 22100 Como, Italy;
| | - Simone Montangero
- Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, 35131 Padova, Italy;
- Istituto Nazionale di Fisica Nucleare, Sezione di Padova, 35131 Padova, Italy
- Padua Quantum Technology Research Center, Università di Padova, 35131 Padova, Italy
| | - Dario Gerace
- Dipartimento di Fisica, Università di Pavia, Via Bassi 6, 27100 Pavia, Italy;
| | - Giuliano Benenti
- Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, Via Valleggio 11, 22100 Como, Italy;
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
- NEST, Istituto Nanoscienze-CNR, 56126 Pisa, Italy
- Correspondence:
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10
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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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11
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Yamada HS, Ikeda KS. Critical phenomena of dynamical delocalization in quantum maps: Standard map and Anderson map. Phys Rev E 2020; 101:032210. [PMID: 32289890 DOI: 10.1103/physreve.101.032210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Accepted: 02/19/2020] [Indexed: 06/11/2023]
Abstract
Following the paper exploring the Anderson localization of monochromatically perturbed kicked quantum maps [Phys. Rev. E 97, 012210 (2018)2470-004510.1103/PhysRevE.97.012210], the delocalization-localization transition phenomena in polychromatically perturbed quantum maps (QM) is investigated focusing particularly on the dependency of critical phenomena on the number M of the harmonic perturbations, where M+1=d corresponds to the spatial dimension of the ordinary disordered lattice. The standard map and the Anderson map are treated and compared. As the basis of analysis, we apply the self-consistent theory (SCT) of the localization for our systems, taking a plausible hypothesis on the mean-free-path parameter which worked successfully in the analyses of the monochromatically perturbed QMs. We compare in detail the numerical results with the predictions of the SCT by largely increasing M. The numerically obtained index of critical subdiffusion t^{α} (t:time) agrees well with the prediction of one-parameter scaling theory α=2/(M+1), but the numerically obtained critical exponent of localization length significantly deviates from the SCT prediction. Deviation from the SCT prediction is drastic for the critical perturbation strength of the transition: If M is fixed, then the SCT presents plausible prediction for the parameter dependence of the critical value, but its value is 1/(M-1) times smaller than the SCT prediction, which implies existence of a strong cooperativity of the harmonic perturbations with the main mode.
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Affiliation(s)
- Hiroaki S Yamada
- Yamada Physics Research Laboratory, Aoyama 5-7-14-205, Niigata 950-2002, Japan
| | - Kensuke S Ikeda
- College of Science and Engineering, Ritsumeikan University Noji-higashi 1-1-1, Kusatsu 525-8577, Japan
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12
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Paul S, Sarkar S, Vishwakarma C, Mangaonkar J, Santhanam MS, Rapol U. Nonmonotonic diffusion rates in an atom-optics Lévy kicked rotor. Phys Rev E 2020; 100:060201. [PMID: 31962514 DOI: 10.1103/physreve.100.060201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2019] [Indexed: 11/07/2022]
Abstract
The dynamics of chaotic Hamiltonian systems such as the kicked rotor continues to guide our understanding of transport and localization processes. The localized states of the quantum kicked rotor decay due to decoherence effects if subjected to noise. The associated quantum diffusion increases monotonically as a function of a parameter characterizing the noise distribution. In this Rapid Communication, for the atom-optics Lévy kicked rotor, the quantum diffusion displays nonmonotonic behavior as a function of a parameter characterizing the Lévy distribution. The optimal diffusion rates are experimentally obtained using an ultracold cloud of rubidium atoms in a pulsed optical lattice. The parameters for optimal diffusion rates are obtained analytically and show a good agreement with our experimental and numerical results. The nonmonotonicity is shown to be a quantum effect that vanishes in the classical limit.
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Affiliation(s)
- Sanku Paul
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Straße 38, 01187-Dresden, Germany
| | - Sumit Sarkar
- Indian Institute of Science Education and Research, Homi Bhabha Road, Pune 411 008, India
| | - Chetan Vishwakarma
- Indian Institute of Science Education and Research, Homi Bhabha Road, Pune 411 008, India
| | - Jay Mangaonkar
- Indian Institute of Science Education and Research, Homi Bhabha Road, Pune 411 008, India
| | - M S Santhanam
- Indian Institute of Science Education and Research, Homi Bhabha Road, Pune 411 008, India
| | - Umakant Rapol
- Indian Institute of Science Education and Research, Homi Bhabha Road, Pune 411 008, India
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13
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Torres-Herrera EJ, Méndez-Bermúdez JA, Santos LF. Level repulsion and dynamics in the finite one-dimensional Anderson model. Phys Rev E 2019; 100:022142. [PMID: 31574697 DOI: 10.1103/physreve.100.022142] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Indexed: 06/10/2023]
Abstract
This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest-neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal on-site disorder strength W. But this is not the case when the model is finite and the localization length is larger than the system size L, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter ξ∝(W^{2}L)^{-1}. As ξ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster than when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for W=0, when it is in fact deeper.
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Affiliation(s)
- E Jonathan Torres-Herrera
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla, 72570, Mexico
| | - J A Méndez-Bermúdez
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla, 72570, Mexico
| | - Lea F Santos
- Department of Physics, Yeshiva University, New York City, New York 10016, USA
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14
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Ermann L, Shepelyansky DL. Incommensurate standard map. Phys Rev E 2019; 99:012215. [PMID: 30780265 DOI: 10.1103/physreve.99.012215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2018] [Indexed: 11/07/2022]
Abstract
We introduce and study the extension of the Chirikov standard map when the kick potential has two and three incommensurate spatial harmonics. This system is called the incommensurate standard map. At small kick amplitudes, the dynamics is bounded by the isolating Kolmogorov-Arnold-Moser surfaces, whereas above a certain kick strength, it becomes unbounded and diffusive. The quantum evolution at small quantum kick amplitudes is somewhat similar to the case of the Aubru-André model studied in mathematics and experiments with cold atoms in a static incommensurate potential. We show that for the quantum map there is also a metal-insulator transition in space whereas in momentum we have localization similar to the case of two-dimensional Anderson localization. In the case of three incommensurate frequencies of the space potential, the quantum evolution is characterized by the Anderson transition similar to the three-dimensional case of the disordered potential. We discuss possible physical systems with such a map description including dynamics of comets and dark matter in planetary systems.
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Affiliation(s)
- Leonardo Ermann
- Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina.,Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Godoy Cruz 2290, C1425FQB, CABA, Argentina
| | - Dima L Shepelyansky
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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15
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Lemarié G. Glassy Properties of Anderson Localization: Pinning, Avalanches, and Chaos. PHYSICAL REVIEW LETTERS 2019; 122:030401. [PMID: 30735426 DOI: 10.1103/physrevlett.122.030401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Indexed: 06/09/2023]
Abstract
I present the results of extensive numerical simulations, which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches, and chaos. I first show that strong localization confines quantum transport along paths that are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent ζ characterizing the transverse fluctuations of these paths and find that its value ζ=2/3 is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely, the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder and more spin-glass-like behavior at strong disorder.
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Affiliation(s)
- G Lemarié
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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16
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Hainaut C, Fang P, Rançon A, Clément JF, Szriftgiser P, Garreau JC, Tian C, Chicireanu R. Experimental Observation of a Time-Driven Phase Transition in Quantum Chaos. PHYSICAL REVIEW LETTERS 2018; 121:134101. [PMID: 30312061 DOI: 10.1103/physrevlett.121.134101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2018] [Indexed: 06/08/2023]
Abstract
We report the first experimental observation of the time-driven phase transition in a canonical quantum chaotic system, the quantum kicked rotor. The transition bears a firm analogy to a thermodynamic phase transition, with the time mimicking the temperature and the quantum expectation of the rotor's kinetic energy mimicking the free energy. The transition signals a sudden change in the system's memory behavior: before the critical time, the system undergoes chaotic motion in phase space and its memory of initial states is erased in the course of time; after the critical time, quantum interference enhances the probability for a chaotic trajectory to return to the initial state, and thus the system's memory is recovered.
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Affiliation(s)
- Clément Hainaut
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France‡
| | - Ping Fang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- CAS Key Laboratory of Frontiers in Theoretical Physics and Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Adam Rançon
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France‡
| | - Jean-François Clément
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France‡
| | - Pascal Szriftgiser
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France‡
| | - Jean-Claude Garreau
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France‡
| | - Chushun Tian
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France‡
- CAS Key Laboratory of Frontiers in Theoretical Physics and Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Radu Chicireanu
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France‡
- CAS Key Laboratory of Frontiers in Theoretical Physics and Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
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17
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Ji K, Fine BV. Suppression of Heating in Quantum Spin Clusters under Periodic Driving as a Dynamic Localization Effect. PHYSICAL REVIEW LETTERS 2018; 121:050602. [PMID: 30118253 DOI: 10.1103/physrevlett.121.050602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2017] [Revised: 05/25/2018] [Indexed: 06/08/2023]
Abstract
We investigate numerically and analytically the heating process in ergodic clusters of interacting spins 1/2 subjected to periodic pulses of an external magnetic field. Our findings indicate that there is a threshold for the pulse strength below which the heating is suppressed. This threshold decreases with the increase of the cluster size, approaching zero in the thermodynamic limit, yet it should be observable in clusters with fairly large Hilbert spaces. We obtain the above threshold quantitatively as a condition for the breakdown of the golden rule in the second-order perturbation theory. It is caused by the phenomenon of dynamic localization.
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Affiliation(s)
- Kai Ji
- Skolkovo Institute of Science and Technology, Nobel Street 3, 143026 Moscow Region, Russia
- Department of Physics, Shanghai Normal University, No. 100 Guilin Road, 200234 Shanghai, China
| | - Boris V Fine
- Skolkovo Institute of Science and Technology, Nobel Street 3, 143026 Moscow Region, Russia
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg, Germany
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18
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Bertoli G, Michal VP, Altshuler BL, Shlyapnikov GV. Finite-Temperature Disordered Bosons in Two Dimensions. PHYSICAL REVIEW LETTERS 2018; 121:030403. [PMID: 30085818 DOI: 10.1103/physrevlett.121.030403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2017] [Indexed: 06/08/2023]
Abstract
We study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At T=0 one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.
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Affiliation(s)
- G Bertoli
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay 91405, France
| | - V P Michal
- QuTech and Kavli Institute of Nanoscience, TU Delft, 2600 GA Delft, Netherlands
| | - B L Altshuler
- Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA
| | - G V Shlyapnikov
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay 91405, France
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Gif sur Yvette 91191, France
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
- 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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19
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Notarnicola S, Iemini F, Rossini D, Fazio R, Silva A, Russomanno A. From localization to anomalous diffusion in the dynamics of coupled kicked rotors. Phys Rev E 2018; 97:022202. [PMID: 29548167 DOI: 10.1103/physreve.97.022202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Indexed: 06/08/2023]
Abstract
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N-coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N-dimensional Anderson model. The thermodynamic limit N→∞, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.
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Affiliation(s)
| | - Fernando Iemini
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
| | - Davide Rossini
- Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Rosario Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | | | - Angelo Russomanno
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
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20
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Yamada HS, Matsui F, Ikeda KS. Scaling properties of dynamical localization in monochromatically perturbed quantum maps: Standard map and Anderson map. Phys Rev E 2018; 97:012210. [PMID: 29448324 DOI: 10.1103/physreve.97.012210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Indexed: 06/08/2023]
Abstract
Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical wave-packet propagation. Some phenomenological formula of the dynamical localization length valid for wide range of control parameters are proposed for both SM and AM. For SM the formula completely agree with the experimental formula, and for AM the presence of a new regime of localization is confirmed. These formula can be derived by the self-consistent mean-field theory of Anderson localization on the basis of a new hypothesis for the cut-off length. Transient diffusion in the large limit of the localization length is also discussed.
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Affiliation(s)
- Hiroaki S Yamada
- Yamada Physics Research Laboratory, Aoyama 5-7-14-205, Niigata 950-2002, Japan
| | - Fumihiro Matsui
- Department of Physics, College of Science and Engineering, Ritsumeikan University Noji-higashi 1-1-1, Kusatsu 525-8577, Japan
| | - Kensuke S Ikeda
- College of Science and Engineering, Ritsumeikan University Noji-higashi 1-1-1, Kusatsu 525-8577, Japan
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21
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Delande D, Morales-Molina L, Sacha K. Three-Dimensional Localized-Delocalized Anderson Transition in the Time Domain. PHYSICAL REVIEW LETTERS 2017; 119:230404. [PMID: 29286692 DOI: 10.1103/physrevlett.119.230404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2017] [Indexed: 06/07/2023]
Abstract
Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modeled with the help of space periodic potentials, crystalline phenomena in time can be modeled by periodically driven systems. Disorder in the periodic driving can lead to Anderson localization in time: the probability for detecting a system at a fixed point of configuration space becomes exponentially localized around a certain moment in time. We here show that a three-dimensional system exposed to a properly disordered pseudoperiodic driving may display a localized-delocalized Anderson transition in the time domain, in strong analogy with the usual three-dimensional Anderson transition in disordered systems. Such a transition could be experimentally observed with ultracold atomic gases.
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Affiliation(s)
- Dominique Delande
- Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - Luis Morales-Molina
- Instituto de Física, Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
| | - Krzysztof Sacha
- Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Profesora Stanisława Łojasiewicza 11, 30-348 Kraków, Poland
- Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński, ulica Profesora Stanisława Łojasiewicza 11, 30-348 Kraków, Poland
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22
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Hainaut C, Manai I, Chicireanu R, Clément JF, Zemmouri S, Garreau JC, Szriftgiser P, Lemarié G, Cherroret N, Delande D. Return to the Origin as a Probe of Atomic Phase Coherence. PHYSICAL REVIEW LETTERS 2017; 118:184101. [PMID: 28524683 DOI: 10.1103/physrevlett.118.184101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2016] [Indexed: 06/07/2023]
Abstract
We report on the observation of the coherent enhancement of the return probability ["enhanced return to the origin" (ERO)] in a periodically kicked cold-atom gas. By submitting an atomic wave packet to a pulsed, periodically shifted, laser standing wave, we induce an oscillation of ERO in time that is explained in terms of a periodic, reversible dephasing in the weak-localization interference sequences responsible for ERO. Monitoring the temporal decay of ERO, we exploit its quantum-coherent nature to quantify the decoherence rate of the atomic system.
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Affiliation(s)
- Clément Hainaut
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Isam Manai
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Radu Chicireanu
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Jean-François Clément
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Samir Zemmouri
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Jean Claude Garreau
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Pascal Szriftgiser
- Université de Lille, CNRS, UMR 8523-PhLAM-Laboratoire de Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Gabriel Lemarié
- Laboratoire de Physique Théorique, UMR 5152, CNRS and Université de Toulouse, F-31062 Toulouse, France
| | - Nicolas Cherroret
- Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - Dominique Delande
- Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
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23
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Sarkar S, Paul S, Vishwakarma C, Kumar S, Verma G, Sainath M, Rapol UD, Santhanam MS. Nonexponential Decoherence and Subdiffusion in Atom-Optics Kicked Rotor. PHYSICAL REVIEW LETTERS 2017; 118:174101. [PMID: 28498690 DOI: 10.1103/physrevlett.118.174101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2016] [Indexed: 06/07/2023]
Abstract
Quantum systems lose coherence upon interaction with the environment and tend towards classical states. Quantum coherence is known to exponentially decay in time so that macroscopic quantum superpositions are generally unsustainable. In this work, slower than exponential decay of coherences is experimentally realized in an atom-optics kicked rotor system subjected to nonstationary Lévy noise in the applied kick sequence. The slower coherence decay manifests in the form of quantum subdiffusion that can be controlled through the Lévy exponent. The experimental results are in good agreement with the analytical estimates and numerical simulations for the mean energy growth and momentum profiles of an atom-optics kicked rotor.
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Affiliation(s)
- Sumit Sarkar
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - Sanku Paul
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - Chetan Vishwakarma
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - Sunil Kumar
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - Gunjan Verma
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - M Sainath
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - Umakant D Rapol
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
- Center for Energy Sciences, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - M S Santhanam
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
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24
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Orso G. Anderson Transition of Cold Atoms with Synthetic Spin-Orbit Coupling in Two-Dimensional Speckle Potentials. PHYSICAL REVIEW LETTERS 2017; 118:105301. [PMID: 28339248 DOI: 10.1103/physrevlett.118.105301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Indexed: 06/06/2023]
Abstract
We investigate the metal-insulator transition occurring in two-dimensional (2D) systems of noninteracting atoms in the presence of artificial spin-orbit interactions and a spatially correlated disorder generated by laser speckles. Based on a high order discretization scheme, we calculate the precise position of the mobility edge and verify that the transition belongs to the symplectic universality class. We show that the mobility edge depends strongly on the mixing angle between Rashba and Dresselhaus spin-orbit couplings. For equal couplings a non-power-law divergence is found, signaling the crossing to the orthogonal class, where such a 2D transition is forbidden.
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Affiliation(s)
- Giuliano Orso
- Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matériaux et Phénomènes Quantiques, UMR 7162, 75013 Paris, France
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25
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Ray S, Ghosh A, Sinha S. Quantum signature of chaos and thermalization in the kicked Dicke model. Phys Rev E 2016; 94:032103. [PMID: 27739832 DOI: 10.1103/physreve.94.032103] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2016] [Indexed: 06/06/2023]
Abstract
We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.
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Affiliation(s)
- S Ray
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia-741246, India
| | - A Ghosh
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia-741246, India
| | - S Sinha
- Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia-741246, India
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26
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Paul S, Pal H, Santhanam MS. Barrier-induced chaos in a kicked rotor: Classical subdiffusion and quantum localization. Phys Rev E 2016; 93:060203. [PMID: 27415192 DOI: 10.1103/physreve.93.060203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Indexed: 06/06/2023]
Abstract
The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of the Kolmogorov-Arnold-Moser (KAM) theorem, namely, the kicked rotor in a discontinuous potential barrier. We show that the discontinuous barrier induces chaos and more than two distinct subdiffusive energy growth regimes, the latter being an unusual feature for Hamiltonian chaos. We show that the dynamical localization in the quantized version of this system carries the imprint of non-KAM classical dynamics through the dependence of quantum break time on subdiffusion exponents. We briefly comment on the experimental feasibility of this system.
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Affiliation(s)
- Sanku Paul
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - Harinder Pal
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Codigo Postal 62210, Cuernavaca, Mexico
| | - M S Santhanam
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
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