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Gershenzon I, Lacroix-A-Chez-Toine B, Raz O, Subag E, Zeitouni O. On-Site Potential Creates Complexity in Systems with Disordered Coupling. PHYSICAL REVIEW LETTERS 2023; 130:237103. [PMID: 37354403 DOI: 10.1103/physrevlett.130.237103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Accepted: 04/04/2023] [Indexed: 06/26/2023]
Abstract
We calculate the average number of critical points N[over ¯] of the energy landscape of a many-body system with disordered two-body interactions and a weak on-site potential. We find that introducing a weak nonlinear on-site potential dramatically increases N[over ¯] to exponential in system size and give a complete picture of the organization of critical points. Our results extend solvable spin-glass models to physically more realistic models and are of relevance to glassy systems, nonlinear oscillator networks, and many-body interacting systems.
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Affiliation(s)
- I Gershenzon
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - B Lacroix-A-Chez-Toine
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
- Department of Mathematics, Kings College London, London WC2R 2LS, United Kingdom
| | - O Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - E Subag
- Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - O Zeitouni
- Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
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2
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One-Dimensional Disordered Bosonic Systems. ATOMS 2021. [DOI: 10.3390/atoms9040112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.
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3
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Hsueh YW, Hsueh CH, Wu WC. Thermalization in a Quantum Harmonic Oscillator with Random Disorder. ENTROPY 2020; 22:e22080855. [PMID: 33286626 PMCID: PMC7517456 DOI: 10.3390/e22080855] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Revised: 07/14/2020] [Accepted: 07/30/2020] [Indexed: 12/02/2022]
Abstract
We propose a possible scheme to study the thermalization in a quantum harmonic oscillator with random disorder. Our numerical simulation shows that through the effect of random disorder, the system can undergo a transition from an initial nonequilibrium state to a equilibrium state. Unlike the classical damped harmonic oscillator where total energy is dissipated, total energy of the disordered quantum harmonic oscillator is conserved. In particular, at equilibrium the initial mechanical energy is transformed to the thermodynamic energy in which kinetic and potential energies are evenly distributed. Shannon entropy in different bases are shown to yield consistent results during the thermalization.
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Affiliation(s)
- Ya-Wei Hsueh
- Department of Physics, National Central University, Jhong-li 32001, Taiwan;
| | - Che-Hsiu Hsueh
- Department of Physics, National Taiwan Normal University, Taipei 11677, Taiwan
- Correspondence: (C.-H.H.); (W.-C.W.)
| | - Wen-Chin Wu
- Department of Physics, National Taiwan Normal University, Taipei 11677, Taiwan
- Correspondence: (C.-H.H.); (W.-C.W.)
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4
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Sakhel RR, Sakhel AR. Effect of trapping geometry on the parametric resonances in a disordered Bose-Einstein condensate driven by an oscillating potential. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:315401. [PMID: 32160602 DOI: 10.1088/1361-648x/ab7f06] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 03/11/2020] [Indexed: 06/10/2023]
Abstract
We report parametric resonances (PRs) in a numerical investigation of a driven one-dimensional, interacting, and disordered Bose-Einstein condensate (BEC) confined in different traps. The BEC is excited by an oscillating Gaussian obstacle along a broad range of driving frequencies Ω. The PRs are detected via a quantity that is closely related to the time-average of the kinetic energy. The significant result of this work is that the trapping geometry plays a major role in defining the values of Ω at which PRs arise and controls their response to disorder. As such, it reveals the interplay of trapping geometry and disorder in these resonances. The dynamics of the modal coefficientC0(t) as well as that of the phase-mismatchδ(t) between theC0(t) andC1(t) are examined at and away from PR. At PR, |C0(t)| is generally found to be lower in magnitude than away from it, demonstrating that the atoms leave then= 0 ground state towards higher states. In the harmonic oscillator trap, the dynamic pattern ofδ(t) is found to be quite robust against changes in the disorder strength contrary to the box potential. This is because in the box the ratio of the random-potential and kinetic energies is higher than in the harmonic trap signaling that the influence of disorder is weaker in the latter.
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Affiliation(s)
- Roger R Sakhel
- Department of Physics, Faculty of Science, Isra University, Amman 11622, Jordan
| | - Asaad R Sakhel
- Department of Physics, Faculty of Science, Balqa Applied University, Salt 19117, Jordan
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5
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Sun ZY, Yu X. Transient diffusion and two-regime localization of discrete breatherlike excitations in nonlinear Schrödinger lattice with disorder. Phys Rev E 2019; 100:022202. [PMID: 31574744 DOI: 10.1103/physreve.100.022202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2019] [Indexed: 11/07/2022]
Abstract
We systematically simulate and analyze the motion of discrete breatherlike excitations (DBEs) in the nonlinear Schrödinger lattice with random potentials. A universal transient diffusion of the DBEs is observed for short timescales (t≲10^{3}). For longer timescales (t up to 10^{5}), the DBEs become localized. Such localization, depending on the DBE powers, has two different regimes: Regime I is the Anderson-like localization induced by the disorder, while Regime II is an enhanced localization attributed to both the disorder and discreteness. Our study is expected to shed light on understanding the interplay between disorder and strong nonlinearity, from the diffusive transport and localization properties of nonlinear localized excitations in random media.
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Affiliation(s)
- Zhi-Yuan Sun
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.,International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
| | - Xin Yu
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
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6
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Moores BA, Sletten LR, Viennot JJ, Lehnert KW. Cavity Quantum Acoustic Device in the Multimode Strong Coupling Regime. PHYSICAL REVIEW LETTERS 2018; 120:227701. [PMID: 29906138 DOI: 10.1103/physrevlett.120.227701] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2017] [Indexed: 06/08/2023]
Abstract
We demonstrate an acoustical analog of a circuit quantum electrodynamics system that leverages acoustic properties to enable strong multimode coupling in the dispersive regime while suppressing spontaneous emission to unconfined modes. Specifically, we fabricate and characterize a device that comprises a flux tunable transmon coupled to a 300 μm long surface acoustic wave resonator. For some modes, the qubit-cavity coupling reaches 6.5 MHz, exceeding the cavity loss rate (200 kHz), qubit linewidth (1.1 MHz), and the cavity free spectral range (4.8 MHz), placing the device in both the strong coupling and strong multimode regimes. With the qubit detuned from the confined modes of the cavity, we observe that the qubit linewidth strongly depends on its frequency, as expected for spontaneous emission of phonons, and we identify operating frequencies where this emission rate is suppressed.
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Affiliation(s)
- Bradley A Moores
- JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Lucas R Sletten
- JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Jeremie J Viennot
- JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - K W Lehnert
- JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
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7
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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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8
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Bai XD, Malomed BA, Deng FG. Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects. Phys Rev E 2016; 94:032216. [PMID: 27739723 DOI: 10.1103/physreve.94.032216] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2016] [Indexed: 11/07/2022]
Abstract
We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.
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Affiliation(s)
- Xiao-Dong Bai
- Department of Physics and Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.,Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg 197101, Russia
| | - Fu-Guo Deng
- Department of Physics and Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
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9
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Deng S, Shi ZY, Diao P, Yu Q, Zhai H, Qi R, Wu H. Observation of the Efimovian expansion in scale-invariant Fermi gases. Science 2016; 353:371-4. [DOI: 10.1126/science.aaf0666] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2015] [Accepted: 06/21/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Shujin Deng
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
| | - Zhe-Yu Shi
- Institute for Advanced Study, Tsinghua University, Beijing 100084, P. R. China
| | - Pengpeng Diao
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
| | - Qianli Yu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, P. R. China
| | - Ran Qi
- Department of Physics, Renmin University of China, Beijing 100872, P. R. China
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
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10
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Sadhukhan D, Prabhu R, Sen De A, Sen U. Quantum correlations in quenched disordered spin models: Enhanced order from disorder by thermal fluctuations. Phys Rev E 2016; 93:032115. [PMID: 27078300 DOI: 10.1103/physreve.93.032115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2015] [Indexed: 06/05/2023]
Abstract
We investigate the behavior of quantum correlations of paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models. We show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can become more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins--for classical and quantum correlations--is related to the quantum critical point in the corresponding ordered system.
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Affiliation(s)
- Debasis Sadhukhan
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - R Prabhu
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Aditi Sen De
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Ujjwal Sen
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
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11
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Sun ZY, Fishman S, Soffer A. Soliton mobility in disordered lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:040903. [PMID: 26565156 DOI: 10.1103/physreve.92.040903] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Indexed: 06/05/2023]
Abstract
We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schrödinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results from a deviation from integrability, which is due to randomness for the AL model, and both randomness and lattice discreteness for the NLS lattice. The statistical properties of such a potential are analyzed, and it is shown how the soliton mobility is affected by its size. The usefulness of this effective potential in studying soliton dynamics is demonstrated numerically. Furthermore, we propose two ways to enhance soliton transport in the presence of disorder: one is to use specific realizations of randomness, and the other is to consider a specific soliton pair.
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Affiliation(s)
- Zhi-Yuan Sun
- Department of Physics, Technion-Israel Institute of Technology, Haifa 320000, Israel
| | - Shmuel Fishman
- Department of Physics, Technion-Israel Institute of Technology, Haifa 320000, Israel
| | - Avy Soffer
- Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854, USA
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12
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Ettoumi W, Kasparian J, Wolf JP. Spin-Glass Model Governs Laser Multiple Filamentation. PHYSICAL REVIEW LETTERS 2015; 115:033902. [PMID: 26230795 DOI: 10.1103/physrevlett.115.033902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Indexed: 06/04/2023]
Abstract
We show that multiple filamentation patterns in high-power laser beams can be described by means of two statistical physics concepts, namely, self-similarity of the patterns over two nested scales and nearest-neighbor interactions of classical rotators. The resulting lattice spin model perfectly reproduces the evolution of intense laser pulses as simulated by the nonlinear Schrödinger equation, shedding new light on multiple filamentation. As a side benefit, this approach drastically reduces the computing time by 2 orders of magnitude as compared to the standard simulation methods of laser filamentation.
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Affiliation(s)
- W Ettoumi
- Université de Genève, GAP-Biophotonics, Chemin de Pinchat 22, CH-1211 Geneva 4, Switzerland
| | - J Kasparian
- Université de Genève, GAP-Non-linear, Chemin de Pinchat 22, CH-1211 Geneva 4, Switzerland
| | - J-P Wolf
- Université de Genève, GAP-Biophotonics, Chemin de Pinchat 22, CH-1211 Geneva 4, Switzerland
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13
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Tsao CW, Cheng YH, Hsueh WJ. Localized modes in one-dimensional symmetric Thue-Morse quasicrystals. OPTICS EXPRESS 2014; 22:24378-24383. [PMID: 25322013 DOI: 10.1364/oe.22.024378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present occurrence of the strongly localized modes with high transmission in one dimensional symmetric Thue-Morse quasicrystals. This quasicrystal has some interesting properties, including (i) there are strongly localized modes in separated regions which are around odd semi-quarter-wave thickness of the system, (ii) both the frequency of localized mode and the thicknesses of the space layer to appear localized modes are variant for different generation orders of the system, and (iii) the sharpness of the resonant peaks in the transmission spectra increases as the generation order of the system increases.
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14
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Wang CH, Hong TM, Lee RK, Wang DW. Particle-wave duality in quantum tunneling of a bright soliton. OPTICS EXPRESS 2012; 20:22675-22682. [PMID: 23037417 DOI: 10.1364/oe.20.022675] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
One of the most fundamental difference between classical and quantum mechanics is observed in the particle tunneling through a localized potential: the former predicts a discontinuous transmission coefficient (T) as a function in incident velocity between one (complete penetration) and zero (complete reflection); while in the latter T always changes smoothly with a wave nature. Here we report a systematic study of the quantum tunneling property for a bright soliton, which behaves as a classical particle (wave) in the limit of small (large) incident velocity. In the intermediate regime, the classical and quantum properties are combined via a finite (but not full) discontinuity in the tunneling transmission coefficient. We demonstrate that the formation of a localized bound state is essential to describe such inelastic collisions, showing a nontrivial nonlinear effect on the quantum transportation of a bright soliton.
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Affiliation(s)
- Ching-Hao Wang
- Department of Physics, National Tsing-Hua University, Hsinchu 30013, Taiwan
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15
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Michaely E, Fishman S. Effective noise theory for the nonlinear Schrödinger equation with disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:046218. [PMID: 22680567 DOI: 10.1103/physreve.85.046218] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2011] [Revised: 01/02/2012] [Indexed: 06/01/2023]
Abstract
For the nonlinear Shrödinger equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear term acts as random noise. In the present work, the properties of this effective noise are studied numerically. Some assumptions made in earlier work were verified, and fine details were obtained. The dependence of various quantities on the localization length of the linear problem were computed. A scenario for the possible breakdown of the theory for a very long time is outlined.
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Affiliation(s)
- Erez Michaely
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
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16
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Prilepsky JE, Derevyanko SA, Gredeskul SA. Controlling soliton refraction in optical lattices. PHYSICAL REVIEW LETTERS 2011; 107:083901. [PMID: 21929169 DOI: 10.1103/physrevlett.107.083901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2011] [Indexed: 05/31/2023]
Abstract
We show in the framework of the 1D nonlinear Schrödinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.
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Affiliation(s)
- Jaroslaw E Prilepsky
- Nonlinearity and Complexity Research Group, Aston University, B4 7ET Birmingham, United Kingdom.
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17
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Terao T. Localization-delocalization transition and subdiffusion of discrete nonlinear Schrödinger equation in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056611. [PMID: 21728686 DOI: 10.1103/physreve.83.056611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2010] [Revised: 03/11/2011] [Indexed: 05/31/2023]
Abstract
Localization-delocalization transition in a three-dimensional discrete nonlinear Schrödinger equation (DNLSE) with random potential is investigated, and the effect of nonlinearity is clarified numerically. By Thouless-number analysis, it is shown that the nonlinearity tends to delocalize the stationary states in a three-dimensional DNLSE. The spreading of a wave packet in a localized regime is also clarified for this system, and the subdiffusive behavior is observed in the three-dimensional system when the nonlinearity of the system is sufficiently strong. In addition, a one-dimensional DNLSE with random potential having a finite correlation length is studied, and it is suggested that the power-law exponent of the subdiffusion in DNLSE is not a universal quantity.
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Affiliation(s)
- Takamichi Terao
- Department of Mathematical and Design Engineering, Gifu University, Gifu 501-1193, Japan
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18
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Zhang Z, Tong P, Gong J, Li B. Wave packet dynamics in one-dimensional linear and nonlinear generalized Fibonacci lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056205. [PMID: 21728628 DOI: 10.1103/physreve.83.056205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2010] [Revised: 02/21/2011] [Indexed: 05/31/2023]
Abstract
The spreading of an initially localized wave packet in one-dimensional linear and nonlinear generalized Fibonacci (GF) lattices is studied numerically. The GF lattices can be classified into two classes depending on whether or not the lattice possesses the Pisot-Vijayaraghavan property. For linear GF lattices of the first class, both the second moment and the participation number grow with time. For linear GF lattices of the second class, in the regime of a weak on-site potential, wave packet spreading is close to ballistic diffusion, whereas in the regime of a strong on-site potential, it displays stairlike growth in both the second moment and the participation number. Nonlinear GF lattices are then investigated in parallel. For the first class of nonlinear GF lattices, the second moment of the wave packet still grows with time, but the corresponding participation number does not grow simultaneously. For the second class of nonlinear GF lattices, an analogous phenomenon is observed for the weak on-site potential only. For a strong on-site potential that leads to an enhanced nonlinear self-trapping effect, neither the second moment nor the participation number grows with time. The results can be useful in guiding experiments on the expansion of noninteracting or interacting cold atoms in quasiperiodic optical lattices.
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Affiliation(s)
- Zhenjun Zhang
- Department of Physics, Nanjing Normal University, Nanjing, Jiangsu 210046, People's Republic of China
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19
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Pikovsky A, Fishman S. Scaling properties of weak chaos in nonlinear disordered lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:025201. [PMID: 21405880 DOI: 10.1103/physreve.83.025201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2010] [Indexed: 05/30/2023]
Abstract
We study the discrete nonlinear Schrödinger equation with a random potential in one dimension. It is characterized by the length, the strength of the random potential, and the field density that determines the effect of nonlinearity. Following the time evolution of the field and calculating the largest Lyapunov exponent, the probability of the system to be regular is established numerically and found to be a scaling function of the parameters. This property is used to calculate the asymptotic properties of the system in regimes beyond our computational power.
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Affiliation(s)
- Arkady Pikovsky
- Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Strasse 24, D-14476 Potsdam, Germany
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20
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Conti C, D'Asaro E, Stivala S, Busacca A, Assanto G. Parametric self-trapping in the presence of randomized quasi phase matching. OPTICS LETTERS 2010; 35:3760-3762. [PMID: 21081988 DOI: 10.1364/ol.35.003760] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We report on experimental evidence of parametric spatial solitons in a quadratic crystal with randomized periodic ferroelectric poling. Two-color self-focusing via quadratic cascading overcomes the diffractive nature of both fundamental and frequency-doubled beams.
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Affiliation(s)
- Claudio Conti
- CNR-ISC-Institute of Complex Systems, Department of Physics, University Sapienza, 00185 Rome, Italy
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21
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Pal H, Santhanam MS. Dynamics of kicked particles in a double-barrier structure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056212. [PMID: 21230568 DOI: 10.1103/physreve.82.056212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2010] [Indexed: 05/30/2023]
Abstract
We study the classical and quantum dynamics of periodically kicked particles placed initially within an open double-barrier structure. This system does not obey the Kolmogorov-Arnold-Moser (KAM) theorem and displays chaotic dynamics. The phase-space features induced by non-KAM nature of the system lead to dynamical features such as the nonequilibrium steady state, classically induced saturation of energy growth and momentum filtering. We also comment on the experimental feasibility of this system as well as its relevance in the context of current interest in classically induced localization and chaotic ratchets.
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Affiliation(s)
- Harinder Pal
- Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.
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22
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Leboeuf P, Moulieras S. Superfluid motion of light. PHYSICAL REVIEW LETTERS 2010; 105:163904. [PMID: 21230975 DOI: 10.1103/physrevlett.105.163904] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2010] [Indexed: 05/30/2023]
Abstract
Superfluidity, the ability of a fluid to move without dissipation, is one of the most spectacular manifestations of the quantum nature of matter. We explore here the possibility of superfluid motion of light. Controlling the speed of a light packet with respect to a defect, we demonstrate the presence of superfluidity and, above a critical velocity, its breakdown through the onset of a dissipative phase. We describe a possible experimental realization based on the transverse motion through an array of waveguides. These results open new perspectives in transport optimization.
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Affiliation(s)
- Patricio Leboeuf
- Laboratoire de Physique Théorique et Modèles Statistiques, CNRS, Université Paris Sud, UMR8626, 91405 Orsay Cedex, France
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23
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Folli V, Conti C. Frustrated brownian motion of nonlocal solitary waves. PHYSICAL REVIEW LETTERS 2010; 104:193901. [PMID: 20866964 DOI: 10.1103/physrevlett.104.193901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2009] [Indexed: 05/29/2023]
Abstract
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
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Affiliation(s)
- V Folli
- Department of Physics, University Sapienza, Piazzale Aldo Moro 2, 00185, Rome, Italy
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24
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Grémaud B, Wellens T. Speckle instability: coherent effects in nonlinear disordered media. PHYSICAL REVIEW LETTERS 2010; 104:133901. [PMID: 20481886 DOI: 10.1103/physrevlett.104.133901] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2008] [Revised: 09/22/2009] [Indexed: 05/29/2023]
Abstract
We numerically investigate the properties of speckle patterns formed by nonlinear point scatterers. We show that, in the weak localization regime, dynamical instability appears, eventually leading to chaotic behavior of the system. Analyzing the statistical properties of the instability thresholds for different values of the system size and disorder strength, a scaling law is emphasized. The later is found to also govern the smallest decay rate of the associated linear system, i.e., the "best" cavity realized by the scatterers, putting thus forward the crucial importance of interference effects. This is also underlined by the fact that coherent backscattering is still observed even in the chaotic regime.
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Affiliation(s)
- Benoît Grémaud
- Laboratoire Kastler Brossel, UPMC-Paris 6, ENS, CNRS; 4 Place Jussieu, F-75005 Paris, France
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25
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Schwiete G, Finkel'stein AM. Nonlinear wave-packet dynamics in a disordered medium. PHYSICAL REVIEW LETTERS 2010; 104:103904. [PMID: 20366428 DOI: 10.1103/physrevlett.104.103904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2009] [Revised: 09/21/2009] [Indexed: 05/29/2023]
Abstract
We develop an effective theory of pulse propagation in a nonlinear and disordered medium in two dimensions. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and diffusive collapse. The equation can be applied to such distinct physical systems as laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered environment.
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Affiliation(s)
- G Schwiete
- Department of Physics, Texas A&M University, College Station, Texas 77843-4242, USA.
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26
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Iomin A. Subdiffusion in the nonlinear Schrödinger equation with disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:017601. [PMID: 20365509 DOI: 10.1103/physreve.81.017601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2009] [Revised: 12/30/2009] [Indexed: 05/29/2023]
Abstract
The nonlinear Schrödinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive spreading of the wave packet is explained in the framework of a continuous time random walk. A probabilistic description of subdiffusion is suggested, and a transport exponent of subdiffusion is obtained to be 2/5.
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27
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Iomin A. Dynamics of wave packets for the nonlinear Schrödinger equation with a random potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:037601. [PMID: 19905253 DOI: 10.1103/physreve.80.037601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2009] [Indexed: 05/28/2023]
Abstract
The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schrödinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator. An analytical expression for a wave function of the initial time dynamics is found by a perturbation approach. As follows from a perturbative solution the initially localized wave function remains localized. At asymptotically large times the dynamics can be described qualitatively in the framework of a phenomenological probabilistic approach by means of a probability distribution function. It is shown that the probability distribution function may be governed by the fractional Fokker-Planck equation and corresponds to subdiffusion.
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28
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Delande D, Zakrzewski J. Compression as a tool to detect bose glass in a cold atomic gas. PHYSICAL REVIEW LETTERS 2009; 102:085301. [PMID: 19257748 DOI: 10.1103/physrevlett.102.085301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2008] [Indexed: 05/27/2023]
Abstract
We suggest that measuring the variation of the radius of an atomic cloud when the harmonic trap confinement is varied makes it possible to monitor the disappearance of the insulating Mott phase of an ultracold atomic gas trapped in a disordered optical lattice. This paves the way for an unambiguous identification of a Bose glass phase in the system.
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Affiliation(s)
- Dominique Delande
- Laboratoire Kastler-Brossel, Université Pierre et Marie Curie-Paris 6, ENS, CNRS; 4 Place Jussieu, F-75005 Paris, France
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29
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García-Mata I, Shepelyansky DL. Delocalization induced by nonlinearity in systems with disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:026205. [PMID: 19391818 DOI: 10.1103/physreve.79.026205] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2008] [Revised: 07/03/2008] [Indexed: 05/27/2023]
Abstract
We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity a spreading over the lattice in time takes place with an algebraic growth of number of populated sites Deltan proportional to tnu. This spreading continues up to a maximal dimensionless time scale t=10(9) reached in the numerical simulations. The numerical values of nu are found to be approximately 0.15-0.2 and 0.25 for the dimension d=1 and 2, respectively, being in a satisfactory agreement with the theoretical value d/(3d+2). During the computational times t<or=10(9) the localization is preserved below a certain critical value of nonlinearity. We also discuss the properties of the fidelity decay induced by a perturbation of nonlinear field.
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Affiliation(s)
- Ignacio García-Mata
- Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Toulouse III, 31062 Toulouse, France
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30
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Fishman S, Iomin A, Mallick K. Asymptotic localization of stationary states in the nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:066605. [PMID: 19256966 DOI: 10.1103/physreve.78.066605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2008] [Indexed: 05/27/2023]
Abstract
The mapping of the nonlinear Schrödinger equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schrödinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.
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31
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Cherroret N, Skipetrov SE. Long-range correlations of density in a Bose-Einstein condensate expanding in a random potential. PHYSICAL REVIEW LETTERS 2008; 101:190406. [PMID: 19113249 DOI: 10.1103/physrevlett.101.190406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2008] [Indexed: 05/27/2023]
Abstract
We study correlations of atomic density in a weakly interacting Bose-Einstein condensate, expanding diffusively in a random potential. We show that these correlations are long range and that they are strongly enhanced at long times. The density at distant points exhibits negative correlations.
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Affiliation(s)
- N Cherroret
- Laboratoire de Physique et Modélisation des Milieux Condensés, Université Joseph Fourier, CNRS, 25 rue des Martyrs, BP 166, 38042 Grenoble, France
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32
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Efremidis NK, Hizanidis K. Disordered lattice solitons. PHYSICAL REVIEW LETTERS 2008; 101:143903. [PMID: 18851530 DOI: 10.1103/physrevlett.101.143903] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2008] [Indexed: 05/26/2023]
Abstract
We study the properties of a nonlinear Schrödinger equation in the presence of a disordered potential modeling a waveguide array. We find that, for both signs of the nonlinearity, there is a large number of soliton families each one possessing different quantitative properties. However, all these families can be categorized to only a few classes with the same qualitative properties. Highly confined solitons exist in each waveguide of the lattice. In addition, solitons families originate from each Anderson mode. Resonant interactions between a soliton and an Anderson mode can take place, leading to broadening of the soliton profile.
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Affiliation(s)
- Nikolaos K Efremidis
- Department of Applied Mathematics, University of Crete, 71409 Heraklion, Crete, Greece
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33
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Hartung M, Wellens T, Müller CA, Richter K, Schlagheck P. Coherent backscattering of Bose-Einstein condensates in two-dimensional disorder potentials. PHYSICAL REVIEW LETTERS 2008; 101:020603. [PMID: 18764169 DOI: 10.1103/physrevlett.101.020603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2008] [Revised: 06/14/2008] [Indexed: 05/26/2023]
Abstract
We study quantum transport of an interacting Bose-Einstein condensate in a two-dimensional disorder potential. In the limit of a vanishing atom-atom interaction, a sharp cone in the angle-resolved density of the scattered matter wave is observed, arising from constructive interference between amplitudes propagating along reversed scattering paths. Weak interaction transforms this coherent backscattering peak into a pronounced dip, indicating destructive instead of constructive interference. We reproduce this result, obtained from the numerical integration of the Gross-Pitaevskii equation, by a diagrammatic theory of weak localization in the presence of nonlinearity.
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Affiliation(s)
- Michael Hartung
- Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
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34
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Albert M, Paul T, Pavloff N, Leboeuf P. Dipole oscillations of a Bose-Einstein condensate in the presence of defects and disorder. PHYSICAL REVIEW LETTERS 2008; 100:250405. [PMID: 18643643 DOI: 10.1103/physrevlett.100.250405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2008] [Indexed: 05/26/2023]
Abstract
We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.
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Affiliation(s)
- M Albert
- Laboratoire de Physique Théorique et Modèles Statistiques, CNRS, Université Paris Sud, UMR8626, 91405 Orsay Cedex, France
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35
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Roati G, D’Errico C, Fallani L, Fattori M, Fort C, Zaccanti M, Modugno G, Modugno M, Inguscio M. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 2008; 453:895-8. [DOI: 10.1038/nature07071] [Citation(s) in RCA: 1256] [Impact Index Per Article: 78.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2008] [Accepted: 05/06/2008] [Indexed: 11/09/2022]
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36
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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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37
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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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38
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Skipetrov SE, Minguzzi A, van Tiggelen BA, Shapiro B. Anderson localization of a Bose-Einstein condensate in a 3D random potential. PHYSICAL REVIEW LETTERS 2008; 100:165301. [PMID: 18518212 DOI: 10.1103/physrevlett.100.165301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2008] [Indexed: 05/26/2023]
Abstract
We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space.
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Affiliation(s)
- S E Skipetrov
- Université Joseph Fourier, Laboratoire de Physique et Modélisation des Mileux Condensés, CNRS, 25 Rue des Martyrs, BP 166, 38042 Grenoble, France
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39
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Pikovsky AS, Shepelyansky DL. Destruction of Anderson localization by a weak nonlinearity. PHYSICAL REVIEW LETTERS 2008; 100:094101. [PMID: 18352712 DOI: 10.1103/physrevlett.100.094101] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2007] [Indexed: 05/26/2023]
Abstract
We study numerically the spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schrödinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time proportional, variant t alpha, with the exponent alpha being in the range 0.3-0.4. For small nonlinearities the distribution remains localized in a way similar to the linear case.
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Affiliation(s)
- A S Pikovsky
- Department of Physics, University of Potsdam, Am Neuen Palais 10, D-14469, Potsdam, Germany
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40
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Kopidakis G, Komineas S, Flach S, Aubry S. Absence of wave packet diffusion in disordered nonlinear systems. PHYSICAL REVIEW LETTERS 2008; 100:084103. [PMID: 18352625 DOI: 10.1103/physrevlett.100.084103] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2007] [Indexed: 05/26/2023]
Abstract
We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schrödinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverges with time. We find that the participation number of a wave packet does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times we find a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wave packet, we rule out the possibility of slow energy diffusion. The dynamical state could approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long time limit.
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Affiliation(s)
- G Kopidakis
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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41
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Nattermann T, Pokrovsky VL. Bose-Einstein condensates in strongly disordered traps. PHYSICAL REVIEW LETTERS 2008; 100:060402. [PMID: 18352445 DOI: 10.1103/physrevlett.100.060402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2007] [Revised: 10/25/2007] [Indexed: 05/26/2023]
Abstract
A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semiquantitative analysis we find the size, shape, and excitation energy as a function of the disorder strength. For positive scattering length and sufficiently strong disorder the condensate decays into fragments each of the size of the Larkin length L. This state is stable over a large range of particle numbers. The frequency of the breathing mode scales as 1/L(2). For negative scattering length a condensate of size L may exist as a metastable state. These findings are generalized to anisotropic traps.
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Affiliation(s)
- T Nattermann
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany.
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42
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Manfredi G, Hervieux PA. Fidelity decay in trapped bose-einstein condensates. PHYSICAL REVIEW LETTERS 2008; 100:050405. [PMID: 18352349 DOI: 10.1103/physrevlett.100.050405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2007] [Indexed: 05/26/2023]
Abstract
The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.
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Affiliation(s)
- G Manfredi
- Institut de Physique et Chimie des Matériaux, CNRS and Université Louis Pasteur, BP 43, F-67034 Strasbourg, France.
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43
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Wellens T, Grémaud B. Nonlinear coherent transport of waves in disordered media. PHYSICAL REVIEW LETTERS 2008; 100:033902. [PMID: 18232981 DOI: 10.1103/physrevlett.100.033902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2007] [Revised: 10/10/2007] [Indexed: 05/25/2023]
Abstract
We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and we corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios such as scattering of light in a nonlinear Kerr medium or propagation of matter waves in disordered potentials.
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Affiliation(s)
- Thomas Wellens
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstrasse 7, Erlangen, Germany
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44
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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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45
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Orso G. BCS-BEC crossover in a random external potential. PHYSICAL REVIEW LETTERS 2007; 99:250402. [PMID: 18233500 DOI: 10.1103/physrevlett.99.250402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2007] [Revised: 10/24/2007] [Indexed: 05/25/2023]
Abstract
We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose-Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter 1/k{F}a, reaching their minimum value near unitarity. We find that, moving away from the weak-coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.
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Affiliation(s)
- G Orso
- Laboratoire Physique Théorique et Modèles Statistiques, Université Paris Sud, Bat. 100, 91405 Orsay Cedex, France
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46
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Lugan P, Clément D, Bouyer P, Aspect A, Sanchez-Palencia L. Anderson localization of Bogolyubov quasiparticles in interacting Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2007; 99:180402. [PMID: 17995384 DOI: 10.1103/physrevlett.99.180402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2007] [Indexed: 05/25/2023]
Abstract
We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with a healing [corrected] length xi) subjected to a random potential (with a finite correlation length sigma(R)). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k, and we study the localization maximum k(max). For 1D speckle potentials, we find that k(max) proportional variant 1/xi when xi>>sigma(R) while k(max) proportional variant 1/sigma(R) when xi<<sigma(R), and that the localization is strongest when xi approximately sigma(R). Numerical calculations support our analysis, and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in experiments with ultracold atoms.
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Affiliation(s)
- P Lugan
- Laboratoire Charles Fabry de l'Institut d'Optique, CNRS and Univ. Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau cedex, France
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47
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Iomin A, Fishman S. Localization length of stationary states in the nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:056607. [PMID: 18233782 DOI: 10.1103/physreve.76.056607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2007] [Indexed: 05/25/2023]
Abstract
For the nonlinear Schrödinger equation (NLSE), in the presence of disorder, exponentially localized stationary states are found. We demonstrate analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the "white noise" random potential, and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust.
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Ghulinyan M. Periodic oscillations in transmission decay of anderson localized one-dimensional dielectric systems. PHYSICAL REVIEW LETTERS 2007; 99:063905. [PMID: 17930826 DOI: 10.1103/physrevlett.99.063905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2007] [Indexed: 05/25/2023]
Abstract
It is well recognized that the transmittance of Anderson localized systems decays exponentially on average with sample size, showing large fluctuations brought up by extremely rare occurrences of necklaces of resonantly coupled states, possessing almost unity transmission. We show here that in a one-dimensional (1D) random photonic system with resonant layers these fluctuations appear to be very regular and have a period defined by the localization length xi of the system. We stress that necklace states are the origin of these well-defined oscillations. We predict that in such a random system efficient transmission channels form regularly each time the increasing sample length fits so-called optimal-order necklaces and demonstrate the phenomenon through numerical experiments. Our results provide new insight into the physics of Anderson localization in random systems with resonant units.
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Affiliation(s)
- Mher Ghulinyan
- Micro-Technology Laboratory, Fondazione Bruno Kessler - irst, via Sommarive 18, I-38050 Povo (Trento), Italy.
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Shapiro B. Expansion of a Bose-Einstein condensate in the presence of disorder. PHYSICAL REVIEW LETTERS 2007; 99:060602. [PMID: 17930810 DOI: 10.1103/physrevlett.99.060602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2007] [Indexed: 05/25/2023]
Abstract
Expansion of a Bose-Einstein condensate (BEC) is studied in the presence of a random potential. The expansion is controlled by a single parameter, (microtau(eff)/variant Planck's over 2pi), where micro is the chemical potential, prior to the release of the BEC from the trap, and tau(eff) is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location.
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Affiliation(s)
- Boris Shapiro
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Sengupta P, Haas S. Quantum glass phases in the disordered Bose-Hubbard model. PHYSICAL REVIEW LETTERS 2007; 99:050403. [PMID: 17930735 DOI: 10.1103/physrevlett.99.050403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2006] [Indexed: 05/25/2023]
Abstract
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.
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Affiliation(s)
- Pinaki Sengupta
- T-CNLS and NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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