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Bhat IA, Dey B. Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential. Phys Rev E 2024; 110:024208. [PMID: 39294963 DOI: 10.1103/physreve.110.024208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2024] [Accepted: 07/24/2024] [Indexed: 09/21/2024]
Abstract
In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.
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Gauthier G, Szigeti SS, Reeves MT, Baker M, Bell TA, Rubinsztein-Dunlop H, Davis MJ, Neely TW. Quantitative Acoustic Models for Superfluid Circuits. PHYSICAL REVIEW LETTERS 2019; 123:260402. [PMID: 31951434 DOI: 10.1103/physrevlett.123.260402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2019] [Indexed: 06/10/2023]
Abstract
We experimentally realize a highly tunable superfluid oscillator circuit in a quantum gas of ultracold atoms and develop and verify a simple lumped-element description of this circuit. At low oscillator currents, we demonstrate that the circuit is accurately described as a Helmholtz resonator, a fundamental element of acoustic circuits. At larger currents, the breakdown of the Helmholtz regime is heralded by a turbulent shedding of vortices and density waves. Although a simple phase-slip model offers qualitative insights into the circuit's resistive behavior, our results indicate deviations from the phase-slip model. A full understanding of the dissipation in superfluid circuits will thus require the development of empirical models of the turbulent dynamics in this system, as have been developed for classical acoustic systems.
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Affiliation(s)
- Guillaume Gauthier
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
| | - Stuart S Szigeti
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
- Department of Quantum Science, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Matthew T Reeves
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
| | - Mark Baker
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
| | - Thomas A Bell
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
| | - Halina Rubinsztein-Dunlop
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
| | - Matthew J Davis
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
| | - Tyler W Neely
- ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
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Masiello DJ, Reinhardt WP. Symmetry-Broken Many-Body Excited States of the Gaseous Atomic Double-Well Bose-Einstein Condensate. J Phys Chem A 2019; 123:1962-1967. [PMID: 30785746 DOI: 10.1021/acs.jpca.8b10583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Macroscopic, many-body self-trapped and quantum superposition states of the gaseous double-well Bose-Einstein condensate (BEC) are investigated within the context of a multiconfigurational bosonic self-consistent field theory based upon underlying spatially symmetry-broken one-body wave functions. To aid in the interpretation of our results, an approximate model is constructed in the extreme Fock state limit, in which self-trapped and superposition states emerge in the many-body spectrum, striking a delicate balance between the degree of symmetry breaking, the effects of the condensate's mean field, and that of atomic correlation. It is found, in both the model and full theory, that the superposition state lies energetically below its related self-trapped counterpart even when many configurations are involved. Noticeably different spatial density profiles are associated with each type of excited state, thus providing a rigorous justification for approximate descriptions of high-lying excited states of the BEC.
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Affiliation(s)
- David J Masiello
- Department of Chemistry , University of Washington , Seattle , Washington 98195 , United States
| | - William P Reinhardt
- Department of Chemistry , University of Washington , Seattle , Washington 98195 , United States
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Guo Q, Chen X, Wu B. Tunneling dynamics and band structures of three weakly coupled Bose-Einstein condensates. OPTICS EXPRESS 2014; 22:19219-19234. [PMID: 25321007 DOI: 10.1364/oe.22.019219] [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 study the tunneling dynamics and energy bands of three Bose-Einstein condensates which are coupled weakly with each other. The study is carried out with both the mean-filed model and the second-quantized model. The results from these two models are compared and found to agree with each other when the particle number is large. Without interaction, this system possesses a Dirac point in its energy band. This Dirac point is immediately destroyed and develops into a loop structure with arbitrary small interaction. This loop structure has a strong effect on the tunneling dynamics. We find that the tunneling dynamics in this system is very sensitive to the system parameter, e.g., the interaction strength. This sensitivity is found to be caused by the chaos in the mean-field model and the avoided energy crossings with tiny gaps in the second-quantized model. This result gives a certain indication on how the classical dynamics and quantum dynamics are connected in the semi-classical limit. Our mean-field results are also valid for three mutually coupled optical nonlinear waveguides.
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Zhuang Q, Wu B. Equilibration of quantum chaotic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062147. [PMID: 24483425 DOI: 10.1103/physreve.88.062147] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2013] [Indexed: 06/03/2023]
Abstract
The quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. 57, 30 (1929)] and again by Reimann [Phys. Rev. Lett. 101, 190403 (2008)] in a more practical and well-defined form. However, it is not clear whether the theorem applies to quantum chaotic systems. With a rigorous proof still elusive, we illustrate and verify this theorem for quantum chaotic systems with examples. Our numerical results show that a quantum chaotic system with an initial low-entropy state will dynamically relax to a high-entropy state and reach equilibrium. The quantum equilibrium state reached after dynamical relaxation bears a remarkable resemblance to the classical microcanonical ensemble. However, the fluctuations around equilibrium are distinct: The quantum fluctuations are exponential while the classical fluctuations are Gaussian.
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Affiliation(s)
- Quntao Zhuang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Biao Wu
- International Center for Quantum Materials, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing, China
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Yan Z, Jiang D. Matter-wave solutions in Bose-Einstein condensates with harmonic and Gaussian potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:056608. [PMID: 23004896 DOI: 10.1103/physreve.85.056608] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2011] [Revised: 02/13/2012] [Indexed: 06/01/2023]
Abstract
We study exact matter-wave solutions of the quasi-one-dimensional Gross-Pitaevskii (GP) equation with the space- and/or time-modulated potential and nonlinearity and the time-dependent gain or loss term in Bose-Einstein condensates. In particular, based on the similarity transformation and symbolic analysis, we report several families of exact solutions of the quasi-one-dimensional GP equation in the combination of the harmonic and Gaussian potentials, in which some physically relevant solutions are described. The stability of the obtained matter-wave solutions is addressed numerically such that some stable solutions are found. Moreover, we also analyze the parameter regimes for the stable solutions. These results may raise the possibility of relative experiments and potential applications.
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Affiliation(s)
- Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.
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Krüger P, Hadzibabic Z, Dalibard J. Critical point of an interacting two-dimensional atomic Bose gas. PHYSICAL REVIEW LETTERS 2007; 99:040402. [PMID: 17678340 DOI: 10.1103/physrevlett.99.040402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2007] [Indexed: 05/16/2023]
Abstract
We have measured the critical atom number in an array of harmonically trapped two-dimensional (2D) Bose gases of rubidium atoms at different temperatures. We found this number to be about 5 times higher than predicted by the semiclassical theory of Bose-Einstein condensation (BEC) in the ideal gas. This demonstrates that the conventional BEC picture is inapplicable in an interacting 2D atomic gas, in sharp contrast to the three-dimensional case. A simple heuristic model based on the Berezinskii-Kosterlitz-Thouless theory of 2D superfluidity and the local density approximation accounts well for our experimental results.
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Affiliation(s)
- Peter Krüger
- Laboratoire Kastler Brossel and CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
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Alon OE, Cederbaum LS. Pathway from condensation via fragmentation to fermionization of cold bosonic systems. PHYSICAL REVIEW LETTERS 2005; 95:140402. [PMID: 16241632 DOI: 10.1103/physrevlett.95.140402] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2005] [Indexed: 05/05/2023]
Abstract
For small scattering lengths, cold bosonic atoms form a condensate the density profile of which is smooth. With increasing scattering length, the density gradually acquires more and more oscillations. Finally, the number of oscillations equals the number of bosons and the system becomes fermionized. On this pathway from condensation to fermionization intriguing phenomena occur, depending on the shape of the trap. These include macroscopic fragmentation and coexistence of condensed and fermionized parts that are separated in space.
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Affiliation(s)
- Ofir E Alon
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany.
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Albiez M, Gati R, Fölling J, Hunsmann S, Cristiani M, Oberthaler MK. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. PHYSICAL REVIEW LETTERS 2005; 95:010402. [PMID: 16090588 DOI: 10.1103/physrevlett.95.010402] [Citation(s) in RCA: 216] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2004] [Indexed: 05/03/2023]
Abstract
We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.
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Affiliation(s)
- Michael Albiez
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, D-69120 Heidelberg, Germany
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