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Spada G, Pilati S, Giorgini S. Quantum Droplets in Two-Dimensional Bose Mixtures at Finite Temperature. PHYSICAL REVIEW LETTERS 2024; 133:083401. [PMID: 39241715 DOI: 10.1103/physrevlett.133.083401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2024] [Accepted: 07/18/2024] [Indexed: 09/09/2024]
Abstract
We investigate the formation of quantum droplets at finite temperature in attractive Bose mixtures subject to a strong transverse harmonic confinement. By means of exact path-integral Monte Carlo methods we determine the equilibrium density of the gas and the liquid as well as the pressure vs volume dependence along isothermal curves. Results for the equation of state and for the gas-liquid coexistence region in quasi-2D configurations are compared with calculations in strictly two dimensions, finding excellent agreement. Within the pure 2D model we explore the relevance of the quantum scale anomaly and we determine the critical interaction strength for the occurrence of the first-order gas to liquid transition. Furthermore, we find that the superfluid response develops suddenly, following the density jump from the gas to the liquid state.
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Affiliation(s)
- G Spada
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, I-38123 Trento, Italy
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN, Sezione di Perugia, I-06123 Perugia, Italy
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2
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Sunami S, Singh VP, Garrick D, Beregi A, Barker AJ, Luksch K, Bentine E, Mathey L, Foot CJ. Universal scaling of the dynamic BKT transition in quenched 2D Bose gases. Science 2023; 382:443-447. [PMID: 37883542 DOI: 10.1126/science.abq6753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 09/16/2023] [Indexed: 10/28/2023]
Abstract
The understanding of nonequilibrium dynamics in many-body quantum systems is a fundamental issue in statistical physics. Experiments that probe universal properties of these systems can address such foundational questions. In this study, we report the measurement of universal dynamics triggered by a quench from the superfluid to normal phase across the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional (2D) Bose gas. We reduced the density by splitting the 2D gas in two, realizing a quench across the critical point. The subsequent relaxation dynamics were probed with matter-wave interferometry to measure the local phase fluctuations. We show that the time evolution of both the phase correlation function and vortex density obeys universal scaling laws. This conclusion is supported by classical-field simulations and interpreted by means of real-time renormalization group theory.
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Affiliation(s)
- Shinichi Sunami
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Vijay Pal Singh
- Institut für Theoretische Physik, Leibniz Universität Hannover, 30167 Hannover, Germany
- Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
| | - David Garrick
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Abel Beregi
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Adam J Barker
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Kathrin Luksch
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Elliot Bentine
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Ludwig Mathey
- Zentrum für Optische Quantentechnologien and Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Hamburg 22761, Germany
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3
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Zhang Z, Chen L, Yao KX, Chin C. Transition from an atomic to a molecular Bose-Einstein condensate. Nature 2021; 592:708-711. [PMID: 33911270 DOI: 10.1038/s41586-021-03443-0] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Accepted: 03/11/2021] [Indexed: 11/09/2022]
Abstract
Molecular quantum gases (that is, ultracold and dense molecular gases) have many potential applications, including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing1-3. For molecules, to reach the quantum regime usually requires efficient cooling at high densities, which is frequently hindered by fast inelastic collisions that heat and deplete the population of molecules4,5. Here we report the preparation of two-dimensional Bose-Einstein condensates (BECs) of spinning molecules by inducing pairing interactions in an atomic condensate near a g-wave Feshbach resonance6. The trap geometry and the low temperature of the molecules help to reduce inelastic loss, ensuring thermal equilibrium. From the equation-of-state measurement, we determine the molecular scattering length to be + 220(±30) Bohr radii (95% confidence interval). We also investigate the unpairing dynamics in the strong coupling regime and find that near the Feshbach resonance the dynamical timescale is consistent with the unitarity limit. Our work demonstrates the long-sought transition between atomic and molecular condensates, the bosonic analogue of the crossover from a BEC to a Bardeen-Cooper-Schrieffer (BCS) superfluid in a Fermi gas7-9. In addition, our experiment may shed light on condensed pairs with orbital angular momentum, where a novel anisotropic superfluid with non-zero surface current is predicted10,11, such as the A phase of 3He.
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Affiliation(s)
- Zhendong Zhang
- James Franck Institute, Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL, USA
| | - Liangchao Chen
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan, China
| | - Kai-Xuan Yao
- James Franck Institute, Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL, USA
| | - Cheng Chin
- James Franck Institute, Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL, USA.
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4
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Wang JG, Yang SJ. Ground-state phases of spin-orbit coupled spin-1 Bose-Einstein condensate in a plane quadrupole field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:295404. [PMID: 29897338 DOI: 10.1088/1361-648x/aacc42] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the ground-state phases of two-dimensional spin-orbit coupled spin-1 Bose-Einstein condensate loaded in a plane quadrupole field. In the absence of rotation, for the fixed spin-orbit coupling strength, the ordinary stripe phase is found when the strength of the magnetic field gradient is small. As the strength of magnetic field gradient enhances, the system realizes the phases with three layer vortices along the radial direction. The number of vortices in the second layer is successively increased and the vortices in the outermost layer disappear when the strength of magnetic field gradient surpass the critical value. For the large strength of magnetic field gradient, the system only has the inner layer vortices. The magnetic field inhibits the region of vortices. For the fixed magnetic field gradient strength, the vortices of the system elongate along the radial direction and form a series of vortex lines, the number of the vortex line increases as the strength of spin-orbit coupling enhances. By adding the rotation, for the fixed strengths of spin-orbit coupling and magnetic field gradient, the number of second layer vortices also successively increases as the rotational frequency increases. The number of vortices in the certain layer of the ground-state density can be regularly changed under the effects of the magnetic field and spin-orbit coupling.
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Affiliation(s)
- Ji-Guo Wang
- Department of Mathematics and Physics, Shijiazhuang TieDao University, Shijiazhuang 050043, People's Republic of China. Institute of Applied Physics, Shijiazhuang TieDao University, Shijiazhuang 050043, People's Republic of China
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5
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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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6
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Cecchini GG, Jones ACL, Fuentes-Garcia M, Adams DJ, Austin M, Membreno E, Mills AP. Detector for positronium temperature measurements by two-photon angular correlation. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:053106. [PMID: 29864868 DOI: 10.1063/1.5017724] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We report on the design and characterization of a modular γ-ray detector assembly developed for accurate and efficient detection of coincident 511 keV back-to-back γ-rays following electron-positron annihilation. Each modular detector consists of 16 narrow lutetium yttrium oxyorthosilicate scintillators coupled to a multi-anode Hamamatsu H12700B photomultiplier tube. We discuss the operation and optimization of 511 keV γ-ray detection resulting from testing various scintillators and detector arrangements concluding with an estimate of the coincident 511 keV detection efficiency for the intended experiment and a preliminary test representing one-quarter of the completed array.
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Affiliation(s)
- G G Cecchini
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - A C L Jones
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - M Fuentes-Garcia
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - D J Adams
- College of Natural and Agricultural Sciences Machine Shop, University of California, Riverside, California 92521, USA
| | - M Austin
- Department of Physics, Marquette University, Milwaukee, Wisconsin 53233, USA
| | - E Membreno
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - A P Mills
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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7
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Hueck K, Luick N, Sobirey L, Siegl J, Lompe T, Moritz H. Two-Dimensional Homogeneous Fermi Gases. PHYSICAL REVIEW LETTERS 2018; 120:060402. [PMID: 29481215 DOI: 10.1103/physrevlett.120.060402] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Revised: 11/07/2017] [Indexed: 06/08/2023]
Abstract
We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as nonlocal properties of strongly interacting many-body systems. As a first benchmark experiment, we use a local probe to measure the density of a noninteracting 2D Fermi gas as a function of the chemical potential and find excellent agreement with the corresponding equation of state. We then perform matter wave focusing to extract the momentum distribution of the system and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of an interacting homogeneous 2D gas in the crossover between attractively interacting fermions and bosonic dimers.
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Affiliation(s)
- Klaus Hueck
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Niclas Luick
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Lennart Sobirey
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jonas Siegl
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Thomas Lompe
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Henning Moritz
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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8
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RuGway W, Manning AG, Hodgman SS, Dall RG, Truscott AG, Lamberton T, Kheruntsyan KV. Observation of transverse Bose-Einstein condensation via Hanbury Brown-Twiss correlations. PHYSICAL REVIEW LETTERS 2013; 111:093601. [PMID: 24033033 DOI: 10.1103/physrevlett.111.093601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2013] [Indexed: 06/02/2023]
Abstract
A fundamental property of a three-dimensional Bose-Einstein condensate is long-range coherence; however, in systems of lower dimensionality, not only is the long-range coherence destroyed but additional states of matter are predicted to exist. One such state is a "transverse condensate," first predicted by van Druten and Ketterle [Phys. Rev. Lett. 79, 549 (1997)], in which the gas condenses in the transverse dimensions of a highly anisotropic trap while remaining thermal in the longitudinal dimension. Here, we detect the transition from a three-dimensional thermal gas to a gas undergoing transverse condensation by probing Hanbury Brown-Twiss correlations.
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Affiliation(s)
- Wu RuGway
- Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200, Australia
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9
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Choi JY, Seo SW, Shin YI. Observation of thermally activated vortex pairs in a quasi-2D Bose gas. PHYSICAL REVIEW LETTERS 2013; 110:175302. [PMID: 23679741 DOI: 10.1103/physrevlett.110.175302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2013] [Indexed: 06/02/2023]
Abstract
We measure the in-plane distribution of thermally activated vortices in a trapped quasi-2D Bose gas, where we enhance the visibility of density-depleted vortex cores by radially compressing the sample before releasing the trap. The pairing of vortices is revealed by the two-vortex spatial correlation function obtained from the vortex distribution. The vortex density decreases gradually as temperature is lowered, and below a certain temperature, a vortex-free region emerges in the center of the sample. This shows the crossover from a Berezinskii-Kosterlitz-Thouless phase containing vortex-pair excitations to a vortex-free Bose-Einstein condensate in a finite-size 2D system.
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Affiliation(s)
- Jae-yoon Choi
- Center for Subwavelength Optics and Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
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10
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Ha LC, Hung CL, Zhang X, Eismann U, Tung SK, Chin C. Strongly interacting two-dimensional Bose gases. PHYSICAL REVIEW LETTERS 2013; 110:145302. [PMID: 25167003 DOI: 10.1103/physrevlett.110.145302] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2012] [Indexed: 06/03/2023]
Abstract
We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction strength 0.05 < g < 3 is covered by tuning the scattering length and by loading the sample into an optical lattice. Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant down-shifts from the mean-field and perturbation calculations when g approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.
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Affiliation(s)
- Li-Chung Ha
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Chen-Lung Hung
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Xibo Zhang
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Ulrich Eismann
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA and Laboratoire Kastler Brossel, ENS, UPMC, CNRS UMR 8552, 24 rue Lhomond, 75231 Paris, France
| | - Shih-Kuang Tung
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Cheng Chin
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA and The Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
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11
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Habibian H, Winter A, Paganelli S, Rieger H, Morigi G. Bose-Glass phases of ultracold atoms due to cavity backaction. PHYSICAL REVIEW LETTERS 2013; 110:075304. [PMID: 25166381 DOI: 10.1103/physrevlett.110.075304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2012] [Revised: 11/16/2012] [Indexed: 06/03/2023]
Abstract
We determine the quantum ground-state properties of ultracold bosonic atoms interacting with the mode of a high-finesse resonator. The atoms are confined by an external optical lattice, whose period is incommensurate with the cavity mode wavelength, and are driven by a transverse laser, which is resonant with the cavity mode. While for pointlike atoms photon scattering into the cavity is suppressed, for sufficiently strong lasers quantum fluctuations can support the buildup of an intracavity field, which in turn amplifies quantum fluctuations. The dynamics is described by a Bose-Hubbard model where the coefficients due to the cavity field depend on the atomic density at all lattice sites. Quantum Monte Carlo simulations and mean-field calculations show that, for large parameter regions, cavity backaction forces the atoms into clusters with a checkerboard density distribution. Here, the ground state lacks superfluidity and possesses finite compressibility, typical of a Bose glass. This system constitutes a novel setting where quantum fluctuations give rise to effects usually associated with disorder.
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Affiliation(s)
- Hessam Habibian
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany and Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
| | - André Winter
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Simone Paganelli
- Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
| | - Heiko Rieger
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - Giovanna Morigi
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
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12
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Choi JY, Seo SW, Kwon WJ, Shin YI. Probing phase fluctuations in a 2D degenerate Bose gas by free expansion. PHYSICAL REVIEW LETTERS 2012; 109:125301. [PMID: 23005954 DOI: 10.1103/physrevlett.109.125301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2012] [Indexed: 06/01/2023]
Abstract
We measure the power spectrum of the density distribution of a freely expanding two-dimensional (2D) degenerate Bose gas, where irregular density modulations gradually develop due to initial phase fluctuations in the sample. The spectrum has an oscillatory shape, where the peak positions are found to be independent of temperature and show scaling behavior in the course of expansion. The relative intensity of phase fluctuations is estimated from the normalized spectral peak strength and observed to decrease at lower temperatures, confirming the thermal nature of the phase fluctuations. We investigate the relaxation dynamics of nonequilibrium states using the power spectrum. Free vortices are observed with ring-shaped density ripples in a perturbed sample after a long relaxation time.
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Affiliation(s)
- Jae-yoon Choi
- Center for Subwavelength Optics, Seoul National University, Korea
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13
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Ramanathan A, Muniz SR, Wright KC, Anderson RP, Phillips WD, Helmerson K, Campbell GK. Partial-transfer absorption imaging: a versatile technique for optimal imaging of ultracold gases. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2012; 83:083119. [PMID: 22938286 DOI: 10.1063/1.4747163] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Partial-transfer absorption imaging is a tool that enables optimal imaging of atomic clouds for a wide range of optical depths. In contrast to standard absorption imaging, the technique can be minimally destructive and can be used to obtain multiple successive images of the same sample. The technique involves transferring a small fraction of the sample from an initial internal atomic state to an auxiliary state and subsequently imaging that fraction absorptively on a cycling transition. The atoms remaining in the initial state are essentially unaffected. We demonstrate the technique, discuss its applicability, and compare its performance as a minimally destructive technique to that of phase-contrast imaging.
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Affiliation(s)
- Anand Ramanathan
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
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14
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Observation of scale invariance and universality in two-dimensional Bose gases. Nature 2011; 470:236-9. [PMID: 21270797 DOI: 10.1038/nature09722] [Citation(s) in RCA: 200] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2010] [Accepted: 12/01/2010] [Indexed: 11/09/2022]
Abstract
The collective behaviour of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics; for example, thermodynamic observables follow generalized scaling laws near the phase transition. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry result in a broad fluctuation regime and an extended range of universal scaling behaviour. Studies of the BKT transition in cold atoms have stimulated great interest in recent years, but a clear demonstration of critical behaviour near the phase transition has remained elusive. Here we report in situ density and density-fluctuation measurements of two-dimensional Bose gases of caesium at different temperatures and interaction strengths, observing scale-invariant, universal behaviours. The extracted thermodynamic functions confirm the existence of a wide universal region near the BKT phase transition, and provide a sensitive test of the universality predicted by classical-field theory and quantum Monte Carlo calculations. Our experimental results provide evidence for growing density-density correlations in the fluctuation region, and call for further explorations of universal phenomena in classical and quantum critical physics.
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15
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Tung S, Lamporesi G, Lobser D, Xia L, Cornell EA. Observation of the presuperfluid regime in a two-dimensional Bose gas. PHYSICAL REVIEW LETTERS 2010; 105:230408. [PMID: 21231437 DOI: 10.1103/physrevlett.105.230408] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2010] [Revised: 09/14/2010] [Indexed: 05/30/2023]
Abstract
In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density ρ increases toward degenerate values, we observe a gradual divergence of the compressibility κ from the value predicted by a bare-atom model, κ(ba). κ/κ(ba) grows to 1.7 before ρ reaches the value for which we observe the sudden emergence of a spike at p = 0 in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D Bose gas.
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Affiliation(s)
- S Tung
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
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16
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Gallego D, Hofferberth S, Schumm T, Krüger P, Schmiedmayer J. Optical lattice on an atom chip. OPTICS LETTERS 2009; 34:3463-3465. [PMID: 19927178 DOI: 10.1364/ol.34.003463] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retroreflected using the atom chip surface as a high-quality mirror, generating a vertical array of purely optical oblate traps. We transfer thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice.
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Affiliation(s)
- D Gallego
- Physikalisches Institut, Universität Heidelberg, 69120 Heidelberg, Germany
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17
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Cladé P, Ryu C, Ramanathan A, Helmerson K, Phillips WD. Observation of a 2D Bose gas: from thermal to quasicondensate to superfluid. PHYSICAL REVIEW LETTERS 2009; 102:170401. [PMID: 19518764 DOI: 10.1103/physrevlett.102.170401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2008] [Indexed: 05/27/2023]
Abstract
We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz, and Thouless (BKT) transition temperature. By measuring the density profile after time of flight and the coherence length, we identify different states of the gas. We observe that the gas develops a bimodal distribution without long range order. In this regime, the gas presents a longer coherence length than the thermal cloud; it is quasicondensed but is not superfluid. Experimental evidence indicates that we also observe the superfluid transition (BKT transition). For a sufficiently long time of flight, we observe a trimodal distribution when the gas has developed a superfluid component.
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Affiliation(s)
- P Cladé
- Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8424, USA
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18
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Bruun GM, Taylor E. Quantum phases of a two-dimensional dipolar fermi gas. PHYSICAL REVIEW LETTERS 2008; 101:245301. [PMID: 19113629 DOI: 10.1103/physrevlett.101.245301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2008] [Revised: 10/15/2008] [Indexed: 05/27/2023]
Abstract
We examine the superfluid and collapse instabilities of a quasi-two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipole-dipole interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii-Kosterlitz-Thouless temperature as a function of the dipole angle.
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Affiliation(s)
- G M Bruun
- CNR-INFM BEC Center, Università di Trento, I-38050 Povo, Trento, Italy
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Sandoval-Figueroa N, Romero-Rochín V. Thermodynamics of trapped gases: generalized mechanical variables, equation of state, and heat capacity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061129. [PMID: 19256824 DOI: 10.1103/physreve.78.061129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2008] [Revised: 10/07/2008] [Indexed: 05/27/2023]
Abstract
We present the full thermodynamics of an interacting fluid confined by an arbitrary external potential. We show that for each confining potential, there emerge "generalized" volume and pressure variables V and P , that replace the usual volume and hydrostatic pressure of a uniform system. This scheme is validated with the derivation of the virial expansion of the grand potential. We discuss how this approach yields experimentally amenable procedures to find the equation of state of the fluid, P=P(VN,T) with N the number of atoms, as well as its heat capacity at constant generalized volume C_{V}=C_{V}(V,N,T) . With these two functions, all the thermodynamics properties of the system may be found. As specific examples we study weakly interacting Bose gases trapped by harmonic and by linear quadrupolar potentials within the Hartree-Fock approximation. We claim that this route provides an additional and useful tool to analyze both the thermodynamic variables of an ultracold trapped gas as well as its elementary excitations.
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Affiliation(s)
- Nadia Sandoval-Figueroa
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México, Distrito Federal Mexico.
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Holzmann M, Krauth W. Kosterlitz-Thouless transition of the quasi-two-dimensional trapped Bose gas. PHYSICAL REVIEW LETTERS 2008; 100:190402. [PMID: 18518427 DOI: 10.1103/physrevlett.100.190402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2007] [Revised: 03/06/2008] [Indexed: 05/26/2023]
Abstract
We use quantum Monte Carlo methods to compute the density profile, the nonclassical moment of inertia, and the condensate fraction of an interacting quasi-two-dimensional trapped Bose gas with up to N ~ 5 x 10(5) atoms and parameters closely related to recent experiments. We locate the Kosterlitz-Thouless temperature T(KT) and discuss intrinsic signatures of the onset of superfluidity in the density profile. Below T(KT), the condensate fraction is macroscopic even for our largest systems and decays only slowly with system size. We show that the thermal population of excited states in the transverse direction changes the two-dimensional density profile noticeably in both the normal and the superfluid phase.
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Pilati S, Giorgini S, Prokof'ev N. Critical temperature of interacting Bose gases in two and three dimensions. PHYSICAL REVIEW LETTERS 2008; 100:140405. [PMID: 18518010 DOI: 10.1103/physrevlett.100.140405] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2008] [Indexed: 05/26/2023]
Abstract
We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.
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Affiliation(s)
- S Pilati
- Dipartimento di Fisica, Università di Trento and CNR-INFM BEC Center, I-38050 Povo, Trento, Italy
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Spielman IB, Phillips WD, Porto JV. Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition. PHYSICAL REVIEW LETTERS 2008; 100:120402. [PMID: 18517841 DOI: 10.1103/physrevlett.100.120402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2007] [Revised: 02/01/2008] [Indexed: 05/26/2023]
Abstract
We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.
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Affiliation(s)
- I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology, USA.
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