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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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Li G, Zhao Z, Jiang X, Chen Z, Liu B, Malomed BA, Li Y. Strongly Anisotropic Vortices in Dipolar Quantum Droplets. PHYSICAL REVIEW LETTERS 2024; 133:053804. [PMID: 39159105 DOI: 10.1103/physrevlett.133.053804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2023] [Accepted: 06/17/2024] [Indexed: 08/21/2024]
Abstract
We construct strongly anisotropic quantum droplets with embedded vorticity in the 3D space, with mutually perpendicular vortex axis and polarization of atomic magnetic moments. Stability of these anisotropic vortex quantum droplets (AVQDs) is verified by means of systematic simulations. Their stability area is identified in the parametric plane of the total atom number and scattering length of the contact interactions. We also construct vortex-antivortex-vortex bound states and find their stability region in the parameter space. The application of a torque perpendicular to the vorticity axis gives rise to robust intrinsic oscillations or rotation of the AVQDs. The effect of three-body losses on the AVQD stability is considered too. The results show that the AVQDs can retain the topological structure (vorticity) for a sufficiently long time if the scattering length exceeds a critical value.
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Affiliation(s)
| | | | | | | | | | | | - Yongyao Li
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528225, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University, Foshan 528225, China
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3
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Deng H, Li J, Chen Z, Liu Y, Liu D, Jiang C, Kong C, Malomed BA. Semivortex solitons and their excited states in spin-orbit-coupled binary bosonic condensates. Phys Rev E 2024; 109:064201. [PMID: 39021016 DOI: 10.1103/physreve.109.064201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 05/03/2024] [Indexed: 07/20/2024]
Abstract
It is known that two-dimensional two-component fundamental solitons of the semivortex (SV) type, with vorticities (s_{+},s_{-})=(0,1) in their components, are stable ground states (GSs) in the spin-orbit-coupled (SOC) binary Bose-Einstein condensate with the contact self-attraction acting in both components, in spite of the possibility of the critical collapse in the system. However, excited states (ESs) of the SV solitons, with the vorticity set (s_{+},s_{-})=(S_{+},S_{+}+1) and S_{+}=1,2,3,..., are unstable in the same system. We construct ESs of SV solitons in the SOC system with opposite signs of the self-interaction in the two components. The main finding is stability of the ES-SV solitons, with the extra vorticity (at least) up to S_{+}=6. The threshold value of the norm for the onset of the critical collapse, N_{thr}, in these excited states is higher than the commonly known critical value, N_{c}≈5.85, associated with the single-component Townes solitons, N_{thr} increasing with the growth of S_{+}. A velocity interval for stable motion of the GS-SV solitons is found too. The results suggest a solution for the challenging problem of the creation of stable vortex solitons with high topological charges.
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Affiliation(s)
- Haiming Deng
- School of Physics and Electronic-Electrical Engineering, Xiangnan University, Chenzhou 423000, China
- Microelectronics and Optoelectronics Technology Key Laboratory of Hunan Higher Education, Xiangnan University, Chenzhou 423000, China
- Hunan Engineering Research Center of Advanced Embedded Computing and Intelligent Medical Systems, Xiangnan University, Chenzhou 423000, China
| | - Jinqing Li
- School of Physics and Electronic-Electrical Engineering, Xiangnan University, Chenzhou 423000, China
- Microelectronics and Optoelectronics Technology Key Laboratory of Hunan Higher Education, Xiangnan University, Chenzhou 423000, China
- Hunan Engineering Research Center of Advanced Embedded Computing and Intelligent Medical Systems, Xiangnan University, Chenzhou 423000, China
| | | | - Yaohui Liu
- Hunan Engineering Research Center of Advanced Embedded Computing and Intelligent Medical Systems, Xiangnan University, Chenzhou 423000, China
| | - Dong Liu
- Hunan Engineering Research Center of Advanced Embedded Computing and Intelligent Medical Systems, Xiangnan University, Chenzhou 423000, China
| | - Chunzhi Jiang
- School of Physics and Electronic-Electrical Engineering, Xiangnan University, Chenzhou 423000, China
- Microelectronics and Optoelectronics Technology Key Laboratory of Hunan Higher Education, Xiangnan University, Chenzhou 423000, China
- Hunan Engineering Research Center of Advanced Embedded Computing and Intelligent Medical Systems, Xiangnan University, Chenzhou 423000, China
| | - Chao Kong
- School of Physics and Electronic-Electrical Engineering, Xiangnan University, Chenzhou 423000, China
- Microelectronics and Optoelectronics Technology Key Laboratory of Hunan Higher Education, Xiangnan University, Chenzhou 423000, China
- Hunan Engineering Research Center of Advanced Embedded Computing and Intelligent Medical Systems, Xiangnan University, Chenzhou 423000, China
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Houwman JJA, Baillie D, Blakie PB, Natale G, Ferlaino F, Mark MJ. Measurement of the Excitation Spectrum of a Dipolar Gas in the Macrodroplet Regime. PHYSICAL REVIEW LETTERS 2024; 132:103401. [PMID: 38518353 DOI: 10.1103/physrevlett.132.103401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Revised: 11/27/2023] [Accepted: 01/08/2024] [Indexed: 03/24/2024]
Abstract
The excitation spectrum of a cigar-shaped strongly dipolar quantum gas at the crossover from a Bose-Einstein condensate to a trapped macrodroplet is predicted to exhibit peculiar features-a strong upward shift of low momentum excitation energies together with a strong multiband response for high momenta. By performing Bragg spectroscopy over a wide range of momenta, we observe both key elements and also confirm the predicted stiffening of excitation modes when approaching the macrodroplet regime. Our measurements are in good agreement with numerical calculations taking into account finite size effects.
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Affiliation(s)
- J J A Houwman
- Universität Innsbruck, Institut für Experimentalphysik, 6020 Innsbruck, Austria
| | - D Baillie
- Department of Physics, Centre for Quantum Science, and The Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
| | - P B Blakie
- Department of Physics, Centre for Quantum Science, and The Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
| | - G Natale
- Universität Innsbruck, Institut für Experimentalphysik, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - F Ferlaino
- Universität Innsbruck, Institut für Experimentalphysik, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - M J Mark
- Universität Innsbruck, Institut für Experimentalphysik, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
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5
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Malomed BA. Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings. ENTROPY (BASEL, SWITZERLAND) 2024; 26:137. [PMID: 38392392 PMCID: PMC10887582 DOI: 10.3390/e26020137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Revised: 01/26/2024] [Accepted: 01/28/2024] [Indexed: 02/24/2024]
Abstract
This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.
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Affiliation(s)
- Boris A Malomed
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile
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Spada G, Pilati S, Giorgini S. Attractive Solution of Binary Bose Mixtures: Liquid-Vapor Coexistence and Critical Point. PHYSICAL REVIEW LETTERS 2023; 131:173404. [PMID: 37955467 DOI: 10.1103/physrevlett.131.173404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Revised: 07/06/2023] [Accepted: 09/29/2023] [Indexed: 11/14/2023]
Abstract
We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral Monte Carlo methods. Our focus is on the regime of interspecies interactions where the ground state is in a self-bound liquid phase, stabilized by beyond mean-field effects. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength and establish the extent of the coexistence region between liquid and vapor using the Maxwell construction. Notably, within the coexistence region, Bose-Einstein condensation occurs in a discontinuous way as the density jumps from the normal gas to the superfluid liquid phase. Furthermore, we determine the critical point where the line of first-order transition ends and investigate the behavior of the density discontinuity in its vicinity. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps.
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Affiliation(s)
- G Spada
- Pitaevskii Center on Bose-Einstein Condensation, CNR-INO and Dipartimento di Fisica, Università di Trento, 38123 Povo, Trento, Italy
| | - S Pilati
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN, Sezione di Perugia, I-06123 Perugia, Italy
| | - S Giorgini
- Pitaevskii Center on Bose-Einstein Condensation, CNR-INO and Dipartimento di Fisica, Università di Trento, 38123 Povo, Trento, Italy
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7
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Liu B, Cai X, Qin X, Jiang X, Xie J, Malomed BA, Li Y. Ring-shaped quantum droplets with hidden vorticity in a radially periodic potential. Phys Rev E 2023; 108:044210. [PMID: 37978625 DOI: 10.1103/physreve.108.044210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 09/20/2023] [Indexed: 11/19/2023]
Abstract
We study the stability and characteristics of two-dimensional circular quantum droplets (QDs) with embedded hidden vorticity (HV), i.e., opposite angular momenta in two components, formed by binary Bose-Einstein condensates (BECs) trapped in a radially periodic potential. The system is modeled by the Gross-Pitaevskii equations with the Lee-Huang-Yang terms, which represent the higher-order self-repulsion induced by quantum fluctuations around the mean-field state, and a potential which is a periodic function of the radial coordinate. Ring-shaped QDs with high winding numbers (WNs) of the HV type, which are trapped in particular circular troughs of the radial potential, are produced by means of the imaginary-time-integration method. Effects of the depth and period of the potential on these QD states are studied. The trapping capacity of individual circular troughs is identified. Stable compound states in the form of nested multiring patterns are constructed too, including ones with WNs of opposite signs. The stably coexisting ring-shaped QDs with different WNs can be used for the design of BEC-based data-storage schemes.
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Affiliation(s)
- Bin Liu
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University, Foshan 528000, China
| | - Xiaoyan Cai
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Xizhou Qin
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University, Foshan 528000, China
| | - Xunda Jiang
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University, Foshan 528000, China
| | - Jianing Xie
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University, Foshan 528000, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
| | - Yongyao Li
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University, Foshan 528000, China
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He L, Li H, Yi W, Yu ZQ. Quantum Criticality of Liquid-Gas Transition in a Binary Bose Mixture. PHYSICAL REVIEW LETTERS 2023; 130:193001. [PMID: 37243630 DOI: 10.1103/physrevlett.130.193001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2022] [Revised: 02/19/2023] [Accepted: 04/17/2023] [Indexed: 05/29/2023]
Abstract
Quantum liquid, in the form of a self-bound droplet, is stabilized by a subtle balance between the mean-field contribution and quantum fluctuations. While a liquid-gas transition is expected when such a balance is broken, it remains elusive whether liquid-gas critical points exist in the quantum regime. Here, we study the quantum criticality in a binary Bose mixture undergoing the liquid-gas transition. We show that, beyond a narrow stability window of the self-bound liquid, a liquid-gas coexistence persists, which eventually transits into a homogeneous mixture. Importantly, we identify two distinct critical points where the liquid-gas coexistence terminates. These critical points are characterized by rich critical behaviors in their vicinity, including divergent susceptibility, unique phonon-mode softening, and enhanced density correlations. The liquid-gas transition and the critical points can be readily explored in ultracold atoms confined to a box potential. Our work highlights the thermodynamic approach as a powerful tool in revealing the quantum liquid-gas criticality, and paves the way for further studies of critical phenomena in quantum liquids.
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Affiliation(s)
- Li He
- College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China
| | - Haowei Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Zeng-Qiang Yu
- Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
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Song J, Yan Z, Malomed BA. Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential. CHAOS (WOODBURY, N.Y.) 2023; 33:033141. [PMID: 37003809 DOI: 10.1063/5.0138420] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 03/03/2023] [Indexed: 06/19/2023]
Abstract
In this paper, vortex solitons are produced for a variety of 2D spinning quantum droplets (QDs) in a PT-symmetric potential, modeled by the amended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. In particular, exact QD states are obtained under certain parameter constraints, providing a guide to finding the respective generic family. In a parameter region of the unbroken PT symmetry, different families of QDs originating from the linear modes are obtained in the form of multipolar and vortex droplets at low and high values of the norm, respectively, and their stability is investigated. In the spinning regime, QDs become asymmetric above a critical rotation frequency, most of them being stable. The effect of the PT-symmetric potential on the spinning and nonspinning QDs is explored by varying the strength of the gain-loss distribution. Generally, spinning QDs trapped in the PT-symmetric potential exhibit asymmetry due to the energy flow affected by the interplay of the gain-loss distribution and rotation. Finally, interactions between spinning or nonspinning QDs are explored, exhibiting elastic collisions under certain conditions.
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Affiliation(s)
- Jin Song
- KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhenya Yan
- KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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Kopyciński J, Łebek M, Górecki W, Pawłowski K. Ultrawide Dark Solitons and Droplet-Soliton Coexistence in a Dipolar Bose Gas with Strong Contact Interactions. PHYSICAL REVIEW LETTERS 2023; 130:043401. [PMID: 36763437 DOI: 10.1103/physrevlett.130.043401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Revised: 11/10/2022] [Accepted: 12/19/2022] [Indexed: 06/18/2023]
Abstract
We look into dark solitons in a quasi-1D dipolar Bose gas and in a quantum droplet. We derive the analytical solitonic solution of a Gross-Pitaevskii-like equation accounting for beyond mean-field effects. The results show there is a certain critical value of the dipolar interactions, for which the width of a motionless soliton diverges. Moreover, there is a peculiar solution of the motionless soliton with a nonzero density minimum. We also present the energy spectrum of these solitons with an additional excitation subbranch appearing. Finally, we perform a series of numerical experiments revealing the coexistence of a dark soliton inside a quantum droplet.
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Affiliation(s)
- Jakub Kopyciński
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - Maciej Łebek
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - Wojciech Górecki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Krzysztof Pawłowski
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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11
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Morera I, Ołdziejewski R, Astrakharchik GE, Juliá-Díaz B. Superexchange Liquefaction of Strongly Correlated Lattice Dipolar Bosons. PHYSICAL REVIEW LETTERS 2023; 130:023602. [PMID: 36706388 DOI: 10.1103/physrevlett.130.023602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Revised: 11/03/2022] [Accepted: 12/07/2022] [Indexed: 06/18/2023]
Abstract
We propose a mechanism for liquid formation in strongly correlated lattice systems. The mechanism is based on an interplay between long-range attraction and superexchange processes. As an example, we study dipolar bosons in one-dimensional optical lattices. We present a perturbative theory and validate it in comparison with full density-matrix renormalization group simulations for the energetic and structural properties of different phases of the system, i.e., self-bound Mott insulator, liquid, and gas. We analyze the nonequilibrium properties and calculate the dynamic structure factor. Its structure differs in compressible and insulating phases. In particular, the low-energy excitations in compressible phases are linear phonons. We extract the speed of sound and analyze its dependence on dipolar interaction and density. We show that it exhibits a nontrivial behavior owing to the breaking of Galilean invariance. We argue that an experimental detection of this previously unknown quantum liquid could provide a fingerprint of the superexchange process and open intriguing possibilities for investigating non-Galilean invariant liquids.
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Affiliation(s)
- Ivan Morera
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, E-08028 Barcelona, Spain
| | - Rafał Ołdziejewski
- Max Planck Institute of Quantum Optics, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstrasse 4, 80799 Munich, Germany
| | - Grigori E Astrakharchik
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, E-08028 Barcelona, Spain
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, Spain
| | - Bruno Juliá-Díaz
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, E-08028 Barcelona, Spain
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Chomaz L, Ferrier-Barbut I, Ferlaino F, Laburthe-Tolra B, Lev BL, Pfau T. Dipolar physics: a review of experiments with magnetic quantum gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 86:026401. [PMID: 36583342 DOI: 10.1088/1361-6633/aca814] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.
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Affiliation(s)
- Lauriane Chomaz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Igor Ferrier-Barbut
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - Bruno Laburthe-Tolra
- Université Sorbonne Paris Nord, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Benjamin L Lev
- Departments of Physics and Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA 94305, United States of America
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
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13
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Weber number and the outcome of binary collisions between quantum droplets. Sci Rep 2022; 12:18467. [PMID: 36323755 PMCID: PMC9630383 DOI: 10.1038/s41598-022-22904-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2022] [Accepted: 10/20/2022] [Indexed: 11/25/2022] Open
Abstract
A theoretical analysis of binary collisions of quantum droplets under feasible experimental conditions is reported. Droplets formed from degenerate dilute Bose gases made up from binary mixtures of ultracold atoms are considered. Reliable expressions for the surface tension of the droplets are introduced based on a study of low energy excitations of their ground state within the random phase approximation. Their relevance is evaluated considering an estimation of the expected excitation energy having in mind the Thouless variational theorem. The surface tension expressions allow calculating the Weber number of the droplets involved in the collisions. Several regimes on the outcomes of the binary frontal collisions that range from the coalescence of the quantum droplets to their disintegration into smaller droplets are identified. Atoms losses of the droplets derived from self-evaporation and three-body scattering are quantified for both homo- and hetero-nuclear mixtures. Their control is mandatory for the observation of some interesting effects arising from droplets collisions.
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14
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Pathak MR, Nath A. Droplet to soliton crossover at negative temperature in presence of bi-periodic optical lattices. Sci Rep 2022; 12:18248. [PMID: 36309597 PMCID: PMC9617923 DOI: 10.1038/s41598-022-23026-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 10/24/2022] [Indexed: 11/21/2022] Open
Abstract
It is shown that the phenomenon of negative temperature essentially occurs in Bose-Einstein condensate due to the realization of the upper bound energy state utilizing a combination of expulsive harmonic oscillator and optical lattice potentials. We study the existence of quantum droplets at negative temperature and droplet-to-soliton crossover in the binary Bose-Einstein condensate mixture in the presence of bi-periodic optical lattices and expulsive-BOL confinements. Based on the beyond mean field approximation, we employ the extended Gross-Pitäevskii equation and calculate the exact analytical form of wavefunction solutions for BOL, expulsive-BOL confinements. An interesting transition of quantum droplets from positive to negative temperatures and the droplet-to-soliton crossover by modulating the disorder in BOL potential are illustrated. The affirmation of such crossover is performed by exploring the profile of atomic condensate density which smoothly transits from being a flat top density in optical lattice confinement to a bright soliton for BOL trap. Further, we confirm the crossover by exploring the energy per particle and the variation in the root mean square size of the condensate with respect to the potential depth of the BOL trap. Eventually, all of this aid us to construct a phase diagram in a space between the amplitude of BOL potential depth and particle number which reveals the formation of droplet and soliton phases. In expulsive-BOL confinement, it is seen that the impact of the expulsive trap is insignificant on atomic condensate density in the droplet phase and it becomes prominent in the soliton region. Further, the variation of total energy reveals that the amplitude of the expulsive oscillator strengthens the droplet phase and leads to an increase in the negative temperature of the considered system.
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Affiliation(s)
- Maitri R Pathak
- Indian Institute of Information Technology Vadodara Gujarat India, Gandhinagar, 382 028, India
| | - Ajay Nath
- Indian Institute of Information Technology Vadodara Gujarat India, Gandhinagar, 382 028, India.
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15
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Luo Z, Liu Y, Li Y, Batle J, Malomed BA. Stability limits for modes held in alternating trapping-expulsive potentials. Phys Rev E 2022; 106:014201. [PMID: 35974589 DOI: 10.1103/physreve.106.014201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 06/09/2022] [Indexed: 06/15/2023]
Abstract
We elaborate a scheme of trapping-expulsion management (TEM), in the form of the quadratic potential periodically switching between confinement and expulsion, as a means of stabilization of two-dimensional dynamical states against the backdrop of the critical collapse driven by the cubic self-attraction with strength g. The TEM scheme may be implemented, as spatially or temporally periodic modulations, in optics or BEC, respectively. The consideration is carried out by dint of numerical simulations and variational approximation (VA). In terms of the VA, the dynamics amounts to a nonlinear Ermakov equation, which, in turn, is tantamount to a linear Mathieu equation. Stability boundaries are found as functions of g and parameters of the periodic modulation of the trapping potential. Below the usual collapse threshold, which is known, in the numerical form, as g<g_{c}^{(num)}≈5.85 (in the standard notation), the stability is limited by the onset of the parametric resonance. This stability limit, including the setup with the self-repulsive sign of the cubic term (g<0), is accurately predicted by the VA. At g>g_{c}^{(num)}, the collapse threshold is found with the help of full numerical simulations. The relative increase of g_{c} above g_{c}^{(num)} is ≈1.5%. It is a meaningful result, even if its size is small, because the collapse threshold is a universal constant which is difficult to change.
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Affiliation(s)
- Zhihuan Luo
- Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China
| | - Yan Liu
- Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China
| | - Yongyao Li
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Josep Batle
- CRISP Centre de Recerca Independent de sa Pobla, C. Albéniz 12, 07420 sa Pobla, Balearic Islands, Spain
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
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16
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Ultradilute Quantum Droplets in the Presence of Higher-Order Quantum Fluctuations. ATOMS 2022. [DOI: 10.3390/atoms10020064] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
We investigate the effects of higher-order quantum fluctuations on the bulk properties of self-bound droplets in three-, two- and one-dimensional binary Bose mixtures using the Hartree–Fock–Bogoliubov theory. We calculate higher-order corrections to the equation of state of the droplet at both zero and finite temperatures. We show that our results for the ground-state energy are in a good agreement with recent quantum Monte Carlo simulations in any dimension. Our study extends to the finite temperature case where it is found that thermal fluctuations may destabilize the droplet state and eventually destroy it. In two dimensions, we reveal that the droplet occurs at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature.
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17
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Abstract
In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross–Pitäevskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov–Kolokolov (VK) criterion.
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18
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Dynamics of quantum droplets in an external harmonic confinement. Sci Rep 2022; 12:6904. [PMID: 35484174 PMCID: PMC9050709 DOI: 10.1038/s41598-022-10468-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 03/31/2022] [Indexed: 11/20/2022] Open
Abstract
Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross–Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov–Kolokolov (VK) criterion and are found stable.
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19
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Yu X, Blakie PB. Propagating Ferrodark Solitons in a Superfluid: Exact Solutions and Anomalous Dynamics. PHYSICAL REVIEW LETTERS 2022; 128:125301. [PMID: 35394308 DOI: 10.1103/physrevlett.128.125301] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Revised: 07/26/2021] [Accepted: 02/01/2022] [Indexed: 06/14/2023]
Abstract
Exact propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as kinks in the transverse magnetization. Propagation is only possible when the symmetry-breaking longitudinal magnetic field is applied. Such solitons have two types: a low energy branch with positive inertial mass and a higher energy branch with negative inertial mass. Both types become identical at the maximum speed, a new speed bound that is different from speed limits set by the elementary excitations. The physical mass, which accounts for the number density dip, is negative for both types. In a finite one-dimensional system subject to a linear potential, the soliton undergoes oscillations caused by transitions between the two types occurring at the maximum speed.
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Affiliation(s)
- Xiaoquan Yu
- Graduate School of China Academy of Engineering Physics, Beijing 100193, China
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
| | - P B Blakie
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
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20
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Karpov P, Piazza F. Light-Induced Quantum Droplet Phases of Lattice Bosons in Multimode Cavities. PHYSICAL REVIEW LETTERS 2022; 128:103201. [PMID: 35333068 DOI: 10.1103/physrevlett.128.103201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 02/07/2022] [Indexed: 06/14/2023]
Abstract
Multimode optical cavities can be used to implement interatomic interactions which are highly tunable in strength and range. For bosonic atoms trapped in an optical lattice we show that, for any finite range of the cavity-mediated interaction, quantum self-bound droplets dominate the ground state phase diagram. Their size and in turn density is not externally fixed but rather emerges from the competition between local repulsion and finite-range cavity-mediated attraction. We identify two different regimes of the phase diagram. In the strongly glued regime, the interaction range exceeds the droplet size and the physics resembles the one of the standard Bose-Hubbard model in a (self-consistent) external potential, where in the phase diagram two incompressible droplet phases with different filling are separated by one with a superfluid core. In the opposite weakly glued regime, we find instead direct first order transitions between the two incompressible phases, as well as pronounced metastability. The cavity field leaking out of the mirrors can be measured to distinguish between the various types of droplets.
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Affiliation(s)
- P Karpov
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- Arnold Sommerfeld Center for Theoretical Physics, Ludwig Maximilian University of Munich, Theresienstr. 37, Munich 80333, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, Munich 80799, Germany
- National University of Science and Technology "MISiS", Moscow 119991, Russia
| | - F Piazza
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
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21
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Abstract
We investigate the properties of a dilute gas of impurities embedded in an ultracold gas of bosons that forms a Bose–Einstein condensate (BEC). This work focuses mainly on the equation of state (EoS) of the impurity gas at zero temperature and the induced interaction between impurities mediated by the host bath. We use perturbative field-theory approaches, such as Hugenholtz–Pines formalism, in the weakly interacting regime. In turn, for strong interactions, we aim at non-perturbative techniques such as quantum–Monte Carlo (QMC) methods. Our findings agree with experimental observations for an ultra dilute gas of impurities, modeled in the framework of the single impurity problem; however, as the density of impurities increases, systematic deviations are displayed with respect to the one-body Bose polaron problem.
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22
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Li J, Zhang Y, Zeng J. Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices. iScience 2022; 25:104026. [PMID: 35345461 PMCID: PMC8957030 DOI: 10.1016/j.isci.2022.104026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Revised: 01/17/2022] [Accepted: 03/01/2022] [Indexed: 11/26/2022] Open
Abstract
Past decades have witnessed the emergence and increasing expansion of parity-time (PT)-symmetric systems in diverse physical fields and beyond as they manifest entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT-symmetric non-Hermitian systems have recently been explored broadly; however, understanding these systems in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Utilizing direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linear band gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, thus opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems 3D parity-time (PT)-symmetric optical lattices are used to overcome the collapse of 3D ultracold atoms. 3D matter-wave gap solitons and vortices are found in PT-symmetric optical lattices. Rich properties and dynamics of 3D matter-wave localized modes are disclosed. In-depth soliton physics is provided in 3D non-Hermitian periodic physical systems.
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23
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Hammond A, Lavoine L, Bourdel T. Tunable Three-Body Interactions in Driven Two-Component Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2022; 128:083401. [PMID: 35275683 DOI: 10.1103/physrevlett.128.083401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Revised: 01/21/2022] [Accepted: 02/07/2022] [Indexed: 06/14/2023]
Abstract
We propose and demonstrate the appearance of an effective attractive three-body interaction in coherently driven two-component Bose-Einstein condensates. It originates from the spinor degree of freedom that is affected by a two-body mean-field shift of the driven transition frequency. Importantly, its strength can be controlled with the Rabi-coupling strength and it does not come with additional losses. In the experiment, the three-body interactions are adjusted to play a predominant role in the equation of state of a cigar-shaped trapped condensate. This is confirmed through two striking observations: a downshift of the radial breathing mode frequency and the radial collapses for positive values of the dressed-state scattering length.
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Affiliation(s)
- A Hammond
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - L Lavoine
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - T Bourdel
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
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24
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Guijarro G, Astrakharchik GE, Boronat J. Ultradilute Quantum Liquid of Dipolar Atoms in a Bilayer. PHYSICAL REVIEW LETTERS 2022; 128:063401. [PMID: 35213182 DOI: 10.1103/physrevlett.128.063401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Revised: 10/07/2021] [Accepted: 01/03/2022] [Indexed: 06/14/2023]
Abstract
We show that ultradilute quantum liquids can be formed with ultracold bosonic dipolar atoms in a bilayer geometry. Contrary to previous realizations of ultradilute liquids, there is no need for stabilizing the system with an additional repulsive short-range potential. The advantage of the proposed system is that dipolar interactions on their own are sufficient for creation of a self-bound state and no additional short-range potential is needed for the stabilization. We perform quantum Monte Carlo simulations and find a rich ground-state phase diagram that contains quantum phase transitions between liquid, solid, atomic gas, and molecular gas phases. The stabilization mechanism of the liquid phase is consistent with the microscopic scenario in which the effective dimer-dimer attraction is balanced by an effective three-dimer repulsion. The equilibrium density of the liquid, which is extremely small, can be controlled by the interlayer distance. From the equation of state, we extract the spinodal density, below which the homogeneous system breaks into droplets. Our results offer a new example of a two-dimensional interacting dipolar liquid in a clean and highly controllable setup.
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Affiliation(s)
- G Guijarro
- Departament de Física, Campus Nord B4-B5, Universitat Politécnica de Catalunya, E-08034 Barcelona, Spain
| | - G E Astrakharchik
- Departament de Física, Campus Nord B4-B5, Universitat Politécnica de Catalunya, E-08034 Barcelona, Spain
| | - J Boronat
- Departament de Física, Campus Nord B4-B5, Universitat Politécnica de Catalunya, E-08034 Barcelona, Spain
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25
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Weakly-Interacting Bose–Bose Mixtures from the Functional Renormalisation Group. CONDENSED MATTER 2022. [DOI: 10.3390/condmat7010009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
We provide a detailed presentation of the functional renormalisation group (FRG) approach for weakly-interacting Bose–Bose mixtures, including a complete discussion on the RG equations. To test this approach, we examine thermodynamic properties of balanced three-dimensional Bose–Bose gases at zero and finite temperatures and find a good agreement with related works. We also study ground-state energies of repulsive Bose polarons by examining mixtures in the limit of infinite population imbalance. Finally, we discuss future applications of the FRG to novel problems in Bose–Bose mixtures and related systems.
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26
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Lavoine L, Hammond A, Recati A, Petrov DS, Bourdel T. Beyond-Mean-Field Effects in Rabi-Coupled Two-Component Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2021; 127:203402. [PMID: 34860048 DOI: 10.1103/physrevlett.127.203402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Revised: 08/09/2021] [Accepted: 10/15/2021] [Indexed: 06/13/2023]
Abstract
We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi-coupling frequency Ω, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang scaling ∝n^{5/2} to an expansion in integer powers of density, where, in addition to a two-body BMF term ∝n^{2}sqrt[Ω], there emerges a repulsive three-body contribution ∝n^{3}/sqrt[Ω]. We experimentally evidence these two contributions, thanks to their different scaling with Ω, in the expansion of a Rabi-coupled two-component ^{39}K condensate in a waveguide. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of the vanishing mean field.
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Affiliation(s)
- L Lavoine
- Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, Avenue Augustin Fresnel, 91127 Palaiseau CEDEX, France
| | - A Hammond
- Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, Avenue Augustin Fresnel, 91127 Palaiseau CEDEX, France
| | - A Recati
- INO-CNR BEC Center and Dipartimento di Fisica, Università degli Studi di Trento, 38123 Povo, Italy and Trento Institute for Fundamental Physics and Applications, INFN, 38123 Trento, Italy
| | - D S Petrov
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
| | - T Bourdel
- Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, Avenue Augustin Fresnel, 91127 Palaiseau CEDEX, France
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27
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Many-body and temperature effects in two-dimensional quantum droplets in Bose-Bose mixtures. Sci Rep 2021; 11:21765. [PMID: 34741072 PMCID: PMC8571397 DOI: 10.1038/s41598-021-01089-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 10/15/2021] [Indexed: 11/25/2022] Open
Abstract
We study the equilibrium properties of self-bound droplets in two-dimensional Bose mixtures employing the time-dependent Hartree–Fock–Bogoliubov theory. This theory allows one to understand both the many-body and temperature effects beyond the Lee–Huang–Yang description. We calculate higher-order corrections to the excitations, the sound velocity, and the energy of the droplet. Our results for the ground-state energy are compared with the diffusion Monte Carlo data and good agreement is found. The behavior of the depletion and anomalous density of the droplet is also discussed. At finite temperature, we show that the droplet emerges at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature. The critical temperature strongly depends on the interspecies interactions. Our study is extended to the finite size droplet by numerically solving the generalized finite-temperature Gross-Pitaevskii equation which is obtained self-consistently from our formalism in the framework of the local density approximation.
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28
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Ma Y, Peng C, Cui X. Borromean Droplet in Three-Component Ultracold Bose Gases. PHYSICAL REVIEW LETTERS 2021; 127:043002. [PMID: 34355973 DOI: 10.1103/physrevlett.127.043002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2021] [Revised: 04/21/2021] [Accepted: 06/25/2021] [Indexed: 06/13/2023]
Abstract
We investigate droplet formation in three-component ultracold bosons. In particular, we identify the formation of a Borromean droplet, where only the ternary bosons can form a self-bound droplet while any binary subsystems cannot, as the first example of Borromean binding due to a collective many-body effect. Its formation is facilitated by an additional attractive force induced by the density fluctuation of a third component, which enlarges the mean-field collapse region in comparison to the binary case and renders the formation of a Borromean droplet after incorporating the repulsive force from quantum fluctuations. Outside the Borromean regime, we demonstrate an interesting phenomenon of droplet phase separation due to the competition between ternary and binary droplets. We further show that the transition between different droplets and gas phase can be conveniently tuned by boson numbers and interaction strengths. The study reveals the rich physics of a quantum droplet in three-component boson mixtures and sheds light on the more intriguing many-body bound state formed in multicomponent systems.
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Affiliation(s)
- Yinfeng Ma
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Cheng Peng
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xiaoling Cui
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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29
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Chen CA, Hung CL. Observation of Scale Invariance in Two-Dimensional Matter-Wave Townes Solitons. PHYSICAL REVIEW LETTERS 2021; 127:023604. [PMID: 34296901 DOI: 10.1103/physrevlett.127.023604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
We report near-deterministic generation of two-dimensional (2D) matter-wave Townes solitons and a precision test on scale invariance in attractive 2D Bose gases. We induce a shape-controlled modulational instability in an elongated 2D matter wave to create an array of isolated solitary waves of various sizes and peak densities. We confirm scale invariance by observing the collapse of solitary-wave density profiles onto a single curve in a dimensionless coordinate rescaled according to their peak densities and observe that the scale-invariant profiles measured at different coupling constants g can further collapse onto the universal profile of Townes solitons. The reported scaling behavior is tested with a nearly 60-fold difference in soliton interaction energies and allows us to discuss the impact of a non-negligible magnetic dipole-dipole interaction (MDDI) on 2D scale invariance. We confirm that the effect of MDDI in our alkali cesium quasi-2D samples effectively conforms to the same scaling law governed by a contact interaction to well within our experiment uncertainty.
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Affiliation(s)
- Cheng-An Chen
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Chen-Lung Hung
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
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30
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Bakkali-Hassani B, Maury C, Zou YQ, Le Cerf É, Saint-Jalm R, Castilho PCM, Nascimbene S, Dalibard J, Beugnon J. Realization of a Townes Soliton in a Two-Component Planar Bose Gas. PHYSICAL REVIEW LETTERS 2021; 127:023603. [PMID: 34296923 DOI: 10.1103/physrevlett.127.023603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 05/07/2021] [Accepted: 05/24/2021] [Indexed: 06/13/2023]
Abstract
Most experimental observations of solitons are limited to one-dimensional (1D) situations, where they are naturally stable. For instance, in 1D cold Bose gases, they exist for any attractive interaction strength g and particle number N. By contrast, in two dimensions, solitons appear only for discrete values of gN, the so-called Townes soliton being the most celebrated example. Here, we use a two-component Bose gas to prepare deterministically such a soliton: Starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We explore various interaction strengths, atom numbers, and sizes and confirm the existence of a solitonic behavior for a specific value of gN and arbitrary sizes, a hallmark of scale invariance.
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Affiliation(s)
- B Bakkali-Hassani
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - C Maury
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Y-Q Zou
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - É Le Cerf
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - R Saint-Jalm
- Department of Physics, Ludwig-Maximilians-Universität München, Schellingstrasse 4, D-80799 München, Germany
| | - P C M Castilho
- Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, Brazil
| | - S Nascimbene
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - J Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - J Beugnon
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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31
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Dong L, Kartashov YV. Rotating Multidimensional Quantum Droplets. PHYSICAL REVIEW LETTERS 2021; 126:244101. [PMID: 34213917 DOI: 10.1103/physrevlett.126.244101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Revised: 04/05/2021] [Accepted: 05/10/2021] [Indexed: 06/13/2023]
Abstract
We predict a new type of two- and three-dimensional stable quantum droplets persistently rotating in broad external two-dimensional and weakly anharmonic potential. Their evolution is described by the system of the Gross-Pitaevskii equations with Lee-Huang-Yang quantum corrections. Such droplets resemble whispering-gallery modes localized in the polar direction due to nonlinear interactions and, depending on their chemical potential and rotation frequency, they appear in rich variety of shapes, ranging from nearly flat-top or strongly localized rotating wave packets, to crescentlike objects extending nearly over the entire range of polar angles. Above critical rotation frequency quantum droplets transform into vortex droplets (in two dimensions) or vortex tori (in three dimensions), whose topological charge gradually increase with the increase of the modulus of chemical potential, and therefore they belong to the family of nonlinear modes connecting fundamental and vortex quantum droplets. Rotating quantum droplets are exceptionally robust objects, stable practically in the entire range of their existence.
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Affiliation(s)
- Liangwei Dong
- Department of Physics, Shaanxi University of Science & Technology, Xi'an 710021, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
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32
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Skov TG, Skou MG, Jørgensen NB, Arlt JJ. Observation of a Lee-Huang-Yang Fluid. PHYSICAL REVIEW LETTERS 2021; 126:230404. [PMID: 34170163 DOI: 10.1103/physrevlett.126.230404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Revised: 04/19/2021] [Accepted: 05/18/2021] [Indexed: 06/13/2023]
Abstract
We observe monopole oscillations in a mixture of Bose-Einstein condensates, where the usually dominant mean-field interactions are canceled. In this case, the system is governed by the next-order Lee-Huang-Yang (LHY) correction to the ground state energy, which describes the effect of quantum fluctuations. Experimentally such a LHY fluid is realized by controlling the atom numbers and interaction strengths in a ^{39}K spin mixture confined in a spherical trap potential. We measure the monopole oscillation frequency as a function of the LHY interaction strength as proposed recently by Jrgensen et al. [Phys. Rev. Lett. 121, 173403 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.173403] and find excellent agreement with simulations of the complete experiment including the excitation procedure and inelastic losses. This confirms that the system and its collective behavior are initially dominated by LHY interactions. Moreover, the monopole oscillation frequency is found to be stable against variations of the involved scattering lengths in a broad region around the ideal values, confirming the stabilizing effect of the LHY interaction. These results pave the way for using the nonlinearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.
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Affiliation(s)
- Thomas G Skov
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Magnus G Skou
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Nils B Jørgensen
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Jan J Arlt
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
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33
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Naidon P, Petrov DS. Mixed Bubbles in Bose-Bose Mixtures. PHYSICAL REVIEW LETTERS 2021; 126:115301. [PMID: 33798344 DOI: 10.1103/physrevlett.126.115301] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Revised: 11/17/2020] [Accepted: 01/14/2021] [Indexed: 06/12/2023]
Abstract
Repulsive Bose-Bose mixtures are known to either mix or phase separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with a pure phase of one of the components. This is a beyond-mean-field effect that occurs for unequal masses or unequal intraspecies coupling constants and is due to a competition between the mean-field term, quadratic in densities, and a nonquadratic beyond-mean-field correction. We find parameters of the mixed-bubble regime in all dimensions and discuss implications for current experiments.
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Affiliation(s)
- P Naidon
- Strangeness Nuclear Physics Laboratory, RIKEN Nishina Centre, Wakō 351-0198, Japan
| | - D S Petrov
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
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34
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Otajonov SR, Tsoy EN, Abdullaev FK. Variational approximation for two-dimensional quantum droplets. Phys Rev E 2021; 102:062217. [PMID: 33466111 DOI: 10.1103/physreve.102.062217] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 12/08/2020] [Indexed: 11/07/2022]
Abstract
The dynamics of a two-dimensional Bose-Einstein condensate in a presence of quantum fluctuations is studied. The properties of localized density distributions, quantum droplets (QDs), are analyzed by means of the variational approach. It is demonstrated that the super-Gaussian function gives a good approximation for profiles of fundamental QDs and droplets with nonzero vorticity. The dynamical equations for parameters of QDs are obtained. Fixed points of these equations determine the parameters of stationary QDs. The period of small oscillations of QDs near the stationary state is estimated. It is obtained that periodic modulations of the strength of quantum fluctuations can actuate different processes, including resonance oscillations of the QD parameters, an emission of waves and a splitting of QDs into smaller droplets.
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Affiliation(s)
- Sherzod R Otajonov
- Physical-Technical Institute of the Uzbek Academy of Sciences, Chingiz Aytmatov str. 2-B, Tashkent 100084, Uzbekistan
| | - Eduard N Tsoy
- Physical-Technical Institute of the Uzbek Academy of Sciences, Chingiz Aytmatov str. 2-B, Tashkent 100084, Uzbekistan
| | - Fatkhulla Kh Abdullaev
- Physical-Technical Institute of the Uzbek Academy of Sciences, Chingiz Aytmatov str. 2-B, Tashkent 100084, Uzbekistan
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35
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Self-Evaporation Dynamics of Quantum Droplets in a 41K-87Rb Mixture. APPLIED SCIENCES-BASEL 2021. [DOI: 10.3390/app11020866] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We theoretically investigate the self-evaporation dynamics of quantum droplets in a 41K-87Rb mixture, in free-space. The dynamical formation of the droplet and the effects related to the presence of three-body losses are analyzed by means of numerical simulations. We identify a regime of parameters allowing for the observation of the droplet self-evaporation in a feasible experimental setup.
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36
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Bisset RN, Ardila LAP, Santos L. Quantum Droplets of Dipolar Mixtures. PHYSICAL REVIEW LETTERS 2021; 126:025301. [PMID: 33512237 DOI: 10.1103/physrevlett.126.025301] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Accepted: 11/03/2020] [Indexed: 05/12/2023]
Abstract
Recently achieved two-component dipolar Bose-Einstein condensates open exciting possibilities for the study of mixtures of ultradilute quantum liquids. While nondipolar self-bound (without external confinement) mixtures are necessarily miscible with an approximately fixed ratio between the two densities, the density ratio for the dipolar case is free. Therefore, self-bound dipolar mixtures present qualitatively novel and much richer physics, characterized by three possible ground-state phases: miscible, symmetric immiscible, and asymmetric immiscible, which may in principle occur at any population imbalance. Self-bound immiscible droplets are possible due to mutual nonlocal intercomponent attraction, which results in the formation of a droplet molecule. Moreover, our analysis of the impurity regime shows that quantum fluctuations in the majority component crucially modify the miscibility of impurities. Our work opens intriguing perspectives for the exploration of spinor physics in ultradilute liquids, which should resemble to some extent that of ^{4}He-^{3}He droplets and impurity-doped helium droplets.
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Affiliation(s)
- R N Bisset
- Institut für Theoretische Physik, Leibniz Universität Hannover, Germany
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck, Austria
| | - L A Peña Ardila
- Institut für Theoretische Physik, Leibniz Universität Hannover, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Germany
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37
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Smith JC, Baillie D, Blakie PB. Quantum Droplet States of a Binary Magnetic Gas. PHYSICAL REVIEW LETTERS 2021; 126:025302. [PMID: 33512210 DOI: 10.1103/physrevlett.126.025302] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Accepted: 11/03/2020] [Indexed: 06/12/2023]
Abstract
Quantum droplets can emerge in bosonic binary magnetic gases (BMGs) from the interplay of short- and long-ranged interactions, and quantum fluctuations. We develop an extended mean field theory for this system and use it to predict equilibrium and dynamical properties of BMG droplets. We present a phase diagram and characterize miscible and immiscible droplet states. We also show that a single-component self-bound droplet can bind another magnetic component, which is not in the droplet regime, due to the interspecies dipole-dipole interactions. Our results should be realizable in experiments with mixtures of highly magnetic lanthanide atoms.
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Affiliation(s)
- Joseph C Smith
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - D Baillie
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - P B Blakie
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Otago, Dunedin 9016, New Zealand
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38
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Morera I, Astrakharchik GE, Polls A, Juliá-Díaz B. Universal Dimerized Quantum Droplets in a One-Dimensional Lattice. PHYSICAL REVIEW LETTERS 2021; 126:023001. [PMID: 33512190 DOI: 10.1103/physrevlett.126.023001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2020] [Accepted: 12/14/2020] [Indexed: 06/12/2023]
Abstract
The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive intercomponent and repulsive intracomponent interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by the density matrix renormalization group method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely, scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state and identify conditions for the formation of a solitonic solution. Our predictions are relevant to experiments with dipolar atoms and two-component mixtures.
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Affiliation(s)
- Ivan Morera
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, Barcelona 08028, Spain
| | - Grigori E Astrakharchik
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, Spain
| | - Artur Polls
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, Barcelona 08028, Spain
| | - Bruno Juliá-Díaz
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028 Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, Barcelona 08028, Spain
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39
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Böttcher F, Schmidt JN, Hertkorn J, Ng KSH, Graham SD, Guo M, Langen T, Pfau T. New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:012403. [PMID: 33176284 DOI: 10.1088/1361-6633/abc9ab] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.
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Affiliation(s)
- Fabian Böttcher
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Jan-Niklas Schmidt
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Jens Hertkorn
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Kevin S H Ng
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Sean D Graham
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Mingyang Guo
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Tim Langen
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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40
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The Breakup of a Helium Cluster After Removing Attractive Interaction Among a Significant Number of Atoms in the Cluster. Sci Rep 2020; 10:5767. [PMID: 32238856 PMCID: PMC7113238 DOI: 10.1038/s41598-020-62732-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 03/13/2020] [Indexed: 11/26/2022] Open
Abstract
The breakup of a quantum liquid droplet is examined through a 4He cluster by removing the attractive tail in the interaction between some of the atoms in the system with the diffusion quantum Monte Carlo simulation. The ground-state energy, kinetic energy, cluster size, and density profile of the cluster are evaluated against the percentage of the atoms without the attractive tail. The condition for the cluster to lose its ability to form a quantum liquid droplet at zero temperature is found and analyzed. The cluster is no longer able to form a quantum liquid droplet when about two-thirds of pairs of attractive interaction are removed. The findings are helpful to the current studies on the formation of quantum liquid droplets from cold atoms.
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41
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Hu H, Liu XJ. Consistent Theory of Self-Bound Quantum Droplets with Bosonic Pairing. PHYSICAL REVIEW LETTERS 2020; 125:195302. [PMID: 33216582 DOI: 10.1103/physrevlett.125.195302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Accepted: 10/06/2020] [Indexed: 06/11/2023]
Abstract
We revisit the Bogoliubov theory of quantum droplets proposed by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302] for an ultracold Bose-Bose mixture, where the mean-field collapse is stabilized by the Lee-Huang-Yang quantum fluctuations. We show that a loophole in Petrov's theory, i.e., the ignorance of the softening complex Bogoliubov spectrum, can be naturally removed by the introduction of bosonic pairing. The pairing leads to weaker mean-field attractions, and also a stronger Lee-Huang-Yang term in the case of unequal intraspecies interactions. As a result, the equilibrium density for the formation of self-bound droplets significantly decreases in the deep droplet regime, in agreement with a recent observation from diffusion Monte Carlo simulations. Our construction of a consistent Bogoliubov theory paves the way to understand the puzzling low critical number of small quantum droplets observed in the experiment [C. Cabrera et al., Science 359, 301 (2018)SCIEAS0036-807510.1126/science.aao5686].
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Affiliation(s)
- Hui Hu
- Centre for Quantum Technology Theory, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| | - Xia-Ji Liu
- Centre for Quantum Technology Theory, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
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42
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Dos Santos MCP, Malomed BA, Cardoso WB. Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions. Phys Rev E 2020; 102:042209. [PMID: 33212641 DOI: 10.1103/physreve.102.042209] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2020] [Accepted: 09/22/2020] [Indexed: 06/11/2023]
Abstract
We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction (z), to a 2D mean-field equation. We address this problem for the confining potential with a singular term, viz., V_{z}(z)=2z^{2}+ζ^{2}/z^{2}, with constant ζ. A quantum phase transition is induced by the latter term, between the ground state (GS) of the harmonic oscillator and the 3D condensate split in two parallel noninteracting layers, which is a manifestation of the "superselection" effect. A realization of the respective physical setting is proposed, making use of resonant coupling to an optical field, with the resonance detuning modulated along z. The reduction of the full 3D Gross-Pitaevskii equation (GPE) to the 2D nonpolynomial Schrödinger equation (NPSE) is based on the factorized ansatz, with the z -dependent multiplier represented by an exact GS solution of the 1D Schrödinger equation with potential V_{z}(z). For both repulsive and attractive signs of the nonlinearity, the 2D NPSE produces GS and vortex states, that are virtually indistinguishable from the respective numerical solutions provided by full 3D GPE. In the case of the self-attraction, the threshold for the onset of the collapse, predicted by the 2D NPSE, is also virtually identical to its counterpart obtained from the 3D equation. In the same case, stability and instability of vortices with topological charge S=1, 2, and 3 are considered in detail. Thus, the procedure of the spatial-dimension reduction, 3D → 2D, produces very accurate results, and it may be used in other settings.
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Affiliation(s)
- Mateus C P Dos Santos
- Instituto de Física, Universidade Federal de Goiás 74.690-970, Goiânia, Goiás, Brazil
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
| | - Wesley B Cardoso
- Instituto de Física, Universidade Federal de Goiás 74.690-970, Goiânia, Goiás, Brazil
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43
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Mordini C, Trypogeorgos D, Wolswijk L, Lamporesi G, Ferrari G. Single-shot reconstruction of the density profile of a dense atomic gas. OPTICS EXPRESS 2020; 28:29408-29418. [PMID: 33114841 DOI: 10.1364/oe.397567] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 07/14/2020] [Indexed: 06/11/2023]
Abstract
Partial transfer absorption imaging (PTAI) of ultracold atoms allows for repeated and minimally-destructive measurements of an atomic ensemble. Here, we present a reconstruction technique based on PTAI that can be used to piece together the non-uniform spatial profile of high-density atomic samples using multiple measurements. We achieved a thirty-fold increase of the effective dynamic range of our imaging, and were able to image otherwise saturated samples with unprecedented accuracy of both low- and high-density features.
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44
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He L, Gao P, Yu ZQ. Normal-Superfluid Phase Separation in Spin-Half Bosons at Finite Temperature. PHYSICAL REVIEW LETTERS 2020; 125:055301. [PMID: 32794831 DOI: 10.1103/physrevlett.125.055301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2019] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Abstract
For pseudospin-half bosons with interspin attraction and intraspin repulsion, the normal phase and Bose condensed phase can coexist at finite temperature. The homogeneous system is unstable against the spinodal decomposition within a medium density interval, and, consequently, a normal-superfluid phase separation takes place. The isothermal equation of state shows a characteristic plateau in the P-V (pressure-volume) diagram, which is reminiscent of a classical gas-liquid transition, although, unlike the latter, the coexistence lines never terminate at a critical point as temperature increases. In a harmonic trap, the phase separation can be revealed by the density profile of the atomic cloud, which exhibits a sudden jump across the phase boundary.
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Affiliation(s)
- Li He
- College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China
| | - Peipei Gao
- Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
| | - Zeng-Qiang Yu
- Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
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45
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Marchukov OV, Malomed BA, Dunjko V, Ruhl J, Olshanii M, Hulet RG, Yurovsky VA. Quantum Fluctuations of the Center of Mass and Relative Parameters of Nonlinear Schrödinger Breathers. PHYSICAL REVIEW LETTERS 2020; 125:050405. [PMID: 32794875 DOI: 10.1103/physrevlett.125.050405] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Revised: 03/06/2020] [Accepted: 07/02/2020] [Indexed: 06/11/2023]
Abstract
We study quantum fluctuations of macroscopic parameters of a nonlinear Schrödinger breather-a nonlinear superposition of two solitons, which can be created by the application of a fourfold quench of the scattering length to the fundamental soliton in a self-attractive quasi-one-dimensional Bose gas. The fluctuations are analyzed in the framework of the Bogoliubov approach in the limit of a large number of atoms N, using two models of the vacuum state: white noise and correlated noise. The latter model, closer to the ab initio setting by construction, leads to a reasonable agreement, within 20% accuracy, with fluctuations of the relative velocity of constituent solitons obtained from the exact Bethe-ansatz results [Phys. Rev. Lett. 119, 220401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.220401] in the opposite low-N limit (for N≤23). We thus confirm, for macroscopic N, the breather dissociation time to be within the limits of current cold-atom experiments. Fluctuations of soliton masses, phases, and positions are also evaluated and may have experimental implications.
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Affiliation(s)
- Oleksandr V Marchukov
- Institute for Applied Physics, Technical University of Darmstadt, 64289 Darmstadt, Germany
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, 6997801 Tel Aviv, Israel
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
| | - Vanja Dunjko
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Joanna Ruhl
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Maxim Olshanii
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Randall G Hulet
- Department of Physics and Astronomy, Rice University, Houston,Texas 77005, USA
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46
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Mestrom PMA, Colussi VE, Secker T, Groeneveld GP, Kokkelmans SJJMF. van der Waals Universality near a Quantum Tricritical Point. PHYSICAL REVIEW LETTERS 2020; 124:143401. [PMID: 32338969 DOI: 10.1103/physrevlett.124.143401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 03/10/2020] [Indexed: 06/11/2023]
Abstract
We study the three-body scattering hypervolume D of atoms whose scattering length a is on the order of or smaller than the typical range r_{vdW} of the van der Waals attraction. We find that the real part of D behaves universally in this weakly interacting regime (|a|/r_{vdW}≲1) in the absence of trimer resonances. This universality originates from hard-spherelike collisions that dominate elastic three-body scattering. We use this result to make quantitative predictions for the thermodynamics and elementary excitations of an atomic Bose-Einstein condensate in the vicinity of a quantum tricritical point, including quantum droplets stabilized by effective three-body interactions.
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Affiliation(s)
- P M A Mestrom
- Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, Netherlands
| | - V E Colussi
- Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, Netherlands
| | - T Secker
- Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, Netherlands
| | - G P Groeneveld
- Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, Netherlands
| | - S J J M F Kokkelmans
- Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, Netherlands
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A Dual-Species Bose-Einstein Condensate with Attractive Interspecies Interactions. CONDENSED MATTER 2020. [DOI: 10.3390/condmat5010021] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We report on the production of a 41 K- 87 Rb dual-species Bose–Einstein condensate with tunable interspecies interaction and we study the mixture in the attractive regime; i.e., for negative values of the interspecies scattering length a 12 . The binary condensate is prepared in the ground state and confined in a pure optical trap. We exploit Feshbach resonances for tuning the value of a 12 . After compensating the gravitational sag between the two species with a magnetic field gradient, we drive the mixture into the attractive regime. We let the system evolve both in free space and in an optical waveguide. In both geometries, for strong attractive interactions, we observe the formation of self-bound states, recognizable as quantum droplets. Our findings prove that robust, long-lived droplet states can be realized in attractive two-species mixtures, despite the two atomic components possibly experiencing different potentials.
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Abstract
This article provides a focused review of recent findings which demonstrate, in some cases quite counter-intuitively, the existence of bound states with a singularity of the density pattern at the center; the states are physically meaningful because their total norm converges. One model of this type is based on the 2D Gross–Pitaevskii equation (GPE), which combines the attractive potential ∼ r − 2 and the quartic self-repulsive nonlinearity, induced by the Lee–Huang–Yang effect (quantum fluctuations around the mean-field state). The GPE demonstrates suppression of the 2D quantum collapse, driven by the attractive potential, and emergence of a stable ground state (GS), whose density features an integrable singularity ∼ r − 4 / 3 at r → 0 . Modes with embedded angular momentum exist too, but they are unstable. A counter-intuitive peculiarity of the model is that the GS exists even if the sign of the potential is reversed from attraction to repulsion, provided that its strength is small enough. This peculiarity finds a relevant explanation. The other model outlined in the review includes 1D, 2D, and 3D GPEs, with the septimal (seventh-order), quintic, and cubic self-repulsive terms, respectively. These equations give rise to stable singular solitons, which represent the GS for each dimension D, with the density singularity ∼ r − 2 / ( 4 − D ) . Such states may be considered the results of screening a “bare” delta-functional attractive potential by the respective nonlinearities.
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Ołdziejewski R, Górecki W, Pawłowski K, Rzążewski K. Strongly Correlated Quantum Droplets in Quasi-1D Dipolar Bose Gas. PHYSICAL REVIEW LETTERS 2020; 124:090401. [PMID: 32202868 DOI: 10.1103/physrevlett.124.090401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2019] [Accepted: 01/27/2020] [Indexed: 06/10/2023]
Abstract
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multiatom Schrödinger equation, we discover that such systems can exhibit not only the well-known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly repelling bosons by incorporating the Lieb-Liniger energy in a local density approximation and approaches the standard Gross-Pitaevskii equation (GPE) in the weakly interacting limit. Not only does such a framework provide an alternative mechanism of the droplet stability, but it also introduces means to further analyze this previously unexplored quantum phase. In the limiting strong repulsion case, yet another simple multiatom model is proposed. We stress that the celebrated Lee-Huang-Yang term in the GPE is not applicable in this case.
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Affiliation(s)
- Rafał Ołdziejewski
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - Wojciech Górecki
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - Krzysztof Pawłowski
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - Kazimierz Rzążewski
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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Mishra C, Santos L, Nath R. Self-Bound Doubly Dipolar Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2020; 124:073402. [PMID: 32142338 DOI: 10.1103/physrevlett.124.073402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2019] [Accepted: 01/28/2020] [Indexed: 06/10/2023]
Abstract
We analyze the physics of self-bound droplets in a doubly dipolar Bose-Einstein condensate composed by particles with both electric and magnetic dipole moments. Using the particularly relevant case of dysprosium, we show that the anisotropy of the doubly dipolar interaction potential is highly versatile and nontrivial, depending critically on the relative orientation and strength between the two dipole moments. This opens novel possibilities for exploring intriguing quantum many-body physics. Interestingly, by varying the angle between the two dipoles we find a dimensional crossover from quasi-one-dimensional to quasi-two-dimensional self-bound droplets. This opens a so far unique scenario in condensate physics, in which a dimensional crossover is solely driven by interactions in the absence of any confinement.
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Affiliation(s)
- Chinmayee Mishra
- Indian Institute of Science Education and Research, Pune 411 008, India
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, DE-30167 Hannover, Germany
| | - Rejish Nath
- Indian Institute of Science Education and Research, Pune 411 008, India
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