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Emergent symmetry at superradiance transition of a Bose condensate in two crossed beam cavities. Sci Bull (Beijing) 2018; 63:542-547. [PMID: 36658840 DOI: 10.1016/j.scib.2018.04.008] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Revised: 04/03/2018] [Accepted: 04/04/2018] [Indexed: 01/21/2023]
Abstract
Recently an experiment on superradiant transition of a Bose condensate in two crossed beam cavities has been reported by Léonard et al. in Nature 543, 87 (2017). The surprise is they find that across the superradiant transition, the cavity light can be emitted in any superposition of these two cavity modes. This indicates an additional U(1) symmetry that does not exist in the full Hamiltonian. In this paper we show that this symmetry is an emergent symmetry in the vicinity of the phase transition. We identify all the necessary conditions that are required for this emergent U(1) symmetry and show that this experiment is a special case that satisfies these conditions. We further show that the superradiant transition in this system can also be driven to a first order one when the system is tuned away from the point having the emergent symmetry.
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Zhao X, Liu N, Liang JQ. Collective atomic-population-inversion and stimulated radiation for two-component Bose-Einstein condensate in an optical cavity. OPTICS EXPRESS 2017; 25:8123-8137. [PMID: 28380930 DOI: 10.1364/oe.25.008123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this paper we investigate the ground-state properties and related quantum phase transitions for the two-component Bose-Einstein condensate in a single-mode optical cavity. Apart from the usual normal and superradiant phases, multi-stable macroscopic quantum states are realized by means of the spin-coherent-state variational method. We demonstrate analytically the stimulated radiation from a collective state of atomic population inversion, which does not exist in the normal Dicke model with single-component atoms. It is also revealed that the stimulated radiation can be generated only from one component of atoms and the other remains in the ordinary superradiant state. However, the order of superradiant and stimulated-radiation states is interchangeable between two components of atoms by tuning the relative atom-field couplings and the frequency detuning as well.
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Zheng W, Cooper NR. Superradiance Induced Particle Flow via Dynamical Gauge Coupling. PHYSICAL REVIEW LETTERS 2016; 117:175302. [PMID: 27824448 DOI: 10.1103/physrevlett.117.175302] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Indexed: 06/06/2023]
Abstract
We study fermions that are gauge coupled to a cavity mode via Raman-assisted hopping in a one-dimensional lattice. For an infinite lattice, we find a superradiant phase with an infinitesimal pumping threshold which induces a directed particle flow. We explore the fate of this flow in a finite lattice with boundaries, studying the nonequilibrium dynamics including fluctuation effects. The short-time dynamics is dominated by superradiance, while the long-time behavior is governed by cavity fluctuations. We show that the steady state in the finite lattice is not unique and can be understood in terms of coherent bosonic excitations above a Fermi surface in real space.
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Affiliation(s)
- W Zheng
- T. C. M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - N R Cooper
- T. C. M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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Fan J, Yu L, Chen G, Jia S. Phase-factor-dependent symmetries and quantum phases in a three-level cavity QED system. Sci Rep 2016; 6:25192. [PMID: 27139573 PMCID: PMC4853727 DOI: 10.1038/srep25192] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2015] [Accepted: 04/12/2016] [Indexed: 11/09/2022] Open
Abstract
Unlike conventional two-level particles, three-level particles may support some unitary-invariant phase factors when they interact coherently with a single-mode quantized light field. To gain a better understanding of light-matter interaction, it is thus necessary to explore the phase-factor-dependent physics in such a system. In this report, we consider the collective interaction between degenerate V-type three-level particles and a single-mode quantized light field, whose different components are labeled by different phase factors. We mainly establish an important relation between the phase factors and the symmetry or symmetry-broken physics. Specifically, we find that the phase factors affect dramatically the system symmetry. When these symmetries are breaking separately, rich quantum phases emerge. Finally, we propose a possible scheme to experimentally probe the predicted physics of our model. Our work provides a way to explore phase-factor-induced nontrivial physics by introducing additional particle levels.
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Affiliation(s)
- Jingtao Fan
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Lixian Yu
- Department of Physics, Shaoxing University, Shaoxing 312000, China
| | - Gang Chen
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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Klinder J, Keßler H, Bakhtiari MR, Thorwart M, Hemmerich A. Observation of a Superradiant Mott Insulator in the Dicke-Hubbard Model. PHYSICAL REVIEW LETTERS 2015; 115:230403. [PMID: 26684102 DOI: 10.1103/physrevlett.115.230403] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Indexed: 06/05/2023]
Abstract
It is well known that the bosonic Hubbard model possesses a Mott insulator phase. Likewise, it is known that the Dicke model exhibits a self-organized superradiant phase. By implementing an optical lattice inside of a high-finesse optical cavity, both models are merged such that an extended Hubbard model with cavity-mediated infinite range interactions arises. In addition to a normal superfluid phase, two superradiant phases are found, one of them coherent and hence superfluid and one incoherent Mott insulating.
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Affiliation(s)
- J Klinder
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - H Keßler
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - M Reza Bakhtiari
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
| | - M Thorwart
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
| | - A Hemmerich
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Wilczek Quantum Center, Zhejiang University of Technology, Hangzhou 310023, China
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Marchetti FM, Keeling J. Collective pairing of resonantly coupled microcavity polaritons. PHYSICAL REVIEW LETTERS 2014; 113:216405. [PMID: 25479511 DOI: 10.1103/physrevlett.113.216405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2013] [Indexed: 06/04/2023]
Abstract
We consider the possible phases of microcavity polaritons tuned near a bipolariton Feshbach resonance. We show that, as well as the regular polariton superfluid phase, a "molecular" superfluid exists, with (quasi-)long-range order only for pairs of polaritons. We describe the experimental signatures of this state. Using variational approaches we find the phase diagram (critical temperature, density, and exciton-photon detuning). Unlike for ultracold atoms, the molecular superfluid is not inherently unstable, and our phase diagram suggests it is attainable in current experiments.
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Affiliation(s)
- F M Marchetti
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid 28049, Spain
| | - Jonathan Keeling
- SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom
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Rajaram S, Trivedi N. Photon counting as a probe of superfluidity in a two-band Bose-Hubbard system coupled to a cavity field. PHYSICAL REVIEW LETTERS 2013; 111:243603. [PMID: 24483660 DOI: 10.1103/physrevlett.111.243603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2012] [Revised: 08/14/2013] [Indexed: 06/03/2023]
Abstract
We show that photon number measurement can be used to detect superfluidity for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon coupling induces transitions between the two internal atomic levels and results in entangled polaritonic states. In the presence of a cavity field, we find different photon numbers in the Mott-insulating versus superfluid phases, providing a method of distinguishing the atomic phases by photon counting. Furthermore, we examine the dynamics of the photon field after a rapid quench to zero atomic hopping by increasing the well depth. We find a robust correlation between the field's quench dynamics and the initial superfluid order parameter, thereby providing a novel and accurate method of determining the order parameter.
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Affiliation(s)
- Sara Rajaram
- The Ohio State University, 191 W. Woodruff Avenue, Columbus, Ohio 43210, USA
| | - Nandini Trivedi
- The Ohio State University, 191 W. Woodruff Avenue, Columbus, Ohio 43210, USA
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Schmidt S, Blatter G. Excitations of strongly correlated lattice polaritons. PHYSICAL REVIEW LETTERS 2010; 104:216402. [PMID: 20867121 DOI: 10.1103/physrevlett.104.216402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2010] [Indexed: 05/29/2023]
Abstract
We present an analytic slave-boson approach to calculate the elementary excitations of the Jaynes-Cummings-Hubbard model (JCHM) describing strongly correlated polaritons on a lattice in various quantum optical systems. In the superfluid phase near the Mott transition we find a gapless, linear Goldstone mode and a gapped amplitude mode corresponding to phase and density fluctuations, respectively. The sound velocity of the Goldstone mode develops a peculiar anomaly as a function of detuning at low densities, which persists into the weakly interacting regime of a polariton BEC.
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Affiliation(s)
- S Schmidt
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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Schmidt S, Blatter G. Strong coupling theory for the Jaynes-Cummings-Hubbard model. PHYSICAL REVIEW LETTERS 2009; 103:086403. [PMID: 19792743 DOI: 10.1103/physrevlett.103.086403] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2009] [Indexed: 05/28/2023]
Abstract
We present an analytic strong-coupling approach to the phase diagram and elementary excitations of the Jaynes-Cummings-Hubbard model describing a superfluid-insulator transition of polaritons in an array of coupled QED cavities. In the Mott phase, we find four modes corresponding to particle or hole excitations with lower and upper polaritons, respectively. Simple formulas are derived for the dispersion and spectral weights within a strong-coupling random-phase approximation (RPA). The phase boundary is calculated beyond RPA by including the leading correction due to quantum fluctuations.
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Affiliation(s)
- S Schmidt
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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