1
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Chepelianskii AD, Shepelyansky DL. Quantum Synchronization and Entanglement of Dissipative Qubits Coupled to a Resonator. ENTROPY (BASEL, SWITZERLAND) 2024; 26:415. [PMID: 38785664 PMCID: PMC11119807 DOI: 10.3390/e26050415] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2024] [Revised: 04/21/2024] [Accepted: 05/10/2024] [Indexed: 05/25/2024]
Abstract
In a dissipative regime, we study the properties of several qubits coupled to a driven resonator in the framework of a Jaynes-Cummings model. The time evolution and the steady state of the system are numerically analyzed within the Lindblad master equation, with up to several million components. Two semi-analytical approaches, at weak and strong (semiclassical) dissipations, are developed to describe the steady state of this system and determine its validity by comparing it with the Lindblad equation results. We show that the synchronization of several qubits with the driving phase can be obtained due to their coupling to the resonator. We establish the existence of two different qubit synchronization regimes: In the first one, the semiclassical approach describes well the dynamics of qubits and, thus, their quantum features and entanglement are suppressed by dissipation and the synchronization is essentially classical. In the second one, the entangled steady state of a pair of qubits remains synchronized in the presence of dissipation and decoherence, corresponding to the regime non-existent in classical synchronization.
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Affiliation(s)
| | - Dima L. Shepelyansky
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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2
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Zhu GL, Hu CS, Wang H, Qin W, Lü XY, Nori F. Nonreciprocal Superradiant Phase Transitions and Multicriticality in a Cavity QED System. PHYSICAL REVIEW LETTERS 2024; 132:193602. [PMID: 38804940 DOI: 10.1103/physrevlett.132.193602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Revised: 02/06/2024] [Accepted: 04/01/2024] [Indexed: 05/29/2024]
Abstract
We demonstrate the emergence of nonreciprocal superradiant phase transitions and novel multicriticality in a cavity quantum electrodynamics system, where a two-level atom interacts with two counterpropagating modes of a whispering-gallery-mode microcavity. The cavity rotates at a certain angular velocity and is directionally squeezed by a unidirectional parametric pumping χ^{(2)} nonlinearity. The combination of cavity rotation and directional squeezing leads to nonreciprocal first- and second-order superradiant phase transitions. These transitions do not require ultrastrong atom-field couplings and can be easily controlled by the external pump field. Through a full quantum description of the system Hamiltonian, we identify two types of multicritical points in the phase diagram, both of which exhibit controllable nonreciprocity. These results open a new door for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering various integrated nonreciprocal quantum devices.
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Affiliation(s)
- Gui-Lei Zhu
- Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wakoshi, Saitama 351-0198, Japan
| | - Chang-Sheng Hu
- Department of Physics, Anhui Normal University, Wuhu 241000, China
| | - Hui Wang
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wakoshi, Saitama 351-0198, Japan
| | - Wei Qin
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wakoshi, Saitama 351-0198, Japan
- Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China
| | - Xin-You Lü
- School of Physics, Huazhong University of Science and Technology and Wuhan Institute of Quantum Technology, Wuhan 430074, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wakoshi, Saitama 351-0198, Japan
- Quantum Computing Center, RIKEN, Wakoshi, Saitama 351-0198, Japan
- Department of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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3
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Sudler AJ, Talukdar J, Blume D. Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response. Phys Rev E 2024; 109:054207. [PMID: 38907472 DOI: 10.1103/physreve.109.054207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 04/23/2024] [Indexed: 06/24/2024]
Abstract
Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three nonlinear dissipative terms. Since two of the nonlinear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.
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Affiliation(s)
- A J Sudler
- Homer L. Dodge Department of Physics and Astronomy, and Center for Quantum Research and Technology, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
| | - J Talukdar
- Homer L. Dodge Department of Physics and Astronomy, and Center for Quantum Research and Technology, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
| | - D Blume
- Homer L. Dodge Department of Physics and Astronomy, and Center for Quantum Research and Technology, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
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4
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He SW, Deng ZJ, Xie Y, Wang YY, Chen PX. Entanglement signatures for quantum synchronization with single-ion phonon laser. OPTICS EXPRESS 2024; 32:13998-14009. [PMID: 38859357 DOI: 10.1364/oe.515903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 03/22/2024] [Indexed: 06/12/2024]
Abstract
The entanglement properties of quantum synchronization, based on a single-ion phonon laser subjected to an external drive, have been studied. It is found that the maximum value of steady-state entanglement between the ion's internal and external states occurs near the noiseless boundary from synchronization to unsynchronization, accompanied by noticeable oscillatory behaviors during the corresponding time evolution of entanglement. In addition, the later time dynamics of entanglement also indicates the occurrence of frequency entrainment, as evidenced by the strong consistency between the bending of the observed frequency and the emergence of Liouvillian exceptional points (LEPs) in the first two eigenvalues of the Liouvillian eigenspectrum. Moreover, the emergence of LEPs, which is intimately associated with frequency entrainment, should be widely observed in quantum synchronization and can be explored in LEPs-based applications.
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Nadolny T, Bruder C. Macroscopic Quantum Synchronization Effects. PHYSICAL REVIEW LETTERS 2023; 131:190402. [PMID: 38000429 DOI: 10.1103/physrevlett.131.190402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 10/16/2023] [Indexed: 11/26/2023]
Abstract
We theoretically describe macroscopic quantum synchronization effects occurring in a network of all-to-all coupled quantum limit-cycle oscillators. The coupling causes a transition to synchronization as indicated by the presence of global phase coherence. We demonstrate that the microscopic quantum properties of the oscillators qualitatively shape the synchronization behavior in a macroscopically large network. Specifically, they result in a blockade of collective synchronization that is not expected for classical oscillators. Additionally, the macroscopic ensemble shows emergent behavior not present at the level of two coupled quantum oscillators.
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Affiliation(s)
- Tobias Nadolny
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Christoph Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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6
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Murtadho T, Vinjanampathy S, Thingna J. Cooperation and Competition in Synchronous Open Quantum Systems. PHYSICAL REVIEW LETTERS 2023; 131:030401. [PMID: 37540879 DOI: 10.1103/physrevlett.131.030401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 06/13/2023] [Indexed: 08/06/2023]
Abstract
Synchronization between limit cycle oscillators can arise through entrainment to an external drive or through mutual coupling. The interplay between the two mechanisms has been studied in classical synchronizing systems, but not in quantum systems. Here, we point out that competition and cooperation between the two mechanisms can occur due to phase pulling and phase repulsion in quantum systems. We study their interplay in collectively driven degenerate quantum thermal machines and show that these mechanisms either cooperate or compete depending on the working mode of the machine (refrigerator or engine). The entrainment-mutual synchronization interplay persists with an increase in the number of degenerate levels, while in the thermodynamic limit of degeneracy, mutual synchronization dominates. Overall, our work investigates the effect of degeneracy and multilevel scaling of quantum synchronization and shows how different synchronizing mechanisms can cooperate and compete in quantum systems.
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Affiliation(s)
- Taufiq Murtadho
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
- Basic Science Program, Korea University of Science and Technology, Daejeon 34113, Republic of Korea
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Sai Vinjanampathy
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
- Centre of Excellence in Quantum Information, Computation, Science and Technology, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore, Singapore
| | - Juzar Thingna
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
- Basic Science Program, Korea University of Science and Technology, Daejeon 34113, Republic of Korea
- Department of Physics and Applied Physics, University of Massachusetts, Lowell, Massachusetts 01854, USA
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7
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Souza LDS, Dos Prazeres LF, Iemini F. Sufficient Condition for Gapless Spin-Boson Lindbladians, and Its Connection to Dissipative Time Crystals. PHYSICAL REVIEW LETTERS 2023; 130:180401. [PMID: 37204909 DOI: 10.1103/physrevlett.130.180401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Revised: 02/06/2023] [Accepted: 04/12/2023] [Indexed: 05/21/2023]
Abstract
We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems and permutationally invariant systems. The condition relates a nonzero macroscopic cumulant correlation in the steady state to the presence of gapless modes in the Lindbladian. In phases arising from competing coherent and dissipative Lindbladian terms, we argue that such gapless modes, concomitant with angular momentum conservation, can lead to persistent dynamics in the spin observables with the possible formation of dissipative time crystals. We study different models within this perspective, from Lindbladians with Hermitian jump operators, to non-Hermitian ones composed by collective spins and Floquet spin-boson systems. We also provide a simple analytical proof for the exactness of the mean-field semiclassical approach in such systems based on a cumulant expansion.
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Affiliation(s)
- Leonardo da Silva Souza
- Instituto de Física, Universidade Federal Fluminense, Avenida General Milton Tavares de Souza s/n, Gragoatá, 24210-346 Niterói, Rio de Janeiro, Brazil
| | - Luis Fernando Dos Prazeres
- Instituto de Física, Universidade Federal Fluminense, Avenida General Milton Tavares de Souza s/n, Gragoatá, 24210-346 Niterói, Rio de Janeiro, Brazil
| | - Fernando Iemini
- Instituto de Física, Universidade Federal Fluminense, Avenida General Milton Tavares de Souza s/n, Gragoatá, 24210-346 Niterói, Rio de Janeiro, Brazil
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8
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Kato Y, Nakao H. Turing instability in quantum activator–inhibitor systems. Sci Rep 2022; 12:15573. [PMID: 36114210 PMCID: PMC9481611 DOI: 10.1038/s41598-022-19010-0] [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: 04/07/2022] [Accepted: 08/23/2022] [Indexed: 11/26/2022] Open
Abstract
Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study, we show that Turing instability can occur in a quantum dissipative system and analyze its quantum features such as entanglement and the effect of measurement. We propose a degenerate parametric oscillator with nonlinear damping in quantum optics as a quantum activator–inhibitor unit and demonstrate that a system of two such units can undergo Turing instability when diffusively coupled with each other. The Turing instability induces nonuniformity and entanglement between the two units and gives rise to a pair of nonuniform states that are mixed due to quantum noise. Further performing continuous measurement on the coupled system reveals the nonuniformity caused by the Turing instability. Our results extend the universality of the Turing mechanism to the quantum realm and may provide a novel perspective on the possibility of quantum nonequilibrium self-organization and its application in quantum technologies.
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9
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Souza LDS, Manzano G, Fazio R, Iemini F. Collective effects on the performance and stability of quantum heat engines. Phys Rev E 2022; 106:014143. [PMID: 35974546 DOI: 10.1103/physreve.106.014143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.
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Affiliation(s)
- Leonardo da Silva Souza
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, Brazil
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos 6627, Belo Horizonte Minas Gerais 31270-901, Brazil
| | - Gonzalo Manzano
- Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC, Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Rosario Fazio
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151, Trieste, Italy
- Dipartimento di Fisica, Università di Napoli "Federico II," Monte S. Angelo, I-80126 Naples, Italy
| | - Fernando Iemini
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, Brazil
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151, Trieste, Italy
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10
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Kato Y, Nakao H. A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint. CHAOS (WOODBURY, N.Y.) 2022; 32:063133. [PMID: 35778147 DOI: 10.1063/5.0088559] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 05/24/2022] [Indexed: 06/15/2023]
Abstract
We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but it has not been defined explicitly for quantum nonlinear oscillators. In this study, we define the asymptotic phase for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the fundamental oscillation frequency. By using the quantum van der Pol oscillator with a Kerr effect as an example, we illustrate that the proposed asymptotic phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes.
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Affiliation(s)
- Yuzuru Kato
- Department of Complex and Intelligent Systems, Future University Hakodate, Hokkaido 041-8655, Japan
| | - Hiroya Nakao
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
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11
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Hotter C, Plankensteiner D, Kazakov G, Ritsch H. Continuous multi-step pumping of the optical clock transition in alkaline-earth atoms with minimal perturbation. OPTICS EXPRESS 2022; 30:5553-5568. [PMID: 35209515 DOI: 10.1364/oe.445976] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/03/2022] [Indexed: 06/14/2023]
Abstract
A suitable scheme to continuously create inversion on an optical clock transition with negligible perturbation is a key missing ingredient required to build an active optical atomic clock. Repumping of the atoms on the narrow transition typically needs several pump lasers in a multi step process involving several auxiliary levels. In general this creates large effective level shifts and a line broadening, strongly limiting clock accuracy. Here we present an extensive theoretical study for a realistic multi-level implementation in search of parameter regimes where a sufficient inversion can be achieved with minimal perturbations. Fortunately we are able to identify a useful operating regime, where the frequency shifts remain small and controllable, only weakly perturbing the clock transition for useful pumping rates. For practical estimates of the corresponding clock performance, we introduce a straightforward mapping of the multilevel pump scheme to an effective energy shift and broadening of parameters for the reduced two-level laser model system. This allows us to evaluate the resulting laser power and spectrum using well-known methods.
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12
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Bychek A, Hotter C, Plankensteiner D, Ritsch H. Superradiant lasing in inhomogeneously broadened ensembles with spatially varying coupling. OPEN RESEARCH EUROPE 2021; 1:73. [PMID: 37645148 PMCID: PMC10446144 DOI: 10.12688/openreseurope.13781.2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/17/2021] [Indexed: 08/31/2023]
Abstract
Background: Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Methods: Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator. Results: We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth. Conclusions: We show how sufficiently large numbers of atoms subject to strong optical pumping can induce synchronization of the atomic dipoles over a large bandwidth. This generates collective stimulated emission of light into the cavity mode leading to narrow-band laser emission at the average of the atomic frequency distribution. The linewidth is orders of magnitudes smaller than that of the cavity as well as the inhomogeneous gain broadening and exhibits reduced sensitivity to cavity frequency noise.
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Affiliation(s)
- Anna Bychek
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, 6020, Austria
| | - Christoph Hotter
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, 6020, Austria
| | - David Plankensteiner
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, 6020, Austria
| | - Helmut Ritsch
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, 6020, Austria
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13
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Shankar A, Reilly JT, Jäger SB, Holland MJ. Subradiant-to-Subradiant Phase Transition in the Bad Cavity Laser. PHYSICAL REVIEW LETTERS 2021; 127:073603. [PMID: 34459626 DOI: 10.1103/physrevlett.127.073603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Accepted: 07/08/2021] [Indexed: 06/13/2023]
Abstract
We show that the onset of steady-state superradiance in a bad cavity laser is preceded by a dissipative phase transition between two distinct phases of steady-state subradiance. The transition is marked by a nonanalytic behavior of the cavity output power and the mean atomic inversion, as well as a discontinuity in the variance of the collective atomic inversion. In particular, for repump rates below a critical value, the cavity output power is strongly suppressed and does not increase with the atom number, while it scales linearly with atom number above this value. Remarkably, we find that the atoms are in a macroscopically entangled steady state near the critical region with a vanishing fraction of unentangled atoms in the large atom number limit.
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Affiliation(s)
- Athreya Shankar
- Center for Quantum Physics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Jarrod T Reilly
- JILA, NIST, and Department of Physics, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Simon B Jäger
- JILA, NIST, and Department of Physics, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Murray J Holland
- JILA, NIST, and Department of Physics, University of Colorado Boulder, Boulder, Colorado 80309, USA
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14
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Entanglement protection of classically driven qubits in a lossy cavity. Sci Rep 2021; 11:16259. [PMID: 34376732 PMCID: PMC8355265 DOI: 10.1038/s41598-021-95623-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2021] [Accepted: 07/28/2021] [Indexed: 11/08/2022] Open
Abstract
Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we investigate the effect of the classical driving field on the generation entanglement between two qubits interacting with a bosonic environment. We discuss the effect of the classical field on the generation of entanglement between two (different) qubits and the conditions under which it has a constructive role in protecting the initial-state entanglement from decay induced by its environment. In particular, in the case of similar qubits, we locate a stationary sub-space of the system Hilbert space, characterized by states non depending on the environment properties as well as on the classical driving-field. Thus, we are able to determine the conditions to achieve maximally entangled stationary states after a transient interaction with the environment. We show that, overall, the classical driving field has a constructive role for the entanglement protection in the strong coupling regime. Also, we illustrate that a factorable initial-state can be driven in an entangled state and, even, in an entangled steady-state after the interaction with the environment.
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15
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Cabot A, Luca Giorgi G, Zambrini R. Synchronization and coalescence in a dissipative two-qubit system. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2020.0850] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The possibility of detuned spins displaying synchronous oscillations in local observables is analysed in the presence of coupling, collective dissipation and incoherent pumping. We show that there exist two distinct scenarios in which synchronization can emerge, related respectively to the presence of a non-degenerate long-lived eigenmode and to the presence of a single-frequency regime. Both scenarios can arise by tuning parameters in this system, owing to the presence of coalascence. The former, known as transient synchronization, is here generalized in the presence of incoherent pumping, and is due to long-lasting coherences leading to a progressive frequency selection. On the other hand, in spite of the spins detuning, the dynamics can be governed by a single frequency. Still, we show that synchronization can be established only after a transient, when phase-locking arises. Spectral features of synchronization in these two scenarios are analysed for two-time correlations.
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Affiliation(s)
- Albert Cabot
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain
| | - Roberta Zambrini
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain
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16
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Zhang Y, Shan C, Mølmer K. Ultranarrow Superradiant Lasing by Dark Atom-Photon Dressed States. PHYSICAL REVIEW LETTERS 2021; 126:123602. [PMID: 33834832 DOI: 10.1103/physrevlett.126.123602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 12/22/2020] [Accepted: 02/22/2021] [Indexed: 06/12/2023]
Abstract
We show that incoherent pumping of an optical lattice clock system with ultracold strontium-88 atoms produces laser light with a ≃10 Hz linewidth when the atoms are exposed to a magnetic field. This linewidth is orders of magnitude smaller than both the cavity linewidth and the incoherent atomic decay and excitation rates. The narrow lasing is due to an interplay of multiatom superradiant effects and the coupling of bright and dark atom-light dressed states by the magnetic field.
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Affiliation(s)
- Yuan Zhang
- Henan Key Laboratory of Diamond Optoelectronic Materials and Devices, Key Laboratory of Material Physics, Ministry of Education, School of Physics and Microelectronics, Zhengzhou University, Daxue Road 75, 450052 Zhengzhou, China
| | - Chongxin Shan
- Henan Key Laboratory of Diamond Optoelectronic Materials and Devices, Key Laboratory of Material Physics, Ministry of Education, School of Physics and Microelectronics, Zhengzhou University, Daxue Road 75, 450052 Zhengzhou, China
| | - Klaus Mølmer
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
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17
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Yusipov II, Denisov SV, Ivanchenko MV. Chaotic spin-photonic quantum states in an open periodically modulated cavity. CHAOS (WOODBURY, N.Y.) 2021; 31:013112. [PMID: 33754782 DOI: 10.1063/5.0030260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed "chaotic." Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here, we consider quantum chaotic states emerging in a leaky cavity when the intracavity photonic mode is coherently pumped with the pumping intensity varying periodically in time. We show that a single spin when placed inside the cavity and coupled to the mode can moderate transitions between regular and chaotic regimes-that are identified by using quantum Lyapunov exponents or features of photon emission statistics-and thus can be used to control the degree of chaos.
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Affiliation(s)
- I I Yusipov
- Department of Applied Mathematics, Lobachevsky University, 603950 Nizhny Novgorod, Russia
| | - S V Denisov
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia
| | - M V Ivanchenko
- Department of Applied Mathematics, Lobachevsky University, 603950 Nizhny Novgorod, Russia
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18
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Liu H, Jäger SB, Yu X, Touzard S, Shankar A, Holland MJ, Nicholson TL. Rugged mHz-Linewidth Superradiant Laser Driven by a Hot Atomic Beam. PHYSICAL REVIEW LETTERS 2020; 125:253602. [PMID: 33416357 DOI: 10.1103/physrevlett.125.253602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 11/19/2020] [Indexed: 06/12/2023]
Abstract
We propose a new type of superradiant laser based on a hot atomic beam traversing an optical cavity. We show that the theoretical minimum linewidth and maximum power are competitive with the best ultracoherent clock lasers. Also, our system operates naturally in continuous wave mode, which has been elusive for superradiant lasers so far. Unlike existing ultracoherent lasers, our design is simple and rugged. This makes it a candidate for the first widely accessible ultracoherent laser, as well as the first to realize sought-after applications of ultracoherent lasers in challenging environments.
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Affiliation(s)
- Haonan Liu
- JILA, National Institute of Standards and Technology, and University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Simon B Jäger
- JILA, National Institute of Standards and Technology, and University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Xianquan Yu
- Centre for Quantum Technologies, Department of Physics, National University of Singapore, Singapore 117543
| | - Steven Touzard
- Centre for Quantum Technologies, Department of Physics, National University of Singapore, Singapore 117543
| | - Athreya Shankar
- JILA, National Institute of Standards and Technology, and University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Murray J Holland
- JILA, National Institute of Standards and Technology, and University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Travis L Nicholson
- Centre for Quantum Technologies, Department of Physics, National University of Singapore, Singapore 117543
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19
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Scholes GD. Polaritons and excitons: Hamiltonian design for enhanced coherence. Proc Math Phys Eng Sci 2020; 476:20200278. [PMID: 33223931 PMCID: PMC7655764 DOI: 10.1098/rspa.2020.0278] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 09/21/2020] [Indexed: 12/11/2022] Open
Abstract
The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian-connections between sites (or molecules) made by electronic coupling-is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.
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20
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Chen B, Guo Y, Shen H. Spontaneous phase locking of mechanical multimodes in anti-parity-time optomechanics. OPTICS EXPRESS 2020; 28:28762-28772. [PMID: 33114787 DOI: 10.1364/oe.400932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 09/02/2020] [Indexed: 06/11/2023]
Abstract
We propose a system for observing the spontaneous phase locking of two frequency separate mechanical modes in an anti-parity-time symmetric optomechanical system. In our approach, a common optical cavity mode mediates the coupling between two phonon modes, leading to the phase locking of the coupled mechanical modes to a common frequency in the symmetry unbroken regime. We furthermore observe the change of quantum correlation near the exceptional point. Our results are also directly relevant to numerous other physical platforms, such as atomic ensembles in cavity quantum electrodynamics (QED) systems and spin interaction mediated by collective motional mode in trapped ions.
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21
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Debnath K, Dold G, Morton JJL, Mølmer K. Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles. PHYSICAL REVIEW LETTERS 2020; 125:137702. [PMID: 33034472 DOI: 10.1103/physrevlett.125.137702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2020] [Accepted: 07/06/2020] [Indexed: 06/11/2023]
Abstract
We show experimentally and describe theoretically how a conventional magnetic resonance Hahn echo sequence can lead to a self-stimulated pulse echo train when an inhomogeneously broadened spin ensemble is coupled to a resonator. Effective strong coupling between the subsystems assures that the first Hahn echo can act as a refocusing pulse on the spins, leading to self-stimulated secondary echoes. Within the framework of mean field theory, we show that this process can continue multiple times leading to a train of echoes. We introduce an analytical model that explains the shape of the first echo and numerical results that account well for the experimentally observed shape and strength of the echo train and provides insights into the collective effects involved.
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Affiliation(s)
- Kamanasish Debnath
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Gavin Dold
- London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
- National Physical Laboratory, Hampton Road, Teddington TW11 0LW, United Kingdom
| | - John J L Morton
- London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, UCL, London WC1E 7JE, United Kingdom
| | - Klaus Mølmer
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
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22
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An H, Jeong Y. Numerical study of superradiant mixing by an unsynchronized superradiant state of multiple atomic ensembles. OPTICS EXPRESS 2020; 28:22276-22286. [PMID: 32752493 DOI: 10.1364/oe.393311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Accepted: 06/22/2020] [Indexed: 06/11/2023]
Abstract
We numerically analyze superradiant dynamics in atomic ensembles that have different transition frequencies using a numerical model that can take account of the transient behavior of an unsynchronized superradiant state. The numerical results unveil that the superradiant emission of a periodic pulse train can be induced by means of collective multiple frequency generation, which we call superradiant mixing. This is, in fact, due to the superradiant coupling of unsynchronized atomic ensembles. We numerically investigate the superradiant mixing in detail, varying the collective decay rate, repumping rate, and the number of the individual atomic ensembles with detuned frequencies. This work broadens our understanding of the collective atomic behavior in a detuned system, and it also suggests a novel method for frequency generation without relying on the conventional Kerr nonlinear effect.
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23
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Kato Y, Nakao H. Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators. Phys Rev E 2020; 101:012210. [PMID: 32069673 DOI: 10.1103/physreve.101.012210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Indexed: 06/10/2023]
Abstract
Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase-reduction theory recently developed for quantum nonlinear oscillators [Y. Kato, N. Yamamoto, and H. Nakao, Phys. Rev. Res. 1, 033012 (2019)10.1103/PhysRevResearch.1.033012], two types of optimization problems, one for the stability and the other for the phase coherence of the entrained state, are considered. The optimal waveforms of the periodic amplitude modulation can be derived by applying the classical optimization methods to the semiclassical phase equation that approximately describes the quantum limit-cycle dynamics. Using a quantum van der Pol oscillator with squeezing and Kerr effects as an example, the performance of optimization is numerically analyzed. It is shown that the optimized waveform for the entrainment stability yields faster entrainment to the driving signal than the case with a simple sinusoidal waveform, while that for the phase coherence yields little improvement from the sinusoidal case. These results are explained from the properties of the phase sensitivity function.
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Affiliation(s)
- Yuzuru Kato
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
| | - Hiroya Nakao
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
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24
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Buča B, Jaksch D. Dissipation Induced Nonstationarity in a Quantum Gas. PHYSICAL REVIEW LETTERS 2019; 123:260401. [PMID: 31951440 DOI: 10.1103/physrevlett.123.260401] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2019] [Indexed: 06/10/2023]
Abstract
Nonstationary longtime dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, M. Landini, K. Kroeger, L. Hruby, T. Donner, and T. Esslinger, arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable-even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the nonstationary behavior.
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Affiliation(s)
- Berislav Buča
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Dieter Jaksch
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
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25
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Liniov A, Meyerov I, Kozinov E, Volokitin V, Yusipov I, Ivanchenko M, Denisov S. Unfolding a quantum master equation into a system of real-valued equations: Computationally effective expansion over the basis of SU(N) generators. Phys Rev E 2019; 100:053305. [PMID: 31869931 DOI: 10.1103/physreve.100.053305] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2019] [Indexed: 11/07/2022]
Abstract
Dynamics of an open N-state quantum system is often modeled with a Markovian master equation describing the evolution of the system density operator. By using generators of SU(N) group as a basis, the density operator can be transformed into a real-valued "coherence-vector." A generator of the dissipative evolution, so-called "Lindbladian," can be expanded over the same basis and recast in the form of a real matrix. Together, these expansions result is a nonhomogeneous system of N^{2}-1 real-valued linear ordinary differential equations. Now one can, e.g., implement standard high-performance algorithms to integrate the system of equations forward in time while being sure in exact preservation of the trace (norm) and Hermiticity of the density operator. However, when performed in a straightforward way, the expansion turns to be an operation of the time complexity O(N^{10}). The complexity can be reduced when the number of dissipative operators is independent of N, which is often the case for physically meaningful models. Here we present an algorithm to transform quantum master equation into a system of real-valued differential equations and propagate it forward in time. By using a specific scalable model, we evaluate computational efficiency of the algorithm and demonstrate that it is possible to handle the model system with N=10^{3} states on a single node of a computer cluster.
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Affiliation(s)
- A Liniov
- Software Engineering Department, Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Russia
| | - I Meyerov
- Mathematical Software and Supercomputing Technologies Department, Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Russia
| | - E Kozinov
- Mathematical Software and Supercomputing Technologies Department, Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Russia
| | - V Volokitin
- Mathematical Software and Supercomputing Technologies Department, Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Russia
| | - I Yusipov
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Russia
| | - M Ivanchenko
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Russia
| | - S Denisov
- Department of Computer Science, OsloMet - Oslo Metropolitan University, N-0130 Oslo, Norway
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26
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Cabot A, Giorgi GL, Galve F, Zambrini R. Quantum Synchronization in Dimer Atomic Lattices. PHYSICAL REVIEW LETTERS 2019; 123:023604. [PMID: 31386511 DOI: 10.1103/physrevlett.123.023604] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2018] [Indexed: 06/10/2023]
Abstract
Synchronization phenomena have been recently reported in the quantum realm at the atomic level due to collective dissipation. In this work we propose a dimer lattice of trapped atoms realizing a dissipative spin model where quantum synchronization occurs instead in the presence of local dissipation. Atom synchronization is enabled by the inhomogeneity of staggered local losses in the lattice and is favored by an increase of spins detuning. A comprehensive approach to quantum synchronization based on different measures considered in the literature allows us to identify the main features of different synchronization regimes.
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Affiliation(s)
- Albert Cabot
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, 07122 Palma de Mallorca, Spain
| | - Gian Luca Giorgi
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, 07122 Palma de Mallorca, Spain
| | - Fernando Galve
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, 07122 Palma de Mallorca, Spain
- I3M (UPV-CSIC) Institute for Instrumentation in Molecular Imaging, Universidad Politécnica de Valencia, 46022, Spain
| | - Roberta Zambrini
- IFISC (UIB-CSIC), Instituto de Física Interdisciplinar y Sistemas Complejos, 07122 Palma de Mallorca, Spain
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27
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Chiacchio EIR, Nunnenkamp A. Dissipation-Induced Instabilities of a Spinor Bose-Einstein Condensate Inside an Optical Cavity. PHYSICAL REVIEW LETTERS 2019; 122:193605. [PMID: 31144960 DOI: 10.1103/physrevlett.122.193605] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2019] [Indexed: 06/09/2023]
Abstract
We investigate the dynamics of a spinor Bose-Einstein condensate inside an optical cavity, driven transversely by a laser with a controllable polarization angle. We focus on a two-component Dicke model with complex light-matter couplings, in the presence of photon losses. We calculate the steady-state phase diagram and find dynamical instabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes that generate nonreciprocal couplings between the two collective spins. Our predictions can be readily tested in state-of-the-art experiments and open up the study of nonreciprocal many-body dynamics out of equilibrium.
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Affiliation(s)
| | - A Nunnenkamp
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
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28
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Qiao GJ, Gao HX, Liu HD, Yi XX. Quantum synchronization of two mechanical oscillators in coupled optomechanical systems with Kerr nonlinearity. Sci Rep 2018; 8:15614. [PMID: 30353112 PMCID: PMC6199267 DOI: 10.1038/s41598-018-33903-z] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2018] [Accepted: 10/08/2018] [Indexed: 11/30/2022] Open
Abstract
We investigate the quantum synchronization phenomena of two mechanical oscillators of different frequencies in two optomechanical systems under periodically modulating cavity detunings or driving amplitudes, which can interact mutually through an optical fiber or a phonon tunneling. The cavities are filled with Kerr-type nonlinear medium. It is found that, no matter which the coupling and periodically modulation we choose, both of the quantum synchronization of nonlinear optomechanical system are more appealing than the linear optomechanical system. It is easier to observe greatly enhanced quantum synchronization with Kerr nonlinearity. In addition, the different influences on the quantum synchronization between the two coupling ways and the two modulating ways are compared and discussed.
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Affiliation(s)
- Guo-Jian Qiao
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China.,National Demonstration Center for Experimental Physics Education, Northeast Normal University, Changchun, 130024, China
| | - Hui-Xia Gao
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China.,National Demonstration Center for Experimental Physics Education, Northeast Normal University, Changchun, 130024, China
| | - Hao-di Liu
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China. .,National Demonstration Center for Experimental Physics Education, Northeast Normal University, Changchun, 130024, China.
| | - X X Yi
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China
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29
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Norcia MA, Lewis-Swan RJ, Cline JRK, Zhu B, Rey AM, Thompson JK. Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser. Science 2018; 361:259-262. [DOI: 10.1126/science.aar3102] [Citation(s) in RCA: 86] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Accepted: 05/25/2018] [Indexed: 11/02/2022]
Affiliation(s)
- Matthew A. Norcia
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA
| | - Robert J. Lewis-Swan
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - Julia R. K. Cline
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA
| | - Bihui Zhu
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
| | - Ana M. Rey
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - James K. Thompson
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA
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30
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Amitai E, Koppenhöfer M, Lörch N, Bruder C. Quantum effects in amplitude death of coupled anharmonic self-oscillators. Phys Rev E 2018; 97:052203. [PMID: 29906836 DOI: 10.1103/physreve.97.052203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Indexed: 06/08/2023]
Abstract
Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest state, therefore quenching their oscillation. This phenomenon is termed "amplitude death." Well known and studied in classical self-oscillators, amplitude death was only recently investigated in quantum self-oscillators [Ishibashi and Kanamoto, Phys. Rev. E 96, 052210 (2017)2470-004510.1103/PhysRevE.96.052210]. Quantitative differences between the classical and quantum descriptions were found. Here, we demonstrate that for quantum self-oscillators with anharmonicity in their energy spectrum, multiple resonances in the mean phonon number can be observed. This is a result of the discrete energy spectrum of these oscillators, and is not present in the corresponding classical model. Experiments can be realized with current technology and would demonstrate these genuine quantum effects in the amplitude death phenomenon.
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Affiliation(s)
- Ehud Amitai
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Martin Koppenhöfer
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Niels Lörch
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Christoph Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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31
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Du L, Fan CH, Zhang HX, Wu JH. Synchronization enhancement of indirectly coupled oscillators via periodic modulation in an optomechanical system. Sci Rep 2017; 7:15834. [PMID: 29158548 PMCID: PMC5696558 DOI: 10.1038/s41598-017-16115-9] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Accepted: 11/07/2017] [Indexed: 11/09/2022] Open
Abstract
We study the synchronization behaviors of two indirectly coupled mechanical oscillators of different frequencies in a doublecavity optomechanical system. It is found that quantum synchronization is roughly vanishing though classical synchronization seems rather good when each cavity mode is driven by an external field in the absence of temporal modulations. By periodically modulating cavity detunings or driving amplitudes, however, it is possible to observe greatly enhanced quantum synchronization accompanied with nearly perfect classical synchronization. The level of quantum synchronization observed here is, in particular, much higher than that for two directly coupled mechanical oscillators. Note also that the modulation on cavity detunings is more appealing than that on driving amplitudes when the robustness of quantum synchronization is examined against the bath’s mean temperature or the oscillators’ frequency difference.
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Affiliation(s)
- Lei Du
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130117, China
| | - Chu-Hui Fan
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130117, China
| | - Han-Xiao Zhang
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130117, China
| | - Jin-Hui Wu
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130117, China.
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32
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Ishibashi K, Kanamoto R. Oscillation collapse in coupled quantum van der Pol oscillators. Phys Rev E 2017; 96:052210. [PMID: 29347706 DOI: 10.1103/physreve.96.052210] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2017] [Indexed: 06/07/2023]
Abstract
The classical self-oscillations can collapse merely due to their mutual couplings. We investigate this oscillation collapse in quantum van der Pol oscillators. For a pair of quantum oscillators, the steady-state mean phonon number is shown to be lower than in the corresponding classical model with a Gaussian white noise that mimics quantum noise. We further show within the mean-field theory that a number of globally coupled oscillators undergo a transition from the synchronized periodic motion to the collective oscillation collapse. A quantum many-body simulation suggests that the increase in the number of oscillators leads to a lower steady-state mean phonon number, bounded below by the mean-field result.
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Affiliation(s)
- Kenta Ishibashi
- Department of Physics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
| | - Rina Kanamoto
- Department of Physics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
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33
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Li W, Zhang W, Li C, Song H. Properties and relative measure for quantifying quantum synchronization. Phys Rev E 2017; 96:012211. [PMID: 29347171 DOI: 10.1103/physreve.96.012211] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2017] [Indexed: 06/07/2023]
Abstract
Although quantum synchronization phenomena and corresponding measures have been widely discussed recently, it is still an open question how to characterize directly the influence of nonlocal correlation, which is the key distinction for identifying classical and quantum synchronizations. In this paper, we present basic postulates for quantifying quantum synchronization based on the related theory in Mari's work [Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605], and we give a general formula of a quantum synchronization measure with clear physical interpretations. By introducing Pearson's parameter, we show that the obvious characteristics of our measure are the relativity and monotonicity. As an example, the measure is applied to describe synchronization among quantum optomechanical systems under a Markovian bath. We also show the potential by quantifying generalized synchronization and discrete variable synchronization with this measure.
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Affiliation(s)
- Wenlin Li
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Wenzhao Zhang
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Chong Li
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Heshan Song
- School of Physics, Dalian University of Technology, Dalian 116024, China
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34
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Lörch N, Nigg SE, Nunnenkamp A, Tiwari RP, Bruder C. Quantum Synchronization Blockade: Energy Quantization Hinders Synchronization of Identical Oscillators. PHYSICAL REVIEW LETTERS 2017; 118:243602. [PMID: 28665640 DOI: 10.1103/physrevlett.118.243602] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Indexed: 06/07/2023]
Abstract
Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization, is blocked. We demonstrate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with superconducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.
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Affiliation(s)
- Niels Lörch
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Simon E Nigg
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Andreas Nunnenkamp
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Rakesh P Tiwari
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
- Department of Physics, McGill University, 3600 rue University, Montreal, Quebec H3A 2T8, Canada
| | - Christoph Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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Li W, Li C, Song H. Quantum synchronization and quantum state sharing in an irregular complex network. Phys Rev E 2017; 95:022204. [PMID: 28297892 DOI: 10.1103/physreve.95.022204] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2016] [Indexed: 06/06/2023]
Abstract
We investigate the quantum synchronization phenomenon of the complex network constituted by coupled optomechanical systems and prove that the unknown identical quantum states can be shared or distributed in the quantum network even though the topology is varying. Considering a channel constructed by quantum correlation, we show that quantum synchronization can sustain and maintain high levels in Markovian dissipation for a long time. We also analyze the state-sharing process between two typical complex networks, and the results predict that linked nodes can be directly synchronized, but the whole network will be synchronized only if some specific synchronization conditions are satisfied. Furthermore, we give the synchronization conditions analytically through analyzing network dynamics. This proposal paves the way for studying multi-interaction synchronization and achieving effective quantum information processing in a complex network.
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Affiliation(s)
- Wenlin Li
- School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024, China
| | - Chong Li
- School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024, China
| | - Heshan Song
- School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024, China
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Norcia MA, Winchester MN, Cline JRK, Thompson JK. Superradiance on the millihertz linewidth strontium clock transition. SCIENCE ADVANCES 2016; 2:e1601231. [PMID: 27757423 PMCID: PMC5065256 DOI: 10.1126/sciadv.1601231] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2016] [Accepted: 08/08/2016] [Indexed: 05/26/2023]
Abstract
Laser frequency noise contributes a significant limitation to today's best atomic clocks. A proposed solution to this problem is to create a superradiant laser using an optical clock transition as its gain medium. This laser would act as an active atomic clock and would be highly immune to the fluctuations in reference cavity length that limit today's best lasers. We demonstrate and characterize superradiant emission from the millihertz linewidth clock transition in an ensemble of laser-cooled 87Sr atoms trapped within a high-finesse optical cavity. We measure a collective enhancement of the emission rate into the cavity mode by a factor of more than 10,000 compared to independently radiating atoms. We also demonstrate a method for seeding superradiant emission and observe interference between two independent transitions lasing simultaneously. We use this interference to characterize the relative spectral properties of the two lasing subensembles.
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Lörch N, Amitai E, Nunnenkamp A, Bruder C. Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators. PHYSICAL REVIEW LETTERS 2016; 117:073601. [PMID: 27563961 DOI: 10.1103/physrevlett.117.073601] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2016] [Indexed: 06/06/2023]
Abstract
We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.
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Affiliation(s)
- Niels Lörch
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Ehud Amitai
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Andreas Nunnenkamp
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Christoph Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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38
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Li W, Li C, Song H. Quantum synchronization in an optomechanical system based on Lyapunov control. Phys Rev E 2016; 93:062221. [PMID: 27415268 DOI: 10.1103/physreve.93.062221] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2015] [Indexed: 06/06/2023]
Abstract
We extend the concepts of quantum complete synchronization and phase synchronization, which were proposed in A. Mari et al., Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605, to more widespread quantum generalized synchronization. Generalized synchronization can be considered a necessary condition or a more flexible derivative of complete synchronization, and its criterion and synchronization measure are proposed and analyzed in this paper. As examples, we consider two typical generalized synchronizations in a designed optomechanical system. Unlike the effort to construct a special coupling synchronization system, we purposefully design extra control fields based on Lyapunov control theory. We find that the Lyapunov function can adapt to more flexible control objectives, which is more suitable for generalized synchronization control, and the control fields can be achieved simply with a time-variant voltage. Finally, the existence of quantum entanglement in different generalized synchronizations is also discussed.
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Affiliation(s)
- Wenlin Li
- School of Physics and Optoelectronic Engineering, Dalian University of Technology, 116024, China
| | - Chong Li
- School of Physics and Optoelectronic Engineering, Dalian University of Technology, 116024, China
| | - Heshan Song
- School of Physics and Optoelectronic Engineering, Dalian University of Technology, 116024, China
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Li T, Bao TY, Zhang YL, Zou CL, Zou XB, Guo GC. Long-distance synchronization of unidirectionally cascaded optomechanical systems. OPTICS EXPRESS 2016; 24:12336-12348. [PMID: 27410149 DOI: 10.1364/oe.24.012336] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Synchronization is of great scientific interest due to the abundant applications in a wide range of systems. We propose an all-optical scheme to achieve the controllable long-distance synchronization of two dissimilar optomechanical systems, which are unidirectionally coupled through a fiber with light. Synchronization, unsynchronization, and the dependence of the synchronization on driving laser strength and intrinsic frequency mismatch are studied based on the numerical simulation. Taking the fiber attenuation into account, we show that two optomechanical resonators can be unidirectionally synchronized over a distance of tens of kilometers. We also analyze the unidirectional synchronization of three optomechanical systems, demonstrating the scalability of our scheme.
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Xu M, Jäger SB, Schütz S, Cooper J, Morigi G, Holland MJ. Supercooling of Atoms in an Optical Resonator. PHYSICAL REVIEW LETTERS 2016; 116:153002. [PMID: 27127966 DOI: 10.1103/physrevlett.116.153002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2015] [Indexed: 06/05/2023]
Abstract
We investigate laser cooling of an ensemble of atoms in an optical cavity. We demonstrate that when atomic dipoles are synchronized in the regime of steady-state superradiance, the motion of the atoms may be subject to a giant frictional force leading to potentially very low temperatures. The ultimate temperature limits are determined by a modified atomic linewidth, which can be orders of magnitude smaller than the cavity linewidth. The cooling rate is enhanced by the superradiant emission into the cavity mode allowing reasonable cooling rates even for dipolar transitions with ultranarrow linewidth.
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Affiliation(s)
- Minghui Xu
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Simon B Jäger
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - S Schütz
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - J Cooper
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Giovanna Morigi
- Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
| | - M J Holland
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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41
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Pikovsky A, Rosenblum M. Dynamics of globally coupled oscillators: Progress and perspectives. CHAOS (WOODBURY, N.Y.) 2015; 25:097616. [PMID: 26428569 DOI: 10.1063/1.4922971] [Citation(s) in RCA: 94] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.
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Affiliation(s)
- Arkady Pikovsky
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
| | - Michael Rosenblum
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
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Xu M, Holland MJ. Conditional ramsey spectroscopy with synchronized atoms. PHYSICAL REVIEW LETTERS 2015; 114:103601. [PMID: 25815931 DOI: 10.1103/physrevlett.114.103601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
We investigate Ramsey spectroscopy performed on a synchronized ensemble of two-level atoms. The synchronization is induced by the collective coupling of the atoms to a heavily damped mode of an optical cavity. We show that, in principle, with this synchronized system it is possible to observe Ramsey fringes indefinitely, even in the presence of spontaneous emission and other sources of individual-atom dephasing. This could have important consequences for atomic clocks and a wide range of precision metrology applications.
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Affiliation(s)
- Minghui Xu
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - M J Holland
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
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