1
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Aifer M, Thingna J, Deffner S. Energetic Cost for Speedy Synchronization in Non-Hermitian Quantum Dynamics. PHYSICAL REVIEW LETTERS 2024; 133:020401. [PMID: 39073943 DOI: 10.1103/physrevlett.133.020401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Accepted: 05/28/2024] [Indexed: 07/31/2024]
Abstract
Quantum synchronization is crucial for understanding complex dynamics and holds potential applications in quantum computing and communication. Therefore, assessing the thermodynamic resources required for finite-time synchronization in continuous-variable systems is a critical challenge. In the present work, we find these resources to be extensive for large systems. We also bound the speed of quantum and classical synchronization in coupled damped oscillators with non-Hermitian anti-PT-symmetric interactions, and show that the speed of synchronization is limited by the interaction strength relative to the damping. Compared to the classical limit, we find that quantum synchronization is slowed by the noncommutativity of the Hermitian and anti-Hermitian terms. Our general results could be tested experimentally, and we suggest an implementation in photonic systems.
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2
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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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3
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Wächtler CW, Moore JE. Topological Quantum Synchronization of Fractionalized Spins. PHYSICAL REVIEW LETTERS 2024; 132:196601. [PMID: 38804931 DOI: 10.1103/physrevlett.132.196601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Revised: 03/10/2024] [Accepted: 04/12/2024] [Indexed: 05/29/2024]
Abstract
The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki model exhibits fractionalized spins at the ends of an open chain. We show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term, which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.
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Affiliation(s)
| | - Joel E Moore
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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4
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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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5
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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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6
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Setoyama W, Hasegawa Y. Lie Algebraic Quantum Phase Reduction. PHYSICAL REVIEW LETTERS 2024; 132:093602. [PMID: 38489612 DOI: 10.1103/physrevlett.132.093602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Revised: 08/10/2023] [Accepted: 01/22/2024] [Indexed: 03/17/2024]
Abstract
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schrödinger equation. Because a perturbation is represented by unitary transformation in quantum dynamics, we calculate phase response curves with respect to generators of a Lie algebra. Our method shows that the continuous measurement yields phase clusters and alters the phase response curves. The observable clusters capture the phase dynamics of individual quantum oscillators, unlike indirect indicators obtained from density operators. Furthermore, our method can be applied to finite-level systems that lack classical counterparts.
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Affiliation(s)
- Wataru Setoyama
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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7
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Schmolke F, Lutz E. Measurement-Induced Quantum Synchronization and Multiplexing. PHYSICAL REVIEW LETTERS 2024; 132:010402. [PMID: 38242665 DOI: 10.1103/physrevlett.132.010402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Revised: 12/08/2023] [Accepted: 12/12/2023] [Indexed: 01/21/2024]
Abstract
Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable synchronization at the level of single trajectories. We formulate general criteria for this quantum phenomenon to occur and demonstrate that the number of synchronized realizations can be controlled from none to all. We additionally find that ergodicity is typically broken, since time and ensemble averages may exhibit radically different synchronization behavior. We further introduce a quantum type of multiplexing that involves individual trajectories with distinct synchronization frequencies. Measurement-induced synchronization appears as a genuine nonclassical form of synchrony that exploits quantum superpositions.
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Affiliation(s)
- Finn Schmolke
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
| | - Eric Lutz
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
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8
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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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9
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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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10
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Shortcut to synchronization in classical and quantum systems. Sci Rep 2023; 13:453. [PMID: 36624171 PMCID: PMC9829672 DOI: 10.1038/s41598-022-27130-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 12/26/2022] [Indexed: 01/11/2023] Open
Abstract
Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization regime more quickly. We exemplify an inverse engineering method to solve this issue on the classical Van der Pol oscillator. This approach cannot be directly transposed to the quantum case as the system is no longer point-like in phase space. We explain how to adapt our method by an iterative procedure to account for the finite-size quantum distribution in phase space. We show that the resulting driving yields a density matrix close to the synchronized one according to the trace distance. Our method provides an example of fast control of a nonlinear quantum system, and raises the question of the quantum speed limit concept in the presence of nonlinearities.
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11
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Schmolke F, Lutz E. Noise-Induced Quantum Synchronization. PHYSICAL REVIEW LETTERS 2022; 129:250601. [PMID: 36608236 DOI: 10.1103/physrevlett.129.250601] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 11/17/2022] [Indexed: 06/17/2023]
Abstract
Synchronization is a widespread phenomenon in science and technology. Here, we study noise-induced synchronization in a quantum spin chain subjected to local Gaussian white noise. We demonstrate stable (anti)synchronization between the endpoint magnetizations of a quantum XY model with transverse field of arbitrary length. Remarkably, we show that noise applied to a single spin suffices to reach stable (anti)synchronization, and find that the two synchronized end spins are entangled. We additionally determine the optimal noise amplitude that leads to the fastest synchronization along the chain, and further compare the optimal synchronization speed to the fundamental Lieb-Robinson bound for information propagation.
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Affiliation(s)
- Finn Schmolke
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
| | - Eric Lutz
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
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12
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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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13
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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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14
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Dynamical Collective Excitations and Entanglement of Two Strongly Correlated Rydberg Superatoms. PHOTONICS 2022. [DOI: 10.3390/photonics9040242] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Based on the dipole blockade effect and with the aid of the superatom (SA) model, we propose a scheme to investigate the correlated evolution of two Rydberg sub-superatoms (SSAs), formed by two spatially separated atomic Rydberg sub-ensembles but in the same blockade region. Starting from the pure separable states, we investigate the in-phase or anti-phase correlated dynamics and explore how two Rydberg SSAs entangle with each other mediated by a single Rydberg excitation. Starting from the entangled states, we discuss the robustness of the system against decoherence induced by the dephasing rate. Our results show that both the correlated evolution of two Rydberg SSAs and their collective-state entanglement are usually sensitive to the number of each Rydberg SSA. This allows us to coherently manipulate the Rydberg ensemble over long distances from the single-quantum level to the mesoscopic level by changing the number of atoms. Furthermore, the method for dividing an SA into two SSAs and obtaining their spin operators without any approximation can be readily generalized to the case of many SSAs. It may have potential promising applications in quantum information processing and provide an attractive platform to study the quantum-classical correspondence, many-body physics and so on.
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15
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Optomechanical synchronization across multi-octave frequency spans. Nat Commun 2021; 12:5625. [PMID: 34561457 PMCID: PMC8463541 DOI: 10.1038/s41467-021-25884-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 09/03/2021] [Indexed: 11/17/2022] Open
Abstract
Experimental exploration of synchronization in scalable oscillator microsystems has unfolded a deeper understanding of networks, collective phenomena, and signal processing. Cavity optomechanical devices have played an important role in this scenario, with the perspective of bridging optical and radio frequencies through nonlinear classical and quantum synchronization concepts. In its simplest form, synchronization occurs when an oscillator is entrained by a signal with frequency nearby the oscillator’s tone, and becomes increasingly challenging as their frequency detuning increases. Here, we experimentally demonstrate entrainment of a silicon-nitride optomechanical oscillator driven up to the fourth harmonic of its 32 MHz fundamental frequency. Exploring this effect, we also experimentally demonstrate a purely optomechanical RF frequency divider, where we performed frequency division up to a 4:1 ratio, i.e., from 128 MHz to 32 MHz. Further developments could harness these effects towards frequency synthesizers, phase-sensitive amplification and nonlinear sensing. Higher order synchronization in optomechanical devices is relatively unexplored. Here the authors use nonlinear parametric effects to entrain an optomechanical oscillator with a drive signal several octaves away from the oscillation frequency, and demonstrate RF frequency division.
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16
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Huan TT, Zhou RG, Ian H. Synchronization of two cavity-coupled qubits measured by entanglement. Sci Rep 2020; 10:12975. [PMID: 32737365 PMCID: PMC7395784 DOI: 10.1038/s41598-020-69903-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Accepted: 07/20/2020] [Indexed: 11/09/2022] Open
Abstract
Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard cooperative radiations as a manifested effect secondary to the intrinsic synchronization among the two-level atoms and propose the entanglement measure, concurrence, as a time-resolved measure of synchronization. Modeled on two cavity-coupled qubits, the evolved concurrence monotonically increases to a saturated level. The finite duration required for the rising to saturation coincides with the time delay characteristic to the initiation of superfluorescence, showing the role of synchronization in establishing the cooperation among the qubits. We verify concurrence to be a good measure of synchronization by comparing it with asynchronicity computed from the difference between the density matrices of the qubits. We find that the feature of time delay agrees in both measures and is determined by the coupling regimes of the cavity-qubit interaction. Specifically, synchronization is impossible in the weak coupling regime.
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Affiliation(s)
- Tian-Tian Huan
- Institute of Applied Physics and Materials Engineering, University of Macau, Macau, China
| | - Ri-Gui Zhou
- College of Information Engineering, Shanghai Maritime University, Shanghai, 201306, China
| | - Hou Ian
- Institute of Applied Physics and Materials Engineering, University of Macau, Macau, China. .,Zhuhai UM Science & Technology Research Institute, Zhuhai, Guangdong, China.
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17
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Laskar AW, Adhikary P, Mondal S, Katiyar P, Vinjanampathy S, Ghosh S. Observation of Quantum Phase Synchronization in Spin-1 Atoms. PHYSICAL REVIEW LETTERS 2020; 125:013601. [PMID: 32678654 DOI: 10.1103/physrevlett.125.013601] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Revised: 04/10/2020] [Accepted: 05/29/2020] [Indexed: 06/11/2023]
Abstract
With growing interest in quantum technologies, possibilities of synchronizing quantum systems have garnered significant recent attention. In experiments with dilute ensemble of laser cooled spin-1 ^{87}Rb atoms, we observe phase difference of spin coherences to synchronize with phases of external classical fields. An initial limit-cycle state of a spin-1 atom localizes in phase space due to dark-state polaritons generated by classical two-photon tone fields. In particular, when the two couplings fields are out of phase, the limit-cycle state synchronizes only with two artificially engineered, anisotropic decay rates. Furthermore, we observe a blockade of synchronization due to quantum interference and emergence of Arnold-tongue-like features. Such anisotropic decay induced synchronization of spin-1 systems with no classical analog can provide insights in open quantum systems and find applications in synchronized quantum networks.
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Affiliation(s)
- Arif Warsi Laskar
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Pratik Adhikary
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Suprodip Mondal
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Parag Katiyar
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
| | - Sai Vinjanampathy
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Saikat Ghosh
- Department of Physics, Indian Institute of Technology-Kanpur, Uttar Pradesh 208016, India
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18
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Jaseem N, Hajdušek M, Vedral V, Fazio R, Kwek LC, Vinjanampathy S. Quantum synchronization in nanoscale heat engines. Phys Rev E 2020; 101:020201. [PMID: 32168700 DOI: 10.1103/physreve.101.020201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Accepted: 01/02/2020] [Indexed: 06/10/2023]
Abstract
Owing to the ubiquity of synchronization in the classical world, it is interesting to study its behavior in quantum systems. Though quantum synchronization has been investigated in many systems, a clear connection to quantum technology applications is lacking. We bridge this gap and show that nanoscale heat engines are a natural platform to study quantum synchronization and always possess a stable limit cycle. Furthermore, we demonstrate an intimate relationship between the power of a coherently driven heat engine and its phase-locking properties by proving that synchronization places an upper bound on the achievable steady-state power of the engine. We also demonstrate that such an engine exhibits finite steady-state power if and only if its synchronization measure is nonzero. Finally, we show that the efficiency of the engine sets a point in terms of the bath temperatures where synchronization vanishes. We link the physical phenomenon of synchronization with the emerging field of quantum thermodynamics by establishing quantum synchronization as a mechanism of stable phase coherence.
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Affiliation(s)
- Noufal Jaseem
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
| | - Michal Hajdušek
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
- Keio University Shonan Fujisawa Campus, 5322 Endo, Fujisawa, Kanagawa 252-0882, Japan
| | - Vlatko Vedral
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
- Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom
| | - Rosario Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Dipartimento di Fisica, Università di Napoli Federico II, Complesso di Monte S. Angelo, 80126 Napoli, Italy
| | - Leong-Chuan Kwek
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
- Institute of Advanced Studies, Nanyang Technological University, Singapore 639673
- National Institute of Education, Nanyang Technological University, Singapore 637616
| | - Sai Vinjanampathy
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
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19
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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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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: 22] [Impact Index Per Article: 4.4] [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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21
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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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Roulet A, Bruder C. Quantum Synchronization and Entanglement Generation. PHYSICAL REVIEW LETTERS 2018; 121:063601. [PMID: 30141656 DOI: 10.1103/physrevlett.121.063601] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2018] [Indexed: 06/08/2023]
Abstract
We study synchronization in a two-node network built out of the smallest possible self-sustained oscillator: a spin-1 oscillator. We first demonstrate that phase locking between the quantum oscillators can be achieved, even for limit cycles that cannot be synchronized to an external semiclassical signal. Building upon the analytical description of the system, we then clarify the relation between quantum synchronization and the generation of entanglement. These findings establish the spin-based architecture as a promising platform for understanding synchronization in complex quantum networks.
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Affiliation(s)
- Alexandre Roulet
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Christoph Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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