1
|
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.
Collapse
|
2
|
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.
Collapse
Affiliation(s)
| | - Dima L. Shepelyansky
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
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.
Collapse
|
6
|
Yang WQ, Niu W, Ma YH, Zhang WZ. Quantum nonlinear effect in a dissipatively coupled optomechanical system. OPTICS EXPRESS 2024; 32:11801-11817. [PMID: 38571019 DOI: 10.1364/oe.518042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 03/01/2024] [Indexed: 04/05/2024]
Abstract
A full-quantum approach is used to study the quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. By deriving the effective Hamiltonian, we find that the reduced system exhibits a Kerr nonlinear term with a complex coefficient, entirely induced by the dissipative and dispersive couplings. Unexpectedly, the nonlinearities resulting from the dissipative coupling possess non-Hermitian Hamiltonian-like properties preserving the quantum nature of the dispersive coupling beyond the traditional system dissipation. This protective mechanism allows the system to exhibit strong quantum nonlinear effects when the detuning (the compound cavity detuning Δc and the auxiliary cavity detuning Δe) and the tunneling coupling strength (J) of two cavities satisfy the relation J2 = ΔcΔe. Moreover, the additive effects of dispersive and dissipative couplings can produce strong anti-bunching effects, which exist in both strong and weak coupling conditions. Our work may provide a new way to study and produce strong quantum nonlinear effects in dissipatively coupled optomechanical systems.
Collapse
|
7
|
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.
Collapse
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
| |
Collapse
|
8
|
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.
Collapse
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
| |
Collapse
|
9
|
Motazedifard A, Dalafi A, Naderi MH. Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes. OPTICS EXPRESS 2023; 31:36615-36637. [PMID: 38017809 DOI: 10.1364/oe.499409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 10/05/2023] [Indexed: 11/30/2023]
Abstract
We propose an experimentally feasible optomechanical scheme to realize a negative cavity photon spectral function (CPSF) which is equivalent to a negative absorption. The system under consideration is an optomechanical system consisting of two mechanical (phononic) modes which are linearly coupled to a common cavity mode via the radiation pressure while parametrically driven through the coherent time-modulation of their spring coefficients. Using the equations of motion for the cavity retarded Green's function obtained in the framework of the generalized linear response theory, we show that in the red-detuned and weak-coupling regimes a frequency-dependent effective cavity damping rate (ECDR) corresponding to a negative CPSF can be realized by controlling the cooperativities and modulation parameters while the system still remains in the stable regime. Nevertheless, such a negativity which acts as an optomechanical gain never occurs in a standard (an unmodulated bare) cavity optomechanical system. Besides, we find that the presence of two modulated mechanical degrees of freedom provides more controllability over the magnitude and bandwidth of the negativity of CPSF, in comparison to the setup with a single modulated mechanical oscillator. Interestingly, the introduced negativity may open a new platform to realize an extraordinary (modified) optomechanically induced transparency (in which the input signal is amplified in the output) leading to a perfect tunable optomechanical filter with switchable bandwidth which can be used as an optical transistor.
Collapse
|
10
|
Shen Y, Soh HY, Kwek LC, Fan W. Fisher Information as General Metrics of Quantum Synchronization. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1116. [PMID: 37628145 PMCID: PMC10453851 DOI: 10.3390/e25081116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Revised: 07/14/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023]
Abstract
Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose using classical and quantum Fisher information (FI) as alternative metrics to detect and measure quantum synchronization. We establish the connection between FI and quantum synchronization, demonstrating that both classical and quantum FI can be deployed as more general indicators of quantum phase synchronization in some regimes where all other existing measures fail to provide reliable results. We show advantages in FI-based measures, especially in 2-to-1 synchronization. Furthermore, we analyze the impact of noise on the synchronization measures, revealing the robustness and susceptibility of each method in the presence of dissipation and decoherence. Our results open up new avenues for understanding and exploiting quantum synchronization.
Collapse
Affiliation(s)
- Yuan Shen
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, Singapore 639798, Singapore
| | - Hong Yi Soh
- National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
| | - Leong-Chuan Kwek
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, Singapore 639798, Singapore
- National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore 117543, Singapore
| | - Weijun Fan
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, Singapore 639798, Singapore
| |
Collapse
|
11
|
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.
Collapse
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
| |
Collapse
|
12
|
Lau HWH, Davidsen J, Simon C. Chimera patterns in conservative Hamiltonian systems and Bose-Einstein condensates of ultracold atoms. Sci Rep 2023; 13:8590. [PMID: 37237118 DOI: 10.1038/s41598-023-35061-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2017] [Accepted: 05/11/2023] [Indexed: 05/28/2023] Open
Abstract
Experimental realizations of chimera patterns, characterized by coexisting regions of phase coherence and incoherence, have so far been achieved for non-conservative systems with dissipation and exclusively in classical settings. The possibility of observing chimera patterns in quantum systems has rarely been studied and it remains an open question if chimera patterns can exist in closed, or conservative quantum systems. Here, we tackle these challenges by first proposing a conservative Hamiltonian system with nonlocal hopping, where the energy is well-defined and conserved. We show explicitly that such a system can exhibit chimera patterns. Then we propose a physical mechanism for the nonlocal hopping by using an additional mediating channel. This leads us to propose a possible experimentally realizable quantum system based on a two-component Bose-Einstein condensate (BEC) with a spin-dependent optical lattice, where an untrapped component serves as the matter-wave mediating field. In this BEC system, nonlocal spatial hopping over tens of lattice sites can be achieved and simulations suggest that chimera patterns should be observable in certain parameter regimes.
Collapse
Affiliation(s)
- Hon Wai Hana Lau
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4, Canada.
- Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, T2N 1N4, Canada.
- Quantum Information Science and Technology Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Kunigami-gun, Okinawa, 904-0495, Japan.
| | - Jörn Davidsen
- Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, T2N 1N4, Canada
- Hotchkiss Brain Institute, University of Calgary, Calgary, T2N 4N1, Canada
| | - Christoph Simon
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4, Canada
- Hotchkiss Brain Institute, University of Calgary, Calgary, T2N 4N1, Canada
| |
Collapse
|
13
|
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.
Collapse
|
14
|
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.
Collapse
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
| |
Collapse
|
15
|
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.
Collapse
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
| |
Collapse
|
16
|
Two-Membrane Cavity Optomechanics: Linear and Non-Linear Dynamics. PHOTONICS 2022. [DOI: 10.3390/photonics9020099] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
In this paper, we review the linear and non-linear dynamics of an optomechanical system made of a two-membrane etalon in a high-finesse Fabry–Pérot cavity. This two-membrane setup has the capacity to modify on demand the single-photon optomechanical coupling, and in the linearized interaction regime to cool simultaneously two mechanical oscillators. It is a promising platform for realizing cavity optomechanics with multiple resonators. In the non-linear regime, an analytical approach based on slowly varying amplitude equations allows us to derive a consistent and full characterization of the non-linear displacement detection, enabling a truthful detection of membrane displacements much above the usual linear sensing limited by the cavity linewidth. Such a high quality system also shows a pre-synchronization regime.
Collapse
|
17
|
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.
Collapse
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
| |
Collapse
|
18
|
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.
Collapse
|
19
|
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.
Collapse
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.
| |
Collapse
|
20
|
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.
Collapse
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
| |
Collapse
|
21
|
Sheng J, Wei X, Yang C, Wu H. Self-Organized Synchronization of Phonon Lasers. PHYSICAL REVIEW LETTERS 2020; 124:053604. [PMID: 32083916 DOI: 10.1103/physrevlett.124.053604] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 01/15/2020] [Indexed: 06/10/2023]
Abstract
Self-organized synchronization is a ubiquitous collective phenomenon, in which each unit adjusts their rhythms to achieve synchrony through mutual interactions. The optomechanical systems, due to their inherently engineerable nonlinearities, provide an ideal platform to study self-organized synchronization. Here, we demonstrate the self-organized synchronization of phonon lasers in a two-membrane-in-the-middle optomechanical system. The probe of each individual membrane enables us to monitor the real-time transient dynamics of synchronization, which reveals that the system enters into the synchronization regime via a torus birth bifurcation line. The phase-locking phenomenon and the transition between in-phase and antiphase regimes are directly observed. Moreover, such a system greatly facilitates the controllable synchronous states, and consequently a phononic memory is realized by tuning the system parameters. This result is an important step towards the future studies of many-body collective behaviors in multiresonator optomechanics with long distances, and might find potential applications in quantum information processing and complex networks.
Collapse
Affiliation(s)
- Jiteng Sheng
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Xinrui Wei
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Cheng Yang
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| |
Collapse
|
22
|
Zheng X, Ma SQ, Zhang GF, Fan H, Liu WM. Unified and Exact Framework for Variance-Based Uncertainty Relations. Sci Rep 2020; 10:150. [PMID: 31924830 PMCID: PMC6954228 DOI: 10.1038/s41598-019-56803-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2019] [Accepted: 11/07/2019] [Indexed: 11/09/2022] Open
Abstract
We provide a unified and exact framework for the variance-based uncertainty relations. This unified framework not only recovers some well-known previous uncertainty relations, but also fixes the deficiencies of them. Utilizing the unified framework, we can construct the new uncertainty relations in both product and sum form for two and more incompatible observables with any tightness we require. Moreover, one can even construct uncertainty equalities to exactly express the uncertainty relation by the unified framework, and the framework is therefore exact in describing the uncertainty relation. Some applications have been provided to illustrate the importance of this unified and exact framework. Also, we show that the contradiction between uncertainty relation and non-Hermitian operator, i.e., most of uncertainty relations will be violated when applied to non-Hermitian operators, can be fixed by this unified and exact framework.
Collapse
Affiliation(s)
- Xiao Zheng
- School of Physics, Beihang University, Xueyuan Road No. 37, Beijing, 100191, China
| | - Shao-Qiang Ma
- School of Physics, Beihang University, Xueyuan Road No. 37, Beijing, 100191, China
| | - Guo-Feng Zhang
- School of Physics, Beihang University, Xueyuan Road No. 37, Beijing, 100191, China.
| | - Heng Fan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
- CAS Central of Excellence in Topological Quantum Computation, Beijing, 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
| |
Collapse
|
23
|
Eneriz H, Rossatto DZ, Cárdenas-López FA, Solano E, Sanz M. Degree of Quantumness in Quantum Synchronization. Sci Rep 2019; 9:19933. [PMID: 31882744 PMCID: PMC6934783 DOI: 10.1038/s41598-019-56468-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Accepted: 12/02/2019] [Indexed: 11/09/2022] Open
Abstract
We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.
Collapse
Affiliation(s)
- H Eneriz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain
- LP2N, Laboratoire Photonique, Numérique et Nanosciences, Université Bordeaux-IOGS-CNRS:UMR 5298, 33400, Talence, France
| | - D Z Rossatto
- Departamento de Física, Universidade Federal de São Carlos, 13565-905, São Carlos, SP, Brazil.
- Universidade Estadual Paulista (Unesp), Campus Experimental de Itapeva, 18409-010, Itapeva, São Paulo, Brazil.
| | - F A Cárdenas-López
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, 200444, Shanghai, China
| | - E Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Physics Department, Shanghai University, 200444, Shanghai, China
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao, Spain
| | - M Sanz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080, Bilbao, Spain.
| |
Collapse
|
24
|
Du L, Chen YT, Li Y, Wu JH. Controllable optical response in a three-mode optomechanical system by driving the cavities on different sidebands. OPTICS EXPRESS 2019; 27:21843-21855. [PMID: 31510254 DOI: 10.1364/oe.27.021843] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Accepted: 06/26/2019] [Indexed: 06/10/2023]
Abstract
We study the controllable optical response in a three-mode optomechanical system comprised of two indirectly coupled cavity modes and an intermediate mechanical mode. The two cavity modes are assumed to have different frequencies and driven by two control fields on the red and blue sidebands, respectively. When the system is perturbed by two probe fields satisfying the specific matching condition, a series of intriguing phenomena can be observed by adjusting phases and amplitudes of the control fields, such as absorption-amplification switching, ultra-narrow response windows, frequency-independent perfect reflection, and ultralong optical group delay. We also compare our system with conventional optomechanical systems to highlight its distinct features. Our results may have potential applications in optical communication and quantum information processing.
Collapse
|
25
|
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.
Collapse
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
| |
Collapse
|
26
|
Kreinberg S, Porte X, Schicke D, Lingnau B, Schneider C, Höfling S, Kanter I, Lüdge K, Reitzenstein S. Mutual coupling and synchronization of optically coupled quantum-dot micropillar lasers at ultra-low light levels. Nat Commun 2019; 10:1539. [PMID: 30948766 PMCID: PMC6449346 DOI: 10.1038/s41467-019-09559-2] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Accepted: 03/19/2019] [Indexed: 11/25/2022] Open
Abstract
Synchronization of coupled oscillators at the transition between classical physics and quantum physics has become an emerging research topic at the crossroads of nonlinear dynamics and nanophotonics. We study this unexplored field by using quantum dot microlasers as optical oscillators. Operating in the regime of cavity quantum electrodynamics (cQED) with an intracavity photon number on the order of 10 and output powers in the 100 nW range, these devices have high β-factors associated with enhanced spontaneous emission noise. We identify synchronization of mutually coupled microlasers via frequency locking associated with a sub-gigahertz locking range. A theoretical analysis of the coupling behavior reveals striking differences from optical synchronization in the classical domain with negligible spontaneous emission noise. Beyond that, additional self-feedback leads to zero-lag synchronization of coupled microlasers at ultra-low light levels. Our work has high potential to pave the way for future experiments in the quantum regime of synchronization.
Collapse
Affiliation(s)
- Sören Kreinberg
- Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
| | - Xavier Porte
- Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany.
| | - David Schicke
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
| | - Benjamin Lingnau
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
| | - Christian Schneider
- Technische Physik, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
| | - Sven Höfling
- Technische Physik, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
- SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews, KY16 9SS, UK
| | - Ido Kanter
- Gonda Brain Research Center and Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Kathy Lüdge
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
| | - Stephan Reitzenstein
- Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany.
| |
Collapse
|
27
|
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: 2] [Impact Index Per Article: 0.3] [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.
Collapse
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
| |
Collapse
|
28
|
Punetha N, Varshney V, Sahoo S, Saxena G, Prasad A, Ramaswamy R. Dynamical effects of breaking rotational symmetry in counter-rotating Stuart-Landau oscillators. Phys Rev E 2018; 98:022212. [PMID: 30253578 DOI: 10.1103/physreve.98.022212] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2018] [Indexed: 11/07/2022]
Abstract
Stuart-Landau oscillators can be coupled so as to either preserve or destroy the rotational symmetry that the uncoupled system possesses. We examine some of the simplest cases of such couplings for a system of two nonidentical oscillators. When the coupling breaks the rotational invariance, there is a qualitative difference between oscillators wherein the phase velocity has the same sign (termed co-rotation) or opposite signs (termed counter-rotation). In the regime of oscillation death the relative sense of the phase rotations plays a major role. In particular, when rotational invariance is broken, counter-rotation or phase velocities of opposite signs appear to destabilize existing fixed points, thereby preserving and possibly extending the range of oscillatory behavior. The dynamical "frustration" induced by counter-rotations can thus suppress oscillation quenching when coupling breaks the symmetry.
Collapse
Affiliation(s)
- Nirmal Punetha
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, D-01187 Dresden, Germany
| | - Vaibhav Varshney
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Samir Sahoo
- School of Physical Sciences, Jawaharlal Nehru University, Delhi 110067, India
| | - Garima Saxena
- Department of Physics, Sri Venkateswara College, University of Delhi, Delhi 110021, India
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Ram Ramaswamy
- School of Physical Sciences, Jawaharlal Nehru University, Delhi 110067, India
| |
Collapse
|
29
|
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.
Collapse
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
| |
Collapse
|
30
|
Sonar S, Hajdušek M, Mukherjee M, Fazio R, Vedral V, Vinjanampathy S, Kwek LC. Squeezing Enhances Quantum Synchronization. PHYSICAL REVIEW LETTERS 2018; 120:163601. [PMID: 29756922 DOI: 10.1103/physrevlett.120.163601] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2018] [Indexed: 06/08/2023]
Abstract
It is desirable to observe synchronization of quantum systems in the quantum regime, defined by the low number of excitations and a highly nonclassical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelm synchronization in this regime. Here, we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible for small values of squeezing, and in this regime, the states are nonclassical. Furthermore, we show that the quality of synchronization measured by the FWHM of the power spectrum is enhanced with squeezing.
Collapse
Affiliation(s)
- Sameer Sonar
- 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, 117543 Singapore, Singapore
| | - Manas Mukherjee
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, National University Singapore, Singapore 117551, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654, Singapore
| | - Rosario Fazio
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- ICTP, Strada Costiera 11, 34151 Trieste, Italy
- NEST, Scuola Normale Superiore and Instituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Vlatko Vedral
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - 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
| | - Leong-Chuan Kwek
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654, Singapore
- Institute of Advanced Studies, Nanyang Technological University, Singapore 639673, Singapore
- National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore
| |
Collapse
|
31
|
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.
Collapse
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.
| |
Collapse
|
32
|
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.
Collapse
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
| |
Collapse
|
33
|
Navarrete-Benlloch C, Weiss T, Walter S, de Valcárcel GJ. General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles. PHYSICAL REVIEW LETTERS 2017; 119:133601. [PMID: 29341698 DOI: 10.1103/physrevlett.119.133601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2017] [Indexed: 06/07/2023]
Abstract
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.
Collapse
Affiliation(s)
- Carlos Navarrete-Benlloch
- Max-Planck-Institut für die Physik des Lichts, Staudtstrasse 2, 91058 Erlangen, Germany
- Institute for Theoretical Physics, Erlangen-Nürnberg Universität, Staudtstrasse 7, 91058 Erlangen, Germany
| | - Talitha Weiss
- Max-Planck-Institut für die Physik des Lichts, Staudtstrasse 2, 91058 Erlangen, Germany
- Institute for Theoretical Physics, Erlangen-Nürnberg Universität, Staudtstrasse 7, 91058 Erlangen, Germany
| | - Stefan Walter
- Max-Planck-Institut für die Physik des Lichts, Staudtstrasse 2, 91058 Erlangen, Germany
- Institute for Theoretical Physics, Erlangen-Nürnberg Universität, Staudtstrasse 7, 91058 Erlangen, Germany
| | - Germán J de Valcárcel
- Departament d'Òptica, Facultat de Física, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Spain
| |
Collapse
|
34
|
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.
Collapse
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
| |
Collapse
|
35
|
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.
Collapse
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
| |
Collapse
|
36
|
Pan Z, de Cagny H, Habibi M, Bonn D. Normal stresses in shear thickening granular suspensions. SOFT MATTER 2017; 13:3734-3740. [PMID: 28463377 DOI: 10.1039/c7sm00167c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
When subjected to shear, granular suspensions exhibit normal stresses perpendicular to the shear plane but the magnitude and sign of the different components of the normal stresses are still under debate. By performing both oscillatory and rotational rheology measurements on shear thickening granular suspensions and systematically varying the particle diameters and the gap sizes between two parallel-plates, we show that a transition from a positive to a negative normal stress can be observed. We find that frictional interactions which determine the shear thickening behavior of suspensions contribute to the positive normal stresses. Increasing the particle diameters or decreasing the gap sizes leads to a growing importance of hydrodynamic interactions, which results in negative normal stresses. We determine a relaxation time for the system, set by both the pore and the gap sizes, that governs the fluid flow through the inter-particle space. Finally, using a two-fluid model we determine the relative contributions from the particle phase and the liquid phase.
Collapse
Affiliation(s)
- Zhongcheng Pan
- Soft Matter group, Van der Waals-Zeeman Institute, IoP, Science Park 904, Amsterdam, The Netherlands.
| | | | | | | |
Collapse
|
37
|
Chen TY, Zhang WZ, Fang RZ, Hang CZ, Zhou L. Multi-path photon-phonon converter in optomechanical system at single-quantum level. OPTICS EXPRESS 2017; 25:10779-10790. [PMID: 28788767 DOI: 10.1364/oe.25.010779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Based on photon-phonon nonlinear interaction, a scheme of controllable photon-phonon converters is proposed at single-quantum level in a composed quadratically coupled optomechanical system. With the assistance of the mechanical oscillator, the Kerr nonlinear effect between photon and phonon is enhanced so that the single-photon state can be converted into the phonon state with high fidelity even under the current experimental condition that the single-photon coupling rate is much smaller than mechanical frequency (g ≪ ωm). The state transfer protocols and their transfer fidelity are discussed analytically and numerically. A multi-path photon-phonon converter is designed by combining the optomechanical system with low frequency resonators, which can be controlled by experimentally adjustable parameters. This work provides us a potential platform for quantum state transfer and quantum information.
Collapse
|
38
|
Witthaut D, Wimberger S, Burioni R, Timme M. Classical synchronization indicates persistent entanglement in isolated quantum systems. Nat Commun 2017; 8:14829. [PMID: 28401881 PMCID: PMC5394286 DOI: 10.1038/ncomms14829] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2016] [Accepted: 12/16/2017] [Indexed: 11/29/2022] Open
Abstract
Synchronization and entanglement constitute fundamental collective phenomena in multi-unit classical and quantum systems, respectively, both equally implying coordinated system states. Here, we present a direct link for a class of isolated quantum many-body systems, demonstrating that synchronization emerges as an intrinsic system feature. Intriguingly, quantum coherence and entanglement arise persistently through the same transition as synchronization. This direct link between classical and quantum cooperative phenomena may further our understanding of strongly correlated quantum systems and can be readily observed in state-of-the-art experiments, for example, with ultracold atoms. Collective phenomena in many-body systems include synchronization in classical and entanglement in quantum systems. Here the authors study isolated many-body quantum systems and demonstrate that synchronization emerges intrinsically, accompanied by the onset of quantum coherence and persistent entanglement.
Collapse
Affiliation(s)
- Dirk Witthaut
- Forschungszentrum Jülich, Institute for Energy and Climate Research (IEK-STE), 52428 Jülich, Germany.,Institute for Theoretical Physics, University of Cologne, Zuelpicher Str. 77, 50937 Köln, Germany.,Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg, 37077 Göttingen, Germany
| | - Sandro Wimberger
- Dipartimento di Scienze Matematiche, Fisiche ed Informatiche, Universitá di Parma, Via G.P. Usberti 7/a, 43124 Parma, Italy.,INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Parco Area delle Scienze, 7/A, 43124 Parma, Italy
| | - Raffaella Burioni
- Dipartimento di Scienze Matematiche, Fisiche ed Informatiche, Universitá di Parma, Via G.P. Usberti 7/a, 43124 Parma, Italy.,INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Parco Area delle Scienze, 7/A, 43124 Parma, Italy
| | - Marc Timme
- Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg, 37077 Göttingen, Germany.,Department of Physics, University of Darmstadt, 64289 Darmstadt, Germany.,Institute for Theoretical Physics, Technical University of Dresden, 01062 Dresden, Germany
| |
Collapse
|
39
|
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.
Collapse
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
| |
Collapse
|
40
|
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.
Collapse
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
| |
Collapse
|
41
|
Lau HW, Davidsen J. Linked and knotted chimera filaments in oscillatory systems. Phys Rev E 2016; 94:010204. [PMID: 27575065 DOI: 10.1103/physreve.94.010204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2015] [Indexed: 06/06/2023]
Abstract
While the existence of stable knotted and linked vortex lines has been established in many experimental and theoretical systems, their existence in oscillatory systems and systems with nonlocal coupling has remained elusive. Here, we present strong numerical evidence that stable knots and links such as trefoils and Hopf links do exist in simple, complex, and chaotic oscillatory systems if the coupling between the oscillators is neither too short ranged nor too long ranged. In this case, effective repulsive forces between vortex lines in knotted and linked structures stabilize curvature-driven shrinkage observed for single vortex rings. In contrast to real fluids and excitable media, the vortex lines correspond to scroll wave chimeras [synchronized scroll waves with spatially extended (tubelike) unsynchronized filaments], a prime example of spontaneous synchrony breaking in systems of identical oscillators. In the case of complex oscillatory systems, this leads to a topological superstructure combining knotted filaments and synchronization defect sheets.
Collapse
Affiliation(s)
- Hon Wai Lau
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada T2N 1N4
| | - Jörn Davidsen
- Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Canada T2N 1N4
| |
Collapse
|
42
|
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.
Collapse
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
| |
Collapse
|
43
|
Bastidas VM, Omelchenko I, Zakharova A, Schöll E, Brandes T. Quantum signatures of chimera states. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062924. [PMID: 26764791 DOI: 10.1103/physreve.92.062924] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2015] [Indexed: 06/05/2023]
Abstract
Chimera states are complex spatiotemporal patterns in networks of identical oscillators, characterized by the coexistence of synchronized and desynchronized dynamics. Here we propose to extend the phenomenon of chimera states to the quantum regime, and uncover intriguing quantum signatures of these states. We calculate the quantum fluctuations about semiclassical trajectories and demonstrate that chimera states in the quantum regime can be characterized by bosonic squeezing, weighted quantum correlations, and measures of mutual information. Our findings reveal the relation of chimera states to quantum information theory, and give promising directions for experimental realization of chimera states in quantum systems.
Collapse
Affiliation(s)
- V M Bastidas
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - I Omelchenko
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - A Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - E Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - T Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| |
Collapse
|
44
|
Zhang M, Shah S, Cardenas J, Lipson M. Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light. PHYSICAL REVIEW LETTERS 2015; 115:163902. [PMID: 26550878 DOI: 10.1103/physrevlett.115.163902] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2015] [Indexed: 06/05/2023]
Abstract
Synchronization of many coupled oscillators is widely found in nature and has the potential to revolutionize timing technologies. Here, we demonstrate synchronization in arrays of silicon nitride micromechanical oscillators coupled in an all-to-all configuration purely through an optical radiation field. We show that the phase noise of the synchronized oscillators can be improved by almost 10 dB below the phase noise limit for each individual oscillator. These results open a practical route towards synchronized oscillator networks.
Collapse
Affiliation(s)
- Mian Zhang
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Shreyas Shah
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Jaime Cardenas
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Michal Lipson
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
- Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, USA
| |
Collapse
|
45
|
Lauter R, Brendel C, Habraken SJM, Marquardt F. Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012902. [PMID: 26274242 DOI: 10.1103/physreve.92.012902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Indexed: 06/04/2023]
Abstract
Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. We find that the full dynamical equations for the phase dynamics of a limit-cycle oscillator array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and nonstationary patterns. Our results are of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays, as well as for any array of coupled limit-cycle oscillators that have undergone a Hopf bifurcation. The possible observation in optomechanical arrays is discussed briefly.
Collapse
Affiliation(s)
- Roland Lauter
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
- Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1/Bau 24, 91058 Erlangen, Germany
| | - Christian Brendel
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Steven J M Habraken
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Florian Marquardt
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
- Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1/Bau 24, 91058 Erlangen, Germany
| |
Collapse
|
46
|
Hermoso de Mendoza I, Pachón LA, Gómez-Gardeñes J, Zueco D. Synchronization in a semiclassical Kuramoto model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052904. [PMID: 25493855 DOI: 10.1103/physreve.90.052904] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2013] [Indexed: 06/04/2023]
Abstract
Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.
Collapse
Affiliation(s)
| | - Leonardo A Pachón
- Grupo de Física Atómica y Molecular, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA; Calle 70 No. 52-21, Medellín, Colombia
| | - Jesús Gómez-Gardeñes
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain and Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, E-50018 Zaragoza, Spain
| | - David Zueco
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain and Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, E-50012 Zaragoza, Spain and Fundación ARAID, Paseo María Agustín 36, E-50004 Zaragoza, Spain
| |
Collapse
|
47
|
Xu M, Tieri DA, Fine EC, Thompson JK, Holland MJ. Synchronization of two ensembles of atoms. PHYSICAL REVIEW LETTERS 2014; 113:154101. [PMID: 25375711 DOI: 10.1103/physrevlett.113.154101] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2013] [Indexed: 06/04/2023]
Abstract
We propose a system for observing the correlated phase dynamics of two mesoscopic ensembles of atoms through their collective coupling to an optical cavity. We find a dynamical quantum phase transition induced by pump noise and cavity output coupling. The spectral properties of the superradiant light emitted from the cavity show that at a critical pump rate the system undergoes a transition from the behavior of two independent oscillators to the phase locking that is the signature of quantum synchronization.
Collapse
Affiliation(s)
- Minghui Xu
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - D A Tieri
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - E C Fine
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - James K Thompson
- 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
| |
Collapse
|
48
|
Wang G, Huang L, Lai YC, Grebogi C. Nonlinear dynamics and quantum entanglement in optomechanical systems. PHYSICAL REVIEW LETTERS 2014; 112:110406. [PMID: 24702337 DOI: 10.1103/physrevlett.112.110406] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2013] [Indexed: 06/03/2023]
Abstract
To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.
Collapse
Affiliation(s)
- Guanglei Wang
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Liang Huang
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA and School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA and Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| |
Collapse
|
49
|
Walter S, Nunnenkamp A, Bruder C. Quantum synchronization of a driven self-sustained oscillator. PHYSICAL REVIEW LETTERS 2014; 112:094102. [PMID: 24655255 DOI: 10.1103/physrevlett.112.094102] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2013] [Indexed: 06/03/2023]
Abstract
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.
Collapse
Affiliation(s)
- Stefan Walter
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Andreas Nunnenkamp
- 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
| |
Collapse
|
50
|
Lee TE, Chan CK, Wang S. Entanglement tongue and quantum synchronization of disordered oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022913. [PMID: 25353551 DOI: 10.1103/physreve.89.022913] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2013] [Indexed: 06/04/2023]
Abstract
We study the synchronization of dissipatively coupled van der Pol oscillators in the quantum limit, when each oscillator is near its quantum ground state. Two quantum oscillators with different frequencies exhibit an entanglement tongue, which is the quantum analog of an Arnold tongue. It means that the oscillators are entangled in steady state when the coupling strength is greater than a critical value, and the critical coupling increases with detuning. An ensemble of many oscillators with random frequencies still exhibits a synchronization phase transition in the quantum limit, and we analytically calculate how the critical coupling depends on the frequency disorder. Our results can be experimentally observed with trapped ions or neutral atoms.
Collapse
Affiliation(s)
- Tony E Lee
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ching-Kit Chan
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Shenshen Wang
- Department of Physics and Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|