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Sudler AJ, Talukdar J, Blume D. Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response. Phys Rev E 2024; 109:054207. [PMID: 38907472 DOI: 10.1103/physreve.109.054207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 04/23/2024] [Indexed: 06/24/2024]
Abstract
Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three nonlinear dissipative terms. Since two of the nonlinear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.
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Affiliation(s)
- A J Sudler
- Homer L. Dodge Department of Physics and Astronomy, and Center for Quantum Research and Technology, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
| | - J Talukdar
- Homer L. Dodge Department of Physics and Astronomy, and Center for Quantum Research and Technology, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
| | - D Blume
- Homer L. Dodge Department of Physics and Astronomy, and Center for Quantum Research and Technology, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
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2
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Nadolny T, Bruder C. Macroscopic Quantum Synchronization Effects. PHYSICAL REVIEW LETTERS 2023; 131:190402. [PMID: 38000429 DOI: 10.1103/physrevlett.131.190402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 10/16/2023] [Indexed: 11/26/2023]
Abstract
We theoretically describe macroscopic quantum synchronization effects occurring in a network of all-to-all coupled quantum limit-cycle oscillators. The coupling causes a transition to synchronization as indicated by the presence of global phase coherence. We demonstrate that the microscopic quantum properties of the oscillators qualitatively shape the synchronization behavior in a macroscopically large network. Specifically, they result in a blockade of collective synchronization that is not expected for classical oscillators. Additionally, the macroscopic ensemble shows emergent behavior not present at the level of two coupled quantum oscillators.
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Affiliation(s)
- Tobias Nadolny
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Christoph Bruder
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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3
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Shen Y, Soh HY, Fan W, Kwek LC. Enhancing quantum synchronization through homodyne measurement, noise, and squeezing. Phys Rev E 2023; 108:024204. [PMID: 37723755 DOI: 10.1103/physreve.108.024204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Accepted: 07/18/2023] [Indexed: 09/20/2023]
Abstract
Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite the rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task but preferably in the semiclassical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart-Landau oscillator and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semiclassical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.
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Affiliation(s)
- Yuan Shen
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, 639798, Singapore
| | - Hong Yi Soh
- National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, 637616, Singapore
| | - Weijun Fan
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, 639798, Singapore
| | - Leong-Chuan Kwek
- School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, 639798, Singapore
- National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, 637616, Singapore
- Centre for Quantum Technologies, National University of Singapore, 117543, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore
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4
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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.
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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
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Murtadho T, Vinjanampathy S, Thingna J. Cooperation and Competition in Synchronous Open Quantum Systems. PHYSICAL REVIEW LETTERS 2023; 131:030401. [PMID: 37540879 DOI: 10.1103/physrevlett.131.030401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 06/13/2023] [Indexed: 08/06/2023]
Abstract
Synchronization between limit cycle oscillators can arise through entrainment to an external drive or through mutual coupling. The interplay between the two mechanisms has been studied in classical synchronizing systems, but not in quantum systems. Here, we point out that competition and cooperation between the two mechanisms can occur due to phase pulling and phase repulsion in quantum systems. We study their interplay in collectively driven degenerate quantum thermal machines and show that these mechanisms either cooperate or compete depending on the working mode of the machine (refrigerator or engine). The entrainment-mutual synchronization interplay persists with an increase in the number of degenerate levels, while in the thermodynamic limit of degeneracy, mutual synchronization dominates. Overall, our work investigates the effect of degeneracy and multilevel scaling of quantum synchronization and shows how different synchronizing mechanisms can cooperate and compete in quantum systems.
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Affiliation(s)
- Taufiq Murtadho
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
- Basic Science Program, Korea University of Science and Technology, Daejeon 34113, Republic of Korea
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Sai Vinjanampathy
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
- Centre of Excellence in Quantum Information, Computation, Science and Technology, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore, Singapore
| | - Juzar Thingna
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
- Basic Science Program, Korea University of Science and Technology, Daejeon 34113, Republic of Korea
- Department of Physics and Applied Physics, University of Massachusetts, Lowell, Massachusetts 01854, USA
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Lippolis D, Shudo A. Towards the Resolution of a Quantized Chaotic Phase-Space: The Interplay of Dynamics with Noise. ENTROPY (BASEL, SWITZERLAND) 2023; 25:411. [PMID: 36981299 PMCID: PMC10047867 DOI: 10.3390/e25030411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/30/2022] [Revised: 02/06/2023] [Accepted: 02/12/2023] [Indexed: 06/18/2023]
Abstract
We outline formal and physical similarities between the quantum dynamics of open systems and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, which, for suitable timescales, becomes analogous to the Fokker-Planck equation describing classical advection and diffusion. This correspondence allows, in principle, to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol-type oscillators.
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Affiliation(s)
- Domenico Lippolis
- Institute for Applied Systems Analysis, Jiangsu University, Zhenjiang 212013, China
| | - Akira Shudo
- Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji 192-0397, Tokyo, Japan
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7
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Bandyopadhyay B, Banerjee T. Aging transition in coupled quantum oscillators. Phys Rev E 2023; 107:024204. [PMID: 36932509 DOI: 10.1103/physreve.107.024204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 01/27/2023] [Indexed: 06/18/2023]
Abstract
Aging transition is an emergent behavior observed in networks consisting of active (self-oscillatory) and inactive (non-self-oscillatory) nodes, where the network transits from a global oscillatory state to an oscillation collapsed state when the fraction of inactive oscillators surpasses a critical value. However, the aging transition in quantum domain has not been studied yet. In this paper we investigate the quantum manifestation of aging transition in a network of active-inactive quantum oscillators. We show that, unlike classical case, the quantum aging is not characterized by a complete collapse of oscillation but by sufficient reduction in the mean boson number. We identify a critical "knee" value in the fraction of inactive oscillators around which quantum aging occurs in two different ways. Further, in stark contrast to the classical case, quantum aging transition depends upon the nonlinear damping parameter. We also explain the underlying processes leading to quantum aging that have no counterpart in the classical domain.
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Affiliation(s)
- Biswabibek Bandyopadhyay
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
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8
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Bandyopadhyay B, Banerjee T. Kerr nonlinearity hinders symmetry-breaking states of coupled quantum oscillators. Phys Rev E 2022; 106:024216. [PMID: 36109913 DOI: 10.1103/physreve.106.024216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2022] [Accepted: 08/18/2022] [Indexed: 06/15/2023]
Abstract
We study the effect of Kerr anharmonicity on the symmetry-breaking phenomena of coupled quantum oscillators. Two types of symmetry-breaking processes are studied, namely, the inhomogeneous steady state (or quantum oscillation death state) and quantum chimera state. Remarkably, it is found that Kerr nonlinearity hinders the process of symmetry breaking in both the cases. We establish our results using direct simulation of the quantum master equation and analysis of the stochastic semiclassical model. Interestingly, in the case of quantum oscillation death, an increase in the strength of Kerr nonlinearity tends to favor the symmetry and at the same time decreases the degree of quantum mechanical entanglement. This paper presents a useful mean to control and engineer symmetry-breaking states for quantum technology.
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Affiliation(s)
- Biswabibek Bandyopadhyay
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
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9
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Kato Y, Nakao H. A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint. CHAOS (WOODBURY, N.Y.) 2022; 32:063133. [PMID: 35778147 DOI: 10.1063/5.0088559] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 05/24/2022] [Indexed: 06/15/2023]
Abstract
We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but it has not been defined explicitly for quantum nonlinear oscillators. In this study, we define the asymptotic phase for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the fundamental oscillation frequency. By using the quantum van der Pol oscillator with a Kerr effect as an example, we illustrate that the proposed asymptotic phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes.
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Affiliation(s)
- Yuzuru Kato
- Department of Complex and Intelligent Systems, Future University Hakodate, Hokkaido 041-8655, Japan
| | - Hiroya Nakao
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
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10
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Bandyopadhyay B, Khatun T, Banerjee T. Quantum Turing bifurcation: Transition from quantum amplitude death to quantum oscillation death. Phys Rev E 2021; 104:024214. [PMID: 34525675 DOI: 10.1103/physreve.104.024214] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 08/09/2021] [Indexed: 11/06/2022]
Abstract
An important transition from a homogeneous steady state to an inhomogeneous steady state via the Turing bifurcation in coupled oscillators was reported recently [Phys. Rev. Lett. 111, 024103 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.024103]. However, the same in the quantum domain is yet to be observed. In this paper, we discover the quantum analog of the Turing bifurcation in coupled quantum oscillators. We show that a homogeneous steady state is transformed into an inhomogeneous steady state through this bifurcation in coupled quantum van der Pol oscillators. We demonstrate our results by a direct simulation of the quantum master equation in the Lindblad form. We further support our observations through an analytical treatment of the noisy classical model. Our study explores the paradigmatic Turing bifurcation at the quantum-classical interface and opens up the door toward its broader understanding.
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Affiliation(s)
- Biswabibek Bandyopadhyay
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Taniya Khatun
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
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11
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Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory. MATHEMATICS 2021. [DOI: 10.3390/math9182188] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable systems undergoing noise-induced oscillations, and also for quantum limit-cycle oscillators in the semiclassical regime.
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12
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Chia A, Hajdušek M, Nair R, Fazio R, Kwek LC, Vedral V. Phase-Preserving Linear Amplifiers Not Simulable by the Parametric Amplifier. PHYSICAL REVIEW LETTERS 2020; 125:163603. [PMID: 33124847 DOI: 10.1103/physrevlett.125.163603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Revised: 04/26/2019] [Accepted: 09/18/2020] [Indexed: 06/11/2023]
Abstract
It is commonly accepted that a parametric amplifier can simulate a phase-preserving linear amplifier regardless of how the latter is realized [C. M. Caves et al., Phys. Rev. A 86, 063802 (2012)PLRAAN1050-294710.1103/PhysRevA.86.063802]. If true, this reduces all phase-preserving linear amplifiers to a single familiar model. Here we disprove this claim by constructing two counterexamples. A detailed discussion of the physics of our counterexamples is provided. It is shown that a Heisenberg-picture analysis facilitates a microscopic explanation of the physics. This also resolves a question about the nature of amplifier-added noise in degenerate two-photon amplification.
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Affiliation(s)
- A Chia
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
| | - M Hajdušek
- Keio University Shonan-Fujisawa Campus, Fujisawa, Kanagawa 252-0882, Japan
| | - R Nair
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Complexity Institute, Nanyang Technological University, Singapore 637460, Singapore
| | - R Fazio
- Abdus Salam ICTP, Trieste 34151, Italy
- Dipartimento di Fisica, Università di Napoli Federico II, Complesso di Monte S. Angelo, Napoli 80126, Italy
| | - L C Kwek
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore
| | - V Vedral
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
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