Dynamics of many-body quantum synchronisation

Davis-Tilley, Claire; Teoh, Chen Khong; Armour, A. D.

doi:10.1088/1367-2630/aae947

Cited by 25 publications

(13 citation statements)

References 55 publications

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“…Firstly, when w w = "j j , the magnetic field in equation (18) breaks the spin SU(2) symmetry of the model:…”

Section: Many-body Synchronisation In the Hubbard Modelmentioning

confidence: 99%

“…The formation of a Bose-Einstein condensate (BEC), for example, could be considered perfect synchronisation [17] due to the collective condensation of the atoms in the bosonic gas. In closer analogy to classical systems, models of self-sustained quantum oscillators, such as quantum Van der Pol oscillators [13,18,19] or pairs of micromasers [20], have been shown to lock phases and reach coupled limit cycles. Quantum effects play a decisive role in either enhancing [21,22] or hindering [23] this synchronicity.…”

Section: Introductionmentioning

confidence: 99%

“…Quantum effects play a decisive role in either enhancing [21,22] or hindering [23] this synchronicity. Under the mean-field approximation, these results have been extended to larger systems of oscillators where the underlying mechanism for synchronisation is a reduction in the uncertainty in the phase distribution at the expense of the certainty in the number distribution [18].…”

Section: Introductionmentioning

confidence: 99%

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Quantum synchronisation enabled by dynamical symmetries and dissipation

et al. 2020

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In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry-an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit longlived signatures of both phase and frequency-locking.

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“…Firstly, when w w = "j j , the magnetic field in equation (18) breaks the spin SU(2) symmetry of the model:…”

Section: Many-body Synchronisation In the Hubbard Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum synchronisation enabled by dynamical symmetries and dissipation

et al. 2020

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“…Although we have only analyzed a singleoscillator problem with a single degree of freedom in this study, the developed framework can be directly extended to two or more quantum oscillators with weak coupling by using standard methods from the classical phase reduction theory. Analysis of large many-body systems and the study of their collective dynamics are of particular interest [24,29,30,47,48].…”

Section: Discussionmentioning

confidence: 99%

Semiclassical phase reduction theory for quantum synchronization

Kato

Yamamoto

Nakao

2019

Phys. Rev. Research

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We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a simple, one-dimensional classical stochastic differential equation approximately describing the phase dynamics of the system under the semiclassical approximation. The density matrix and power spectrum of the original quantum system can be approximately reconstructed from the reduced phase equation. The developed framework enables us to analyze synchronization dynamics of quantum limit-cycle oscillators using the standard methods for classical limit-cycle oscillators in a quantitative way. As an example, we analyze synchronization of a quantum van der Pol oscillator under harmonic driving and squeezing, including the case that the squeezing is strong and the oscillation is asymmetric. The developed framework provides insights into the relation between quantum and classical synchronization and will facilitate systematic analysis and control of quantum nonlinear oscillators.

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“…Appealing examples with interesting applications comprise synchronization between hearth cardiac pacemaker cells [2], chaotic laser signals [3] or micromechanical oscillators [4][5][6].In the last decade, the interest on this paradigmatic phenomenon has been extended to the quantum realm, see e.g. [14][15][16][17][18][19][20][21][22][23]. Quantum mechanics plays a crucial role when exploring this phenomenon beyond the classical regime [24] and in relation to the degree of synchronization that systems can reach [11].…”

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confidence: 99%

Synchronization along quantum trajectories

Es'haqi-Sani

Manzano

Zambrini

et al. 2020

Phys. Rev. Research

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We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol oscillators interacting through dissipative coupling. We show the deep impact of synchronization on the statistics of phase-locking indicators and other correlation measures defined for single trajectories. Our results shed new light on fundamental issues regarding quantum synchronization providing new methods for its precise quantification. PACS numbers: 05.30.-d 03.67.-a 42.50.DvSynchronization is one of the most universal manifestations of emergent cooperative behavior, observed in a broad range of physical, chemical and biological systems [1,2]. It can be defined as the progressive adjustment of rhythms between oscillatory units due to their weak interaction and despite their different natural frequencies. Appealing examples with interesting applications comprise synchronization between hearth cardiac pacemaker cells [2], chaotic laser signals [3] or micromechanical oscillators [4][5][6].In the last decade, the interest on this paradigmatic phenomenon has been extended to the quantum realm, see e.g. [14][15][16][17][18][19][20][21][22][23]. Quantum mechanics plays a crucial role when exploring this phenomenon beyond the classical regime [24] and in relation to the degree of synchronization that systems can reach [11]. Quantum synchronization can be characterized with different outcomes [25] using local or global indicators in the system observables [24]. It has been shown that the emergence of this phenomenon is often connected to the generation of quantum correlations such as discord [9,10,[26][27][28] or entanglement [7,10,29,[31][32][33]. However, a universal relation between quantum correlations and synchronization is not expected in general, and thus whether quantum synchronization may be used for witnessing quantum correlations is still an open question. In addition, quantum synchronization may also find applications for probing spectral densities in natural or engineered environments [34,35].In classical systems, spontaneous synchronization is usually characterized through the trajectories in phasespace [2]. In contrast, measuring synchronization in open quantum systems becomes more challenging and different avenues have been explored. For instance, temporal correlations in local observables can be quantified by using the Pearson correlation coefficient [9] or global quantum correlations can be addressed through the synchronization error [11]. Quantitative measures of phase-locking based on the expectation values of different non-local correlators [11,16,18,36] have been proposed, but they are often not indicative of the underlying processes [37]. Finally, information measures of correlations like the mutual information [38] or have also been also employed. In all these approaches, synchronization is computed through the expectation values of different (local or global) obse...

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Dynamics of many-body quantum synchronisation

Cited by 25 publications

References 55 publications

Quantum synchronisation enabled by dynamical symmetries and dissipation

Quantum synchronisation enabled by dynamical symmetries and dissipation

Semiclassical phase reduction theory for quantum synchronization

Synchronization along quantum trajectories

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