Observing quantum synchronization blockade in circuit quantum electrodynamics

Nigg, Simon E.

doi:10.1103/physreva.97.013811

Cited by 38 publications

(24 citation statements)

References 49 publications

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“…To conclude we mention that the approach outlined here is rather general and can be used to shed light on the spectral properties of other small driven-dissipative quantum models. Interesting future directions include for example the study of resonance fluorescence lineshapes beyond the two-level system limit [50,51], the spectral features of a coherently driven cavity across a zero-dimensional dissipative phase transition [52][53][54] or applications related to quantum synchronization [55,56].…”

Section: Discussionmentioning

confidence: 99%

Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

2019

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Keywords: open quantum systems, quantum van der pol oscillator, driven and dissipative quantum systems AbstractWe study the spectral properties of Markovian driven-dissipative quantum systems, focusing on the nonlinear quantum van der Pol oscillator as a paradigmatic example. We discuss a generalized Lehmann representation, in which single-particle Greenʼs functions are expressed in terms of the eigenstates and eigenvalues of the Liouvillian. Applying it to the quantum van der Pol oscillator, we find a wealth of phenomena that are not apparent in the steady-state density matrix alone. Unlike the steady state, the photonic spectral function has a strong dependence on interaction strength. Further, we find that the interplay of interaction and non-equilibrium effects can result in a surprising 'negative density of states', associated with a negative temperature, even in absence of steady state population inversion.

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Section: Discussionmentioning

confidence: 99%

Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

2019

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“…However we shall restrict in this paper to study synchronization at room temperature T 300 K only, which justifies a classical treatment of the above Langevin equations and implies a different treatment of optical and mechanical noise terms. In fact, at optical frequencies ω f /2π = ω c /2π 10 14 Hz, so thatn f 0, while at mechanical frequencies ω f /2π = ω 1 /2π ω 2 /2π 10 6 Hz implyingn f k b T / ω 1 1.…”

Section: System Dynamicsmentioning

confidence: 99%

Noise robustness of synchronization of two nanomechanical resonators coupled to the same cavity field

Piergentili

et al. 2020

Phys. Rev. A

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We study synchronization of a room temperature optomechanical system formed by two resonators coupled via radiation pressure to the same driven optical cavity mode. By using stochastic Langevin equations and effective slowly-varying amplitude equations, we explore the long-time dynamics of the system. We see that thermal noise can induce significant non-Gaussian dynamical properties, including the coexistence of multi-stable synchronized limit cycles and phase diffusion. Synchronization in this optomechanical system is very robust with respect to thermal noise: in fact, even though each oscillator phase progressively diffuses over the whole limit cycle, their phase difference is locked, and such a phase correlation remains strong in the presence of thermal noise.

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“…Recent progress in experimental studies has revealed that synchronization can take place in coupled nonlinear oscillators with intrinsically quantum-mechanical origins, such as micro and nanomechanical oscillators [16][17][18][19][20], spin torque oscillators [21], and cooled atomic ensembles [22,23]. Moreover, theoretical studies have been performed on the synchronization of nonlinear oscillators which explicitly show quantum signatures , such as optomechanical oscillators [24][25][26], cooled atomic ensembles [27,28], trapped ions [29][30][31], spins [32], and superconducting circuits [33]. In particular, a number of studies have analyzed the quantum van der Pol (vdP) oscillator [29], which is a typical model of quantum self-sustained oscillators, for example, synchronization of a quantum vdP oscillator by harmonic driving [26,34] or squeezing [35], mutual synchronization of coupled quantum vdP oscillators [30,36], and quantum fluctuations around oscillating and locked states of a quantum vdP oscillator [40,41].…”

Section: Introductionmentioning

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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Observing quantum synchronization blockade in circuit quantum electrodynamics

Cited by 38 publications

References 49 publications

Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

Noise robustness of synchronization of two nanomechanical resonators coupled to the same cavity field

Semiclassical phase reduction theory for quantum synchronization

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