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Physical Review A

Quantum synchronization and correlations of two mechanical resonators in a dissipative optomechanical system

Chang-Geng Liao, Rongxin Chen, Hong Xie, Meng-Ying He, Xiu‐Min Lin

Published Mar 11, 2019• 47 citations
Publisher

Abstract

Quantum synchronization and its connection with other quantum correlations have attracted considerable attention. Here we present a theoretical scheme to simultaneously represent and significantly enhance the level of quantum synchronization and entanglement between two indirectly coupled mechanical membranes, which are coupled to a common optical field within a cavity. By applying a two-tone driving laser with weighted amplitudes and specific frequencies, both synchronization gauged by Mari's criterion and entanglement estimated by logarithmic negativity can be greatly enhanced. We then clarify the relationship between quantum synchronization and entanglement in detail. Numerical simulation results show that the influence of the coupling asymmetry ${G}_{2}/{G}_{1}$ on quantum complete synchronization behaves similarly to that on the purity while the influence of the coupling asymmetry ${G}_{2}/{G}_{1}$ on quantum phase synchronization is more similar to that on quantum entanglement. Besides, we demonstrate that although quantum synchronization and quantum entanglement are not directly related, both of them are sensitive to the squeezing parameter and the cooling effect. Furthermore, it is also shown that detuning the frequencies of two mechanical oscillators can actually help quantum synchronization and entanglement, which is somewhat similar to the case of quantum synchronization blockade.

DOI
10.1103/physreva.99.033818

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Quantum synchronization and its connection with other quantum correlations have attracted considerable attention. Here we present a theoretical scheme to simultaneously represent and significantly enhance the level of quantum synchronization and entanglement between two indirectly coupled mechanical membranes, which are coupled to a common optical field within a cavity. By applying a two-tone driving laser with weighted amplitudes and specific frequencies, both synchronization gauged by Mari's criterion and entanglement estimated by logarithmic negativity can be greatly enhanced. We then clarify the relationship between quantum synchronization and entanglement in detail. Numerical simulation results show that the influence of the coupling asymmetry G2/G1{G}_{2}/{G}_{1}G2​/G1​ on quantum complete synchronization behaves similarly to that on the purity while the influence of the coupling asymmetry G2/G1{G}_{2}/{G}_{1}G2​/G1​ on quantum phase synchronization is more similar to that on quantum entanglement. Besides, we demonstrate that although quantum synchronization and quantum entanglement are not directly related, both of them are sensitive to the squeezing parameter and the cooling effect. Furthermore, it is also shown that detuning the frequencies of two mechanical oscillators can actually help quantum synchronization and entanglement, which is somewhat similar to the case of quantum synchronization blockade.
In this work, we study the quantum synchronization and quantum $\ensuremath{\phi}$ synchronization of two mechanical oscillators in a coupled optomechanical system. The oscillators are coupled to an optical cavity filled with a Kerr nonlinear medium and subjected to periodic modulation of the cavity detunings and driving amplitudes by a common driving field. Our results show that the quantum synchronization and quantum $\ensuremath{\phi}$ synchronization in nonlinear systems exhibit more favorable behaviors than in linear systems. In addition, we have investigated the performances of two synchronization measurements to various parameters by analyzing the sensitivity of $\ensuremath{\phi}$. Accordingly, perfect synchronization can be achieved under specific parameters by periodically modulating the cavity and driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations.
Abstract In this work, we investigate the quantum synchronization and ϕ synchronization of two mechanical oscillators of different frequencies in two optomechanical systems with asymmetric coupling interaction. The whole system can be modulated by cavity detuning or driving amplitudes. Under certain parameters, quantum ϕ synchronization can be enhanced by asymmetric coupling in optomechanical systems, and the phase difference ϕ has an inversion. Moreover, we show that with the introduction of Kerr nonlinear medium, nonlinearity is dominated in achieving synchronization within asymmetric coupled cavities and ϕ can be corrected. Apart from achieving quantum synchronization, quantum anti-synchronization can be observed depending on the asymmetric coupling and the asymmetric external driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations in asymmetric coupled optomechanical systems.
We investigate the quantum synchronization of two indirectly coupled mechanical oscillators with different frequencies in the Kerr resonator optomechanical system, where the two driving fields are modulated. Our findings indicate that Kerr nonlinearity facilitates quantum synchronization, while quadratic coupling tends to suppress it. When both nonlinearities are present, quadratic coupling enhances synchronization in the presence of weak Kerr nonlinearity, whereas strong Kerr nonlinearity causes it to suppress synchronization. These results imply the existence of an optimal parameter regime for maximizing quantum synchronization. Moreover, under the joint influence of Kerr nonlinearity and quadratic coupling, perfect synchronization can be achieved under specific parameters. Our results provide insight into the manipulation of quantum synchronization utilizing nonlinearities in cavity optomechanical systems.
Spontaneous synchronization is a significant collective behavior of weakly coupled systems. Due to their inherent nonlinear nature, optomechanical systems can exhibit self-sustained oscillations which can be exploited for synchronizing different mechanical resonators. In this paper, we explore the synchronization dynamics of two membranes coupled to a common optical field within a cavity, and pumped with a strong blue-detuned laser drive. We focus on the system quantum dynamics in the parameter regime corresponding to synchronization of the classical motion of the two membranes. With an appropriate definition of the phase difference operator for the resonators, we study synchronization in the quantum case through the covariance matrix formalism. We find that for sufficiently large driving, quantum synchronization is robust with respect to quantum fluctuations and to thermal noise up to not too large temperatures. Under synchronization, the two membranes are never entangled, while quantum discord behaves similarly to quantum synchronization, that is, it is larger when the variance of the phase difference is smaller.
In this work, we investigate the dynamics of quantum synchronization in a four-mode optomechanical system, focusing on the influence of the Coulomb interaction between two mechanical resonators. We analyze the effect of the Coulomb coupling on three distinct synchronization regimes, i.e., complete quantum synchronization, φφφ-synchronization, and quantum phase synchronization. Our results show that while the Coulomb interaction plays a pivotal role in significantly enhancing quantum phase synchronization by facilitating energy exchange and phase coherence, it has little impact on complete and φφφ-synchronization. This indicates that amplitude and frequency locking are primarily determined by the optical driving, whereas phase alignment depends critically on inter-resonator coupling. We also demonstrate that the oscillations of the two optical cavities, which are indirectly coupled via the mechanical resonators, can become aligned over time, resulting in classical synchronization. These findings provide a robust mechanism for controlling collective quantum dynamics and offer a foundation for applications in quantum communication, precision sensing, and the development of synchronized quantum networks.
We investigate synchronization and entanglement in two coupled cavity optomechanical systems. The classical synchronization, quantum synchronization and entanglement of the two cavity fields and the two mechanical oscillators are analysed, respectively. Our results show that the two cavity resonators are synchronization without entanglement, while the two mechanical oscillators are entangled with quantum-phase synchronization. We conclude that the quantum synchronization and entanglement have no affirmatory relationship although they are both signature of correlation.