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Physical Review A

Dynamics of ground-state cooling and quantum entanglement in a modulated optomechanical system

Guoyao Li, Wenjie Nie, Xiyun Li, Aixi Chen

Published Dec 2, 2019• 22 citations
Publisher

Abstract

We theoretically study the dynamics of the ground-state cooling and the quantum entanglement in a modulated optomechanical system, where the frequency of the mechanical oscillator and the optical field or the strength of the driving laser is time dependent. In this paper, we focus mainly on the fact that the system works in the regime of blue detuning. It is found that in the long-time limit the steady-state phonon number can be decreased significantly so that the mechanical oscillator is cooled to the ground state by appropriately selecting the frequency and the amplitude of the modulation. Further, with the help of the dynamical modulation in the system, the time evolution of the entanglement preevaluation value displays the death and rebirth of quantum entanglement between the mechanical oscillator and the optical field, which correspond, respectively, to the increase and decrease of the effective phonon number of the mechanical oscillator. In particular, when the steady-state dynamics of the system is quasiperiodic, the dynamics of the entanglement preevaluation value exhibits a quasiperiodic behavior, which means that the quantum phenomena can be represented in nonlinear classical dynamics.

DOI
10.1103/physreva.100.063805

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We theoretically study the dynamics of the ground-state cooling and the quantum entanglement in a modulated optomechanical system, where the frequency of the mechanical oscillator and the optical field or the strength of the driving laser is time dependent. In this paper, we focus mainly on the fact that the system works in the regime of blue detuning. It is found that in the long-time limit the steady-state phonon number can be decreased significantly so that the mechanical oscillator is cooled to the ground state by appropriately selecting the frequency and the amplitude of the modulation. Further, with the help of the dynamical modulation in the system, the time evolution of the entanglement preevaluation value displays the death and rebirth of quantum entanglement between the mechanical oscillator and the optical field, which correspond, respectively, to the increase and decrease of the effective phonon number of the mechanical oscillator. In particular, when the steady-state dynamics of the system is quasiperiodic, the dynamics of the entanglement preevaluation value exhibits a quasiperiodic behavior, which means that the quantum phenomena can be represented in nonlinear classical dynamics.
Cavity optomechanical systems involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter regimes, with one of them enabling us to study quantum-classical correspondence in system dynamics, while there exist no classical counterparts of the quantum features for the other. For the detuning of the laser pumping around the mechanical frequency, as the parametric gain of OPA increases to a critical value, the classical dynamics of the optical or mechanical modes can experience a transition from the regular periodic oscillation to a period-doubling motion, in which case the light-mechanical entanglement can be well studied by the logarithmic negativity and can manifest the dynamical transition the classical nonlinear dynamics. In addition, the optomechanical entanglement shows a second-order transition characteristic at the critical parametric gain. For the laser detuning being about twice the mechanical frequency, the kind of normal mode splitting comes up in the laser detuning dependence of optomechanical entanglement, which is induced by the squeezing of the optical and mechanical hybrid modes and finds no classical correspondence. The OPA-assisted optomechanical systems therefore offer a simple way to study and exploit quantum manifestations of classical nonlinear dynamics.
A controllable entanglement scheme of two mechanical oscillators is proposed in a composite optomechanical system. In the case of strong driving and high dissipation, the dynamics of the movable mirror of the optomechanical cavity is characterized by an effective frequency in the long-time evolution of the system. Considering the classical nonlinear effects in an optomechanical system, we investigate the relationship between the effective frequency of the movable mirror and the adjustable parameters of the cavity. It shows that the effective frequency of the movable mirror can be adjusted ranging from ω m (the resonance frequency of the coupling oscillator) to − ω m . Under the condition of experimental realization, we can generate and control steady-state entanglement between two oscillators by adjusting the effective frequency of the movable mirror and reducing the effective dissipation by selecting the parameter of the cavity driving laser appropriately. Our scheme provides a promising platform to control the steady-state behavior of solid-state qubits using classical manipulation, which is significant for quantum information processing and fundamental research.
We propose an approach for generating steady-state mechanical entanglement in a coupled optomechanical system. By applying four-tone driving lasers with weighted amplitudes and specific frequencies, we obtain an effective Hamiltonian that couples the delocalized Bogoliubov modes of the two mechanical oscillators to the cavity modes via beam-splitter-like interactions. When the mechanical decay rate is small, the Bogoliubov modes can be effectively cooled by the dissipative dynamics of the cavity modes, generating steady-state entanglement of the mechanical modes. The mechanical entanglement obtained in the stationary regime is strongly dependent on the values of the ratio of the effective optomechanical coupling strengths. Numerical simulation with the full linearized Hamiltonian shows that significant amount of mechanical entanglement can indeed be obtained by balancing the opposing effects of varying the ratio and by carefully avoiding the system parameters that may lead to amplified oscillations of the mechanical mean values detrimental to the entanglement generation.
Quantum entanglement in mechanical systems is not only a key signature of macroscopic quantum effects but has wide applications in quantum technologies. Here we propose an effective approach for creating strong steady-state entanglement between two directly coupled mechanical oscillators (or a mechanical oscillator and a microwave resonator) in a modulated optomechanical system. The entanglement is achieved by combining the processes of a cavity cooling and the two-mode parametric interaction, which can surpass the bound on the maximal stationary entanglement from the two-mode parametric interaction. In principle, our proposal allows one to cool the system from an initial thermal state to an entangled state with high purity by a monochromatic driving laser. Also, the obtained entangled state can be used to implement the continuous-variable teleportation with high fidelity. Moreover, our proposal is robust against the thermal fluctuations of the mechanical modes under the condition of strong optical pumping.
The radiation-pressure-induced coupling between an optical cavity field and a mechanical oscillator can create entanglement between them. In previous works this entanglement was treated as that of the quantum fluctuations of the cavity and mechanical modes around their classical mean values. Here we provide a fully quantum approach to optomechanical entanglement, which goes beyond the approximation of classical mean motion plus quantum fluctuation and applies to arbitrary cavity drive. We illustrate the real-time evolution of optomechanical entanglement under drive of arbitrary detuning to show the existence of high, robust, and stable entanglement in the blue-detuned regime and highlight the quantum noise effects that can cause entanglement sudden death and revival.
We study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical behavior of the mechanical entanglement, which is extremely robust against the oscillator temperature. Moreover, we have shown that this entanglement dynamics is strongly related to the stability of the normal modes. Taking mechanical damping effects into account, an analytical expression corresponding to the critical mechanical coupling strength, where the transition from stationary to dynamical entanglement occurs, is also reported. The proposed scheme is analyzed with experimentally realistic parameters, making it a promising means to realize macroscopic quantum entanglement within current state-of-the-art experimental setups.