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Communications in Theoretical Physics

Numerical studies on the boundary entanglement in an optomechanical phonon laser system

Qing-Xia Meng, Zhi-Jiao Deng, Shi-Wei Cui

Published Oct 27, 2020• 1 citation
Publisher

Abstract

Abstract In our previous work (Meng et al 2020 Phys. Rev. A 101 023838), we discover the phenomenon that the quantum entanglement on the driving threshold line remains a constant in a three-mode optomechanical phonon laser system. In this paper, to find the conditions under which the constant boundary entanglement shows up, we explicitly study how this boundary entanglement depends on various parameters through numerical integrations. The results show that the necessary and sufficient condition is a resonant frequency match between the optical frequency difference and the mechanical vibrational frequency, and this constant value is proportional to the multiplication of the square of the optomechanical coupling strength and the resonant driving threshold power.

DOI
10.1088/1572-9494/abb7db

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Abstract In our previous work (Meng et al 2020 Phys. Rev. A 101 023838), we discover the phenomenon that the quantum entanglement on the driving threshold line remains a constant in a three-mode optomechanical phonon laser system. In this paper, to find the conditions under which the constant boundary entanglement shows up, we explicitly study how this boundary entanglement depends on various parameters through numerical integrations. The results show that the necessary and sufficient condition is a resonant frequency match between the optical frequency difference and the mechanical vibrational frequency, and this constant value is proportional to the multiplication of the square of the optomechanical coupling strength and the resonant driving threshold power.
In order to understand our previous numerical finding that steady-state entanglement along the instability boundary remains unchanged in a three-mode optomechanical system [Phys. Rev. A 101 023838 (2020)], we investigate in detail the boundary entanglement in a simpler two-mode optomechanical system. Studies show that both the mechanism to generate entanglement and the parameter dependence of boundary entanglement are quite similar in these two models. Therefore, the two-mode system has captured the main features in the three-mode system. With the help of analytical calculations and discussing in a much bigger parameter interval, we find that the unchanging behavior previously discovered is actually an extremely slow changing behavior of the boundary entanglement function, and most importantly, this nearly invariant boundary entanglement is a general phenomenon via parametric down conversion process in the weak dissipation regime. This is by itself interesting as threshold quantum signatures in optomechanical phonon lasers, or may have potential value in related applications based on boundary quantum properties.
Abstract By considering a 3-mode optomechanical system formed by two cavities interacting with a common mechanical mode, we demonstrate that phonon-counting measurements lead to a significant enhancement of entanglement in the output of the two cavities. This conclusion still holds for an inefficient detector, but the dependence on system parameters changes qualitatively from the ideal limit of perfect projective measurements. We find non-trivial optimal points for the entanglement as functions of detector efficiency, measurement outcome, and optical drive strengths. We characterize both the highest achievable entanglement as well as a ‘typical’ value, obtained at the most likely measurement outcome. Numerical results are well understood within an approximate analytical approach based on perturbation theory around the ideal detector limit.
Radiation pressure in an optomechanical system can be used to generate various quantum entanglements between the subsystems. Recently, one paid more attention to the study of quantum entanglement in an optomechanical system. Here in this work, we study the properties of output entanglement between two filtered output optical fields by the logarithmic negativity method in a double-cavity optomechanical system. Our calculations show that the decay rate of the mechanical resonator, the bandwidth of filter function, and non-equal-coupling will evidently affect the value of the output entanglement. In particular, under the parameters of equal-coupling and zero filter bandwidth, the output entanglement in the vicinity of resonant frequency (=0 in the rotating frame) will decease with mechanical decay rate increasing. But under the parameters of equal-coupling and non-zero filter bandwidth, the output entanglement will be suppressed if the center frequency of output field is in the vicinity of the resonant frequency. However, the output entanglement can be enhanced if we adopt a non-equal-coupling to counteract the suppression effect of the filter bandwidth. Furthermore, we find that there are three peaks in the whole center frequency domain of the output field if we adopt strong non-equal-coupling. This is because the normal mode of Hamiltonian Hint will split into three normal modes in this case. Our results can also be used in other parametrically coupled three-mode bosonic systems and may be applied to realizing the state transfer process and quantum teleportation in an optomechanical system.
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.
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.