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Fundamental Research

Dynamical approach to quantum optomechanics: Motivation, method, and applications

Bing He, Qing Lin

Published Nov 20, 2022• 8 citations
Publisher

Abstract

We present an overall summary on a method to deal with quantum dynamics of optomechanical systems. The method is based on the dynamical evolution processes instead of the finally evolved steady states, which are a prerequisite to the standard approach, and well captures the features in optomechanical cooling, entanglement and other scenarios.

DOI
10.1016/j.fmre.2022.11.002

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We present an overall summary on a method to deal with quantum dynamics of optomechanical systems. The method is based on the dynamical evolution processes instead of the finally evolved steady states, which are a prerequisite to the standard approach, and well captures the features in optomechanical cooling, entanglement and other scenarios.
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In this dissertation, I theoretically investigate the open system dynamics of cavity optomechanical systems in the quantum limit, where a mechanical resonator couples to a cavity mode via radiation pressure force. Recent developments in nano-fabrication and cooling techniques make it possible to optically control and manipulate the motion of micro- and nano-mechanical resonator. Several experiments have demonstrated the possibility of preparing macroscopic mechanical resonators into their quantum ground state, which makes optomechanical systems an ideal candidate for studying the quantum behavior of macroscopic objects. One important direction in quantum optomechanics is the study of the decoherence of optomechanical system due to the interaction with their external environments. This dissertation explores the decoherence effects by considering the influence of the radiation pressure coupling on the interaction between optomechanical system and its environments. Because the effects of the nonlinear interaction vary with the optomechanical coupling strength, three different interaction regimes are fully studied here: the weak coupling, the intermediate coupling and the strong coupling.
We present a detailed study of a double-cavity optomechanical system, focusing on the dynamics of the entanglement between the cavity and mechanical modes, as well as the entanglement between two cavity modes. The discussions are based on a complete quantum approach without the standard practice of fluctuation expansion. The entanglement evolutions for various combinations of two different drives, such as those of the same blue detuning, of the same red detuning, and one red detuning and one blue detuning, are investigated. The relation of the entanglement and the rate of photon hopping between two cavities is also discussed.
We study the simplest optomechanical system with a focus on the bistable regime. The covariance matrix formalism allows us to study both cooling and entanglement in a unified framework. We identify two key factors governing entanglement; namely, the bistability parameter (i.e., the distance from the end of a stable branch in the bistable regime) and the effective detuning, and we describe the optimum regime where entanglement is greatest. We also show that, in general, entanglement is a nonmonotonic function of optomechanical coupling. This is especially important in understanding the optomechanical entanglement of the second stable branch.
The squeezing of a mechanical mode can break through the “standard quantum limit”, which has significant applications in high-precision measurement. In this paper, we employ a full quantum stochastic method to investigate the dynamics of an optomechanical system under multi-tone driving. Previous method usually sets the classical mean value as a constant. For the dynamic process, this mean value should be time dependent, especially under the multi-tone driving. Here, we use the full quantum stochastic method, and we find that the mechanical squeezing exhibits nonmonotonic behavior with the enhancement of blue-sideband driving, which declines after reaching its maximum value; meanwhile, this system requires a longer time to evolve into a steady state. Moreover, the nonmonotonic trend of squeezing can also be observed by enhancing the strengths of both red- and blue-sideband driving simultaneously, and a shorter time is required to reach the steady state. This work provides valuable insights into the dynamics of an optomechanical system under multi-tone driving for the first time, which is of significant importance for improving the sensitivity of quantum precision measurement.