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Australian Control Conference

Synchronisation of micro-mechanical oscillators inside one cavity using feedback control

Zibo Miao, Mahdi Hosseini, Giovanni Guccione, M. R. James

Published Nov 1, 2014• 2 citations
Publisher

Abstract

The purpose of this work is to develop a systematic approach towards synchronisation of two micro-mechanical oscillators inside one optical cavity using feedback control. We first obtain the linear quantum stochastic state space model for the optomechanical system considered in this paper. Then we design a measurement-based optimal controller, aimed at achieving complete quantum synchronisation of the two mechanical oscillators with different natural frequencies, in the linear quadratic Gaussian setting. In addition, simulation results are provided, which show how system parameters impact on the control effect. These findings shed light on the synchronised network of oscillators that can be used for memory and quantum state transfer.

DOI
10.1109/aucc.2014.7358650

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The purpose of this work is to develop a systematic approach towards synchronisation of two micro-mechanical oscillators inside one optical cavity using feedback control. We first obtain the linear quantum stochastic state space model for the optomechanical system considered in this paper. Then we design a measurement-based optimal controller, aimed at achieving complete quantum synchronisation of the two mechanical oscillators with different natural frequencies, in the linear quadratic Gaussian setting. In addition, simulation results are provided, which show how system parameters impact on the control effect. These findings shed light on the synchronised network of oscillators that can be used for memory and quantum state transfer.
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We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the linear quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop models based on quantum stochastic differential equations to show that coherent control schemes, where we embed the resonator in an interferometer to achieve all-optical feedback, can outperform optimal measurement-based feedback control schemes in the quantum regime of low steady-state excitation number. These performance gains are attributed to the coherent controller's ability to simultaneously process both quadratures of an optical probe field without measurement or loss of fidelity, and may guide the design of coherent feedback schemes for more general problems of robust nonlinear and robust control.
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Abstract Quantum synchronization and synchronization transmission among three mechanical oscillators are investigated in a coupled multimode optomechanical system. The system consists of three subsystems, each comprising an optical cavity and a mechanical oscillator. The tripartite synchronization among the oscillators can be visualized through the joint limit-cycle trajectories and Wigner functions. Quantum synchronization and anti-synchronization of two oscillators can be achieved simultaneously in the coupled multimode optomechanical system. For three coupled optomechanical systems, some parameter ranges for achieving synchronization are presented. Moreover, the synchronization transmission among mechanical oscillators is also investigated by manipulating the driving laser. In addition, the circular optomechanical configuration is also identified as an effective platform for studying quantum synchronization. The differences between the two optomechanical system configurations are analyzed and compared. These results provide a promising platform for studying quantum correlations and quantum information processing with mechanical oscillators based on controllable multimode optomechanical systems.
We analyze an optomechanical system that can be used to efficiently transfer a quantum state between an optical cavity and a distant mechanical oscillator coupled to a second optical cavity. We show that for a moderate mechanical QQQ factor it is possible to achieve a transfer efficiency of 99.499.4%99.4 by using adjustable cavity damping rates and destructive interference. We also show that the quantum mechanical oscillator can be used as a quantum memory device with an efficiency of 9696%96 employing a pulsed optomechanical coupling. Although the mechanical dissipation slightly decreases the efficiency, its effect can be significantly reduced by designing a high-QQQ mechanical oscillator.
Abstract Cavity optomechanical systems are one of the leading experimental platforms for controlling mechanical motion in the quantum regime. We exemplify that the control over cavity optomechanical systems greatly increases by coupling the cavity also to a two-level system, thereby creating a hybrid optomechanical system. If the two-level system can be driven largely independently of the cavity, we show that the nonlinearity thus introduced enables us to steer the extended system to non-classical target states of the mechanical oscillator with Wigner functions exhibiting significant negative regions. We illustrate how to use optimal control techniques beyond the linear regime to drive the hybrid system from the near ground state into a Fock target state of the mechanical oscillator. We base our numerical optimization on realistic experimental parameters for exemplifying how optimal control enables the preparation of decidedly non-classical target states, where naive control schemes fail. Our results thus pave the way for applying the toolbox of optimal control in hybrid optomechanical systems for generating non-classical mechanical states.