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arXiv:1206.0829 · Physical Review Letters

Advantages of Coherent Feedback for Cooling Quantum Oscillators

Ryan Hamerly, Hideo Mabuchi

Published Oct 23, 2012• 135 citations
arXivHTMLPDF

Abstract

We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process noncommuting output field quadratures simultaneously without loss of fidelity, and may provide important clues for the design of coherent feedback schemes for more general problems of nonlinear and robust control.

DOI
10.1103/physrevlett.109.173602

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We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process noncommuting output field quadratures simultaneously without loss of fidelity, and may provide important clues for the design of coherent feedback schemes for more general problems of nonlinear and robust control.
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Abstract A theoretical scheme is proposed for improving the performance of cooling and entanglement, where the physical model is based on a double cavity optomechanical system assisted by the field‐mediated coherent feedback. The cooling performance is evaluated by calculating the final mean phonon number. The steady‐state bipartite entanglement between the optical mode and mechanical mode is measured by the logarithmic negativity. The result manifests that with assistance of the quantum coherent feedback, the mechanical resonator (MR) can be cooled close to its quantum ground state and the steady‐state optomechanical entanglement is simultaneously created, all of which are obtained under the condition beyond the resolved sideband. The presented feedback strategy is measurement‐independent, which can effectively preserve the quantum coherence of system. The scheme is conducive to relaxing the current experimental condition and it may provide a new path for the optomechanical manipulation involving the low‐frequency MR.
Coherent feedback control, which does not destroy the coherence of quantum signals by measurement, outperforms measurement-based feedback control in quantum systems. Nevertheless, systematic methods for designing coherent feedback controllers are absent so far. Thus, expectations for controller design methods are growing from control engineering perspectives. This paper proposes a method for designing a coherent feedback controller based on frequency analysis. Previous studies have rarely considered frequency analysisbased approaches. The paper theoretically reveals that groundstate cooling in the unresolved sideband regime is possible using a simple feedback structure with only a single double-sided cavity as the controller. While the proposed design method is a natural extension of the method based on classical control theory, it has rarely been used in coherent feedback control, thus offering new possibilities for coherent controller design methods.
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.
We consider a wide family of optical coherent feedback loops acting on an optomechanical system operating in the linearized regime. We assess the efficacy of such loops in improving key operations, such as cooling, steady-state squeezing and entanglement, as well as optical-to-mechanical state transfer. We find that mechanical sideband cooling can be enhanced through passive, interferometric coherent feedback, achieving lower steady-state occupancies and considerably speeding up the cooling process; we also quantify the detrimental effect of nonzero delay times on the cooling performance. Steady-state entanglement generation in the blue sideband can also be assisted by passive interferometric feedback, which allows one to stabilize otherwise unstable systems, though active feedback (including squeezing elements) does not help to this aim. We show that active feedback loops only allow for the generation of optical, but not mechanical, squeezing. Finally, we prove that passive feedback can assist state transfer at transient times for red-sideband-driven systems in the strong-coupling regime.