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arXiv:2405.13624 · Physical Review A

Coherent feedback control for cavity optomechanical systems with a frequency-dependent mirror

Lei Du, Juliette Monsel, Witlef Wieczorek, Janine Splettstoesser

Published Jan 6, 2025• 5 citations
arXivHTMLPDF

Abstract

Ground-state cooling of mechanical resonators is a prerequisite for the observation of various quantum effects in optomechanical systems and thus has always been a crucial task in quantum optomechanics. In this paper, we study how to realize ground-state cooling of the mechanical mode in a Fano-mirror optomechanical setup, which allows for enhanced effective optomechanical interaction but typically works in the (deeply) unresolved-sideband regime. We reveal that for such a two-sided cavity geometry with very different decay rates at the two cavity mirrors, it is possible to cool the mechanical mode down to its ground state within a broad range of parameters by using an appropriate single-sided coherent feedback. This is possible even if the total optical loss is more than seven orders of magnitude larger than the mechanical frequency and the feedback efficiency is relatively low. Importantly, we show that a more standard double-sided feedback scheme is not appropriate to cooperate with a Fano-mirror system.

DOI
10.1103/physreva.111.013506

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Abstract We theoretically investigate a cooling scheme assisted by a quantum well (QW) and coherent feedback within a hybrid optomechanical system. Although the exciton mode in the QW and the mechanical resonator (MR) are initially uncoupled, their interaction via the microcavity field leads to an indirect exciton-mode–mechanical-mode coupling. The coherent feedback loop is applied by feeding back a fraction of the output field of the cavity through a controllable beam splitter to the cavity’s input mirror. It is shown that the cooling capability is enhanced by effectively suppressing the Stokes process through coupling with the QW. Furthermore, the effect of the anti-Stokes process is enhanced through the application of the coherent feedback loop. This particular system configuration enables cooling of the mechanical resonator even in the unresolved sideband regime (USR). This study has some important guiding significance in the field of quantum information processing.
Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive element – either a narrow linewidth cavity or a mirror with a delay line – an optomechanical system in the deeply sideband-unresolved regime will exhibit dynamics similar to one that is sideband-resolved. With this new approach, the experimental realization of groundstate cooling and optomechanical entanglement is well within reach of current integrated state-of-the-art high-Q mechanical resonators.
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.
Abstract Ground-state cooling of mesoscopic mechanical objects is still a major challenge in the unresolved-sideband regime. We present a frequency modulation (FM) scheme to achieve cooling of the mechanical resonator to its ground-state in a double-cavity optomechanical system containing a mechanical resonator. The mean phonon number is determined by numerically solving a set of differential equations derived from the quantum master equations. Due to efficient suppression of Stokes heating processes in the presence of FM, the ground-state cooling, indicated by numerical calculations, is significantly achievable, regardless of whether in the resolved-sideband regime or the unresolved-sideband regime. Furthermore, by choosing parameters reasonably, the improvement of the quantum cooling limit is found to be capable of being positively correlated with the modulation frequency. This method provides new insight into quantum manipulation and creates more possibilities for applications of quantum devices.
We propose an alternative experimentally feasible approach to achieve high-efficiency ground-state cooling of a mechanical oscillator in an optomechanical system under the deeply unresolved sideband condition with the assistance of both intracavity and extracavity squeezing. In the scheme, a degenerate optical parametric amplifier is placed inside the optical cavity, generating the intracavity squeezing; in addition, the optical cavity is driven by the extracavity squeezed light, namely the extracavity squeezing. The quantum interference effect generated by intracavity squeezing and extracavity squeezing can completely suppress the nonresonant Stokes heating process while greatly enhancing the anti-Stokes cooling process. Therefore, the joint-squeezing scheme is capable of cooling the mechanical oscillators to their quantum ground state in a regime far away from the resolved sideband condition. Compared with other traditional optomechanical cooling schemes, the single-photon cooling rate in this joint-squeezing scheme can be tremendously enlarged by nearly three orders of magnitude. At the same time, the coupling strength required to achieve ground-state cooling can be significantly reduced. This scheme is promising for cooling large-mass and low-frequency mechanical oscillators, which provides a prerequisite for preparing and manipulating nonclassical states in macroscopic quantum systems and lays a significant foundation for quantum manipulation.