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arXiv:2604.01891

A Loop-Shaping Approach to Coherent Feedback Control in Cavity Optomechanical Cooling

Aoi Fujimoto, Hiroyuki Ichihara, Rina Kanamoto

quant-phSubmitted Apr 2, 2026• Announced Apr 3, 2026• 0 citations
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Abstract

We present a loop-shaping approach to coherent feedback (CF) control. By formulating the coupling between a quantum system and its environment in terms of the noise power spectrum, our method enables direct manipulation of the effective dissipation coefficients through spectral shaping. A systematic design framework for CF controllers is also developed, in which transfer functions are shaped to realize desired spectral responses. Applying this framework to optomechanical sideband cooling, we demonstrate that suppression of the Stokes process and enhancement of the anti-Stokes process can be simultaneously achieved, enabling ground-state cooling even in the unresolved-sideband regime. This loop-shaping framework provides an intuitive and general foundation for the design of CF controllers and can be extended to a wide class of quantum systems in which interactions with environments are characterized by noise power spectra.

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5 pages, 3 figures

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We present a loop-shaping approach to coherent feedback (CF) control. By formulating the coupling between a quantum system and its environment in terms of the noise power spectrum, our method enables direct manipulation of the effective dissipation coefficients through spectral shaping. A systematic design framework for CF controllers is also developed, in which transfer functions are shaped to realize desired spectral responses. Applying this framework to optomechanical sideband cooling, we demonstrate that suppression of the Stokes process and enhancement of the anti-Stokes process can be simultaneously achieved, enabling ground-state cooling even in the unresolved-sideband regime. This loop-shaping framework provides an intuitive and general foundation for the design of CF controllers and can be extended to a wide class of quantum systems in which interactions with environments are characterized by noise power spectra.
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.
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.
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.
Microcavities are used in a wide range of classical and quantum applications, from precision measurements, laser technologies, to control of mechanical motion. The dissipative photon loss via absorption, ubiquitous in any optical cavity, is known to introduce thermo-optical effects and impose fundamental limits on precision measurements. We reveal that such dissipative photon absorption can lead to a quantum feedback, via in-loop field detection of the absorbed optical field, whose field fluctuations can be squashed or anti-squashed. A closed-loop dissipative quantum feedback to the cavity field arises. This modifies the optical cavity susceptibility and causes excess noise and correlations when performing coherent response and quantum optomechanical measurements. We experimentally observe such unanticipated dissipative dynamics in optomechanical spectroscopy of sideband-cooled optomechanical crystals at cryogenic temperature (∼\sim∼ 8K) and ambient conditions. The dissipative feedback introduces effective modifications to the optical cavity linewidth and the optomechanical scattering rate, and gives rise to excess imprecision noise in the interferometric quantum measurement of mechanical motion. Such dissipative feedback differs fundamentally from a quantum non-demolition feedback, e.g. optical Kerr squeezing. The dissipative feedback itself always results in anti-squeezed out-of-loop optical field, while it can improve the coexisting Kerr squeezing under certain conditions. Our result applies to cavity spectroscopy in both optical and superconducting microwave cavities , and equally applies to any dissipative feedback mechanism of different bandwidth inside the cavity. It has wide-ranging implications for future dissipation engineering, such as dissipation enhanced sideband cooling and Kerr squeezing, quantum frequency conversion, and nonreciprocity in photonic systems.
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.
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.