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Quantum

Coherent feedback in optomechanical systems in the sideband-unresolved regime

Jingkun Guo, Simon Gröblacher

Published Nov 3, 2022• 12 citations
Publisher

Abstract

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.

DOI
10.22331/q-2022-11-03-848

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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.
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.
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.
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.
Optical-to-mechanical quantum state transfer is an important capability for future quantum networks, quantum communication, and distributed quantum sensing. However, existing continuous state transfer protocols operate in the resolved sideband regime, necessitating a high-quality optical cavity and a high mechanical resonance frequency. Here, we propose a continuous protocol that operates in the unresolved sideband regime. The protocol is based on feedback cooling, can be implemented with current technology, and is able to transfer non-Gaussian quantum states with high fidelity. Our protocol significantly expands the kinds of optomechanical devices for which continuous optical-to-mechanical state transfer is possible, paving the way toward quantum technological applications and the preparation of macroscopic superpositions to test the fundamentals of quantum science.
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 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.