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arXiv:2604.16831

Simultaneous cooling of degenerate mechanical modes in unresolved sideband regime via optical and mechanical nonlinearities

Shuang-Shuo Chu, Han-Qiu Zhang, Jian-Song Zhang, Wen-Xue Zhong, Guang-Ling Cheng, Ai-Xi Chen

quant-phSubmitted Apr 18, 2026• Announced Apr 21, 2026
arXivHTMLPDF

Abstract

We propose a scheme to simultaneously cool multiple degenerate mechanical modes in optomechanical systems beyond the resolved sideband regime. In general, one of the main obstacles for cooling degenerate mechanical modes is the so-called dark-mode effect. The Duffing nonlinearities (mechanical nonlinearities) can be used to overcome the dark-mode effect of degenerate mechanical modes. A second-order nonlinear medium (optical nonlinearity) is introduced to accomplish the ground-state cooling of degenerate mechanical modes beyond the resolved sideband regime. We find the dark mode of degenerate mechanical modes can be broken when the mechanical nonlinearities of different mechanical modes are not very close. Our scheme paves the way toward the implementation of simultaneous ground-state cooling of degenerate mechanical modes of optomechanical systems beyond the resolved sideband regime in experiments.

Journal reference
Phys. Rev. A 109, 033509 (2024)
DOI
10.1103/PhysRevA.109.033509
Comments
10 pages, 7 figures

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We propose a scheme to simultaneously cool multiple degenerate mechanical modes in optomechanical systems beyond the resolved sideband regime. In general, one of the main obstacles for cooling degenerate mechanical modes is the so-called dark-mode effect. The Duffing nonlinearities (mechanical nonlinearities) can be used to overcome the dark-mode effect of degenerate mechanical modes. A second-order nonlinear medium (optical nonlinearity) is introduced to accomplish the ground-state cooling of degenerate mechanical modes beyond the resolved sideband regime. We find the dark mode of degenerate mechanical modes can be broken when the mechanical nonlinearities of different mechanical modes are not very close. Our scheme paves the way toward the implementation of simultaneous ground-state cooling of degenerate mechanical modes of optomechanical systems beyond the resolved sideband regime in experiments.
We theoretically investigate a quadratic optomechanical system comprising a single-mode optical cavity linearly coupled to one mechanical resonator and quadratically coupled to a second resonator. By tuning the cavity detuning and optomechanical coupling strengths, we demonstrate the transition from optical bistability to multistability with up to seven steady-state solutions. Notably, simultaneous ground-state cooling of both mechanical resonators occurs on the dynamically stable branch of the nonlinear steady-state solutions, offering new opportunities for combined nonlinear optical and quantum cooling functionalities. Beyond the multistable regime, we systematically study dual-mode ground-state cooling and find that robust simultaneous cooling can be achieved over a broad parameter range, except when the linear and quadratic couplings become comparable, where a dark-mode effect arises. In this case, tuning the second-order optomechanical-induced frequency shifts effectively suppresses dark-mode interference, enabling controllable and simultaneous ground-state cooling. Our results provide a versatile framework for engineering multimode quantum states in optomechanical systems and open new avenues for the development of multifunctional quantum devices, including ultra-sensitive sensors, scalable quantum memories, and integrated quantum networks.
We propose a method to break the dark mode of two degenerate mechanical resonators (MRs) in optomechanical systems via the Coulomb interaction. Two degenerate MRs can be cooled to their ground-state simultaneously beyond the resolved sideband regime using the Coulomb interaction and an optical parametric amplifier (OPA). We show that strong and robust mechanical squeezing beyond 3 dB can be generated using the OPA and mechanical parametric amplification (MPA) introduced by the Coulomb interaction. Our results manifests that robust bipartite and genuine tripartite entanglement can be produced in a degenerate optomechanical system.
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.
Abstract In the conventional scheme of generating strong mechanical squeezing by the joint effect between mechanical parametric amplification and sideband cooling, the resolved sideband condition is required so as to overcome the quantum backaction heating. In the unresolved sideband regime, to suppress the quantum backaction, a χ(2) nonlinear medium is introduced to the cavity. The result shows that the quantum backaction heating effect caused by unwanted counter‐rotating term can be completely removed. Hence, the strong mechanical squeezing can be obtained even for the system far from the resolved‐sideband regime.
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.
Resolved-sideband cooling is a standard technique in cavity optomechanics enabling quantum control of mechanical motion, but its performance is ultimately limited by quantum backaction heating. This fundamental effect imposes a limit on the minimum achievable mechanical phonon number, establishing a finite-temperature floor regardless of the applied cooling strength. We generalize the semi-classical model for optomechanical cooling to describe universal cavity Hamiltonians incorporating both passive and active nonlinearities. As a concrete demonstration, we analyze the simplest circuit optomechanical system that implements a nonlinear drive via a Josephson junction. Our analysis reveals that this active nonlinear drive can eliminate the residual heating backaction, thereby comparing favorably with alternative optomechanical cooling schemes based on passive nonlinearities arXiv:2202.13228. By successfully overcoming the finite-temperature floor that limits conventional schemes, our method paves the way for unprecedented quantum control over mechanical systems and establishes the experimental viability of zero-heating optomechanical cooling.