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arXiv:2509.16371 · Physical Review A

Multimode Gaussian steady-state engineering in optomechanical systems with a squeezed reservoir

Nahid Yazdi, Stefano Zippilli, David Vitali

Published May 4, 2026• 0 citations
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Abstract

We investigate a theoretical protocol for the dissipative stabilization of mechanical quantum states in a multimode optomechanical system composed of multiple optical and mechanical modes. The scheme employs a single squeezed reservoir that drives one of the optical modes, while the remaining optical modes mediate an effective phonon-phonon interaction Hamiltonian. The interplay between these coherent interactions and the dissipation provided by the squeezed bath enables the steady-state preparation of targeted quantum states of the mechanical modes. In the absence of significant uncontrolled noise sources, the resulting dynamics closely approximate the model introduced in [Zippilli , ]. We analyze the performance of this protocol in generating mechanical cluster states defined on rectangular graphs.

DOI
10.1103/s2xw-djhs

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We investigate a theoretical protocol for the dissipative stabilization of mechanical quantum states in a multimode optomechanical system composed of multiple optical and mechanical modes. The scheme employs a single squeezed reservoir that drives one of the optical modes, while the remaining optical modes mediate an effective phonon-phonon interaction Hamiltonian. The interplay between these coherent interactions and the dissipation provided by the squeezed bath enables the steady-state preparation of targeted quantum states of the mechanical modes. In the absence of significant uncontrolled noise sources, the resulting dynamics closely approximate the model introduced in [Zippilli , ]. We analyze the performance of this protocol in generating mechanical cluster states defined on rectangular graphs.
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We study an optomechanical system for the purpose of generating a nonclassical mechanical state when a mechanical oscillator is quadratically coupled to a single-mode cavity field driven by a squeezed optical field. The system corresponds to a regime where the optical dissipation dominates both the mechanical damping and the optomechanical coupling. We identify that multiphonon processes emerge in the optomechanical system and show that a mechanical oscillator prepared in the ground state will evolve into an amplitude-squared squeezed vacuum state. The Wigner distribution of the steady state of the mechanical oscillator is non-Gaussian exhibiting quantum interference and fourfold symmetry. This nonclassical mechanical state, generated via reservoir engineering, can be used for quantum correlation measurements of the position and momentum of the mechanics below the standard quantum limit.
We study theoretically a three-mode optomechanical system where two mechanical oscillators are independently coupled to a single cavity mode. By optimized two-tone or four-tone driving of the cavity, one can prepare the mechanical oscillators in an entangled two-mode squeezed state, even if they start in a thermal state. The highly pure, symmetric steady state achieved allows the optimal fidelity of standard continuous-variable teleportation protocols to be achieved. In contrast to other reservoir engineering approaches to generating mechanical entanglement, only a single reservoir is required to prepare the highly pure entangled steady state, greatly simplifying experimental implementation. The entanglement may be verified via a bound on the Duan inequality obtained from the cavity output spectrum. A similar technique may be used for the preparation of a highly pure two-mode squeezed state of two cavity modes, coupled to a common mechanical oscillator.
We theoretically propose a scheme to generate strong genuine tripartite entanglement among three mechanical oscillators in a multimode optomechanical system. In our setup, each mechanical oscillator is independently coupled to three optical modes supported by a single optical cavity, with each optical mode driven by a six-tone driving field. By appropriately tailoring the amplitudes of the driving fields, the mechanical steady state can be engineered into a three-mode squeezed vacuum state exhibiting significant genuine tripartite entanglement. We further investigate the effects of mechanical thermal reservoirs and demonstrate that the entanglement generated by our scheme persists at a significant level even at dilution refrigerator temperatures. Our results offer a feasible route toward the generation and utilization of multipartite entanglement in quantum optomechanical platforms, with potential applications in quantum devices.
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement involves Gaussian optomechanical interactions (linearized regime) to generate two-mode squeezed vacuum states, entangling two-modes exploiting the bare non-Gaussian optomechanical interaction (nonlinear strong single-photon regime) remains less covered. This work proposes an on-demand scheme to engineer phononic non-Gaussian bipartite entanglement in the nonlinear regime by exploiting cavity dissipation. Interestingly, our protocol (operating in the resolved sideband and photon blockade regime) renders the possibility of achieving a high degree of steady-state entanglement. We further show that our deterministic scheme is robust in the presence of decoherence and temperature within state-of-the-art optomechanics, along with the required conditions to obtain non-Gaussianity of the achieved bipartite mechanical steady-state.