Generating two-mechanical mode entangled cat states, and steady-state entanglement, in cavity optomechanics in the presence of dissipation

This paper investigates how to generate and control non-Gaussian quantum states, specifically two-mode Schrödinger cat states (SCS), in a hybrid cavity optomechanical system. The authors seek to overcome the limitations of weak Kerr nonlinearity by using reservoir engineering to stabilize these states in the presence of environmental dissipation.

The researchers model a single lossy cavity mode coupled to two degenerate mechanical oscillators. By applying a bichromatic drive to the cavity and utilizing the adiabatic elimination of the cavity mode, they engineer an effective nonlinear dissipative environment for the mechanical subsystem. This setup allows for the creation of collective mechanical modes—termed bright and dark modes—whose dynamics are governed by phase-dependent phonon-hopping interactions. The authors use numerical simulations and analytical approximations to track the formation of cat states and the resulting bipartite entanglement between these modes.

The study reveals that the phase of the phonon-hopping interaction acts as a critical control parameter. When the phase is set to 0 or π, the system generates a Schrödinger cat state in either the bright or dark mode, respectively, while the other mode remains Gaussian. At an intermediate phase of π/2, the system generates a two-mode entangled state. Furthermore, the authors demonstrate that the phonon-hopping interaction strength and phase can be used to tune the steady-state entanglement between the bare mechanical modes, even when the system is subjected to thermal excitations.

Schrödinger cat states are essential resources for bosonic quantum information processing, including error correction and fault-tolerant computation. By providing a feasible, tunable method for generating these states in mechanical systems, this work offers a path toward more robust quantum state preparation in hybrid optomechanical platforms, which are often more accessible than purely optical or microwave systems.