Unconditional Wigner-negative mechanical entanglement with linear-and-quadratic optomechanical interactions

TL;DR

This paper proposes two reservoir engineering schemes to generate unconditional Wigner-negative entangled states in mechanical resonators using linear and quadratic optomechanical interactions, demonstrating robustness against thermal decoherence.

Contribution

It introduces novel schemes for unconditional generation of Wigner-negative entangled states in mechanical systems with combined linear and quadratic optomechanical couplings.

Findings

Both schemes stabilize a Wigner-negative cubic-phase entangled state.

Numerical simulations show robustness of entanglement against thermal decoherence.

Analytical proof of state stabilization under specified conditions.

Abstract

The generation of entangled states that display negative values of the Wigner function in the quantum phase space is a challenging task, particularly elusive for massive, and possibly macroscopic, systems such as mechanical resonators. In this work, we propose two schemes based on reservoir engineering for generating Wigner-negative entangled states unconditionally. We consider two non-interacting mechanical resonators that are radiation-pressure coupled to either one or two common cavity fields; the optomechanical coupling with the field(s) features both a linear and quadratic part in the mechanical displacement and the cavity is driven at multiple frequencies. We show analytically that both schemes stabilize a Wigner-negative entangled state that combines the entanglement of a two-mode squeezed vacuum with a cubic nonlinearity, which we dub cubic-phase entangled (CPE) state. We then perform extensive numerical simulations to test the robustness of Wigner-negative entanglement attained by approximate CPE states stabilized in the presence of thermal decoherence.