Phase-controlled bipartite and tripartite entanglement and Bell nonlocality in a closed-loop optomechanical system

This paper investigates the generation, manipulation, and verification of multipartite quantum correlations—specifically entanglement and Bell nonlocality—in a closed-loop optomechanical system. The researchers aim to determine how the relative phase of coupling between two optical modes and a mechanical resonator can be used to control the distribution of these correlations and to clarify the relationship between genuine tripartite entanglement and tripartite Bell nonlocality.

The authors propose a three-mode optomechanical system where two optical modes are coupled to a mechanical mode via radiation pressure and to each other through direct field transmission. This cyclic topology creates a phase-sensitive interference effect. The team employs the standard linearization approach to derive the system's covariance matrix and uses logarithmic negativity and residual contangle to quantify bipartite and tripartite entanglement, respectively. To test Bell nonlocality, they utilize displaced-parity measurements in phase space, constructing bipartite and tripartite Bell inequalities.

The study shows that the relative phase between the coupling strengths acts as a control knob for quantum correlations. By tuning this phase, the system can deterministically switch bipartite entanglement between different optical-mechanical pairs. At symmetric phase points, the system maximizes genuine tripartite entanglement. A key counterintuitive finding is that tripartite Bell nonlocality can exist even when genuine tripartite entanglement is absent, proving that the latter is not a necessary condition for the former. Furthermore, while increasing the effective squeezing parameter enhances entanglement, it also reveals that Bell nonlocality is more sensitive to mechanical dissipation and thermal noise than entanglement itself.