Breaking mechanical dark mode via the Coulomb interaction

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 manifest that robust bipartite and genuine tripartite entanglement can be produced in a degenerate optomechanical system.