Robust mechanical entanglement in an atom-assisted hybrid optomechanical system

We theoretically explore the bipartite robust steady-state entanglement between two charged nanomechanical oscillators in an atom-assisted hybrid optomechanical system. The logarithmic negativity is adopted to measure entanglement. We find that the mechanical entanglement induced by Coulomb interaction could only survive at ultralow temperature of a few tens of mK in case of bare cavity. However, by adding the atomic degrees of freedom, the entanglement properties could be effectively modified including a further enhanced degree and broadened range of entanglement. In addition, the enhanced entanglement becomes more robust against thermal noise. This robustness is more evident when appropriately increasing the laser power. Compared to the case of no atoms, the critical temperature is raised by about two orders of magnitude.