  Stationary entanglement in a four-mode optomechanical system, especially
under roomtemperature, is discussed. In this scheme, when the coupling
strengths between the two target modes and the mechanical resonator are equal,
the results cannot be explained by the Bogoliubov mode- based scheme. This is
related to the idea of quantum-mechanics-free subspace, which plays an
important role when the thermal noise of the mechanical modes is considered.
Significantly prominent steady-state entanglement can be available under
room-temperature.
