Enhanced entanglement of two different mechanical resonators via coherent feedback

It is shown [New J. Phys. 17, 103037 (2015)] that extremely large and robust entanglement between two different mechanical resonators could be achieved, either dynamically or in the steady state, in an optomechanical system in which a single cavity mode driven by a suitably chosen two-tone field is coupled to two mechanical modes. The main limitation of the scheme is that the cavity decay rate must be much smaller than the two mechanical frequencies and their difference, allowing taking the rotating wave approximation where counter-rotating, non-resonant terms associated with the bichromatic driving are negligible. Here we show that, by simply adding a coherent feedback loop, the large entanglement can be remarkably enhanced and the effective cavity decay rate can be significantly reduced. Therefore, it improves the results of Ref. [New J. Phys. 17, 103037 (2015)] and meantime greatly extends the validity of the scheme.