Phonon blockade in a quadratically coupled optomechanical system

Phonon blockade is achieved in a quadratically coupled optomechanical system, in which the nonlinear interaction between phonons is induced by a driving field via radiation pressure. It is different from the previous standard methods, where the nonlinear interaction for observing phonon blockade is obtained by coupling the mechanical resonator to a two-level system. The effective coupling strength can be tuned by controlling the amplitudes of the driving field, which allows large nonlinearities for the optomechanical system. The second-order correlation function is discussed both analytically and numerically to characterize the phonon statistical properties and the results show that the phonon blockade is available when the effective coupling strength is larger than the mechanical decay rate. This work provides a possible way to experimentally realize phonon blockade.