Optically induced phonon blockade in an optomechanical system with second-order nonlinearity.

Quantum control of phonons has being become a focus of attention for developing quantum technologies. Here, we propose a proposal to realize phonon blockade in a quadratically coupled optomechanical system, where a strong nonlinear interaction between photons and phonons can be induced by an external field coherently driving the cavity, and the effective coupling strength is tunable by adjusting the amplitude of the driving field. This optically induced nonlinearity is different from standard methods for realization of phonon blockade, where the nonlinearity is achieved by coupling the mechanical system to superconducting qubits. We both analytically and numerically study the phonon statistical properties via the steady-state solution of the second-order correlation function, and find phonon blockade can be efficiently realized for a large cooperativity of the system, which is achievable based on the optically enhanced nonlinear coupling and high quality mechanical system.