Phonon blockade in a nanomechanical resonator quadratically coupled to a two-level system

We investigate phonon statistics in a nanomechanical resonator (NAMR), which is quadratically coupled to a two-level system, by driving the NAMR and two-level system simultaneously. We find that unconventional phonon blockade (UCPNB), i.e., strong phonon anti bunching effect based on quantum interference, can be observed when driven fields are weak. By increasing the strengths of the driving fields, we show the crossover from the UCPNB to the conventional phonon blockade (CPNB), which is induced by the strong nonlinear interaction of the system. Moreover, under the strong coupling condition for CPNB, quantum interference effect can also be used to enhanced the phonon blockade by optimizing the phase difference of the two external driving fields.