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Phonon blockade is a purely quantum phenomenon, analogous to Coulomb andphoton blockades, in which a single phonon in an anharmonic mechanicalresonator can impede the excitation of a second phonon. We propose anexperimental method to realize phonon blockade in a driven harmonicnanomechanical resonator coupled to a qubit, where the coupling is proportionalto the second-order nonlinear susceptibility $\chi^{(2)}$. This is in contrastto the standard realizations of phonon and photon blockade effects in Kerr-type$\chi^{(3)}$ nonlinear systems. The nonlinear coupling strength can be adjustedconveniently by changing the coherent drive field.As an example, we apply thismodel to predict and describe phonon blockade in a nanomechanical resonatorcoupled to a Cooper-pair box (i.e., a charge qubit) with a linear longitudinalcoupling. By obtaining the solutions of the steady state for this compositesystem, we give the conditions forobserving strong antibunching andsub-Poissonian phonon-number statistics in this induced second-order nonlinearsystem. Besides using the qubit to produce phonon blockade states, the qubititself can also be employed to detect blockade effects by measuring its states.Numerical simulations indicate that the robustness of the phonon blockade, andthe sensitivity of detecting it, will benefit from this strong inducednonlinear coupling.

Method for observing robust and tunable phonon blockade in a nanomechanical resonator coupled to a charge qubit