Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators

The observation of quantized nanomechanical oscillations by detecting\nfemtometer-scale displacements is a significant challenge for experimentalists.\nWe propose that phonon blockade can serve as a signature of quantum behavior in\nnanomechanical resonators. In analogy to photon blockade and Coulomb blockade\nfor electrons, the main idea for phonon blockade is that the second phonon\ncannot be excited when there is one phonon in the nonlinear oscillator. To\nrealize phonon blockade, a superconducting quantum two-level system is coupled\nto the nanomechanical resonator and is used to induce the phonon\nself-interaction. Using Monte Carlo simulations, the dynamics of the induced\nnonlinear oscillator is studied via the Cahill-Glauber $s$-parametrized\nquasiprobability distributions. We show how the oscillation of the resonator\ncan occur in the quantum regime and demonstrate how the phonon blockade can be\nobserved with currently accessible experimental parameters.\n