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

TL;DR

This paper proposes a method to observe and control phonon blockade in a nanomechanical resonator coupled to a charge qubit, utilizing second-order nonlinear susceptibility to achieve tunable and robust quantum phonon effects.

Contribution

It introduces a novel experimental approach using second-order nonlinear coupling for phonon blockade in a driven harmonic resonator coupled to a charge qubit, differing from traditional Kerr-type systems.

Findings

Predicted strong antibunching and sub-Poissonian phonon statistics.

Demonstrated tunability of nonlinear coupling via drive field.

Showed enhanced robustness and detection sensitivity of phonon blockade.

Abstract

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