Deterministic quantum superpositions and Fock states of mechanical oscillators via quantum interference in single-photon cavity optomechanics

Abstract

In this paper, we propose a scheme for deterministically preparing a quantum superposition $|{\ensuremath{\psi}}_{s}{\ensuremath{\rangle}}_{b}={C}_{0}{|0\ensuremath{\rangle}}_{b}+{C}_{\mathcal{N}}{|\mathcal{N}\ensuremath{\rangle}}_{b}$ between vacuum and an arbitrary Fock state ${|\mathcal{N}\ensuremath{\rangle}}_{b}$ of mechanical oscillators via strong single-photon optomechanical coupling. We consider an optomechanical cavity which contains a Kerr medium and is driven by two lasers, with one laser tuned to the cavity resonance and the other to the $\mathcal{N}$th lower sideband of the cavity. The amplitudes ${C}_{0}$ and ${C}_{\mathcal{N}}$ are determined only by the drive strengths in the absence of mechanical damping and the approximate Fock state $|{\ensuremath{\psi}}_{s}{\ensuremath{\rangle}}_{b}\ensuremath{\approx}{|\mathcal{N}\ensuremath{\rangle}}_{b}$ can be obtained with appropriate relative strengths of the lasers. It is revealed that the superposition results from destructive quantum interference. The analytical results are confirmed by exact numerical calculation, and it is also shown that the nonclassical state is robust against thermal mechanical noise.