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Physical Review A

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

Huatang Tan

Published May 27, 2014• 20 citations
Publisher

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.

DOI
10.1103/physreva.89.053829

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In this paper, we propose a feasible scheme for generating the Schr\"odinger-cat-like states of a macroscopic mechanical resonator in pulsed cavity optomechanics via photon detection. Starting with cooling the mechanical oscillator to its ground state, a red pulse and a blue pulse with different powers are simultaneously employed to dissipatively generate squeezed mechanical states. Subsequently, a second red pulse is utilized to achieve large-amplitude mechanical catlike states with high fidelities, conditioned on the multiphoton detection of cavity output and assisted by squeezing injection into the cavity. This combination effectively overcomes the difficulty that only a kitten can be produced by single-photon detection. Finally, after being stored in the resonator for a period of time during which thermal effect is analytically revealed, the mechanical quantum superpositions are mapped, with a third red pulse, to the cavity output field for state verification. Our scheme is generic and can also be used to produce other kinds of non-Gaussian mechanical states, such as optical-catalysis nonclassical states.