Abstract
We consider transfer of a highly nonclassical quantum state through an optomechanical system. That is we investigate a protocol consisting of sequential upload, storage and reading out of the quantum state from a mechanical mode of an optomechanical system. We show that provided the input state is in a test-bed single-photon Fock state, the Wigner function of the recovered state can have negative values at the origin, which is a manifest of nonclassicality of the quantum state of the macroscopic mechanical mode and the overall transfer protocol itself. Moreover, we prove that the recovered state is quantum non-Gaussian for wide range of setup parameters. We verify that current electromechanical and optomechanical experiments can test this complete transfer of single photon.
Highlights
The pulse in single-photon state in the optical mode described by annihilation operator Ain is shone upon the cavity at its resonance frequency ωcav
During this time the mechanical environment admixes thermal noise to the quantum state of the mechanical mode. This effect can be described by an effective transmittance δ = e−γτs, where γ is the mechanical damping rate. This admixture happens as well during the upload stage, but we omit it for the state swap stages as this effect can be reduced by shortening the pulses durations
A major impediment to the successful photon-phonon-photon transfer preserving the negativity of Wigner function is the initial occupation of the mechanical mode
Summary
It has been shown previously[32] that in presence of a strong red-detuned coherent pulse, the quantum states of the mechanical mode of an optomechanical cavity and the resonant with the cavity pulse can in principle be swapped. The scheme analyzed here uses this state swap twice: first time to upload a highly nonclassical (single-photon) quantum state to the mechanical mode and second time to read the evolved state out (see Fig. 1). This effect can be described by an effective transmittance δ = e−γτs, where γ is the mechanical damping rate This admixture happens as well during the upload stage (and consequent readout), but we omit it for the state swap stages as this effect can be reduced by shortening the pulses durations. A major impediment to the successful photon-phonon-photon transfer preserving the negativity of Wigner function is the initial occupation of the mechanical mode. Critically coupled systems with η = 0.5 are incapable of transferring the negativity regardless of the effectiveness of state upload and readout For these systems we consider another measure of nonclassicality, namely the quantum non-Gaussianity. Due to the initial occupation of the mechanical modes a very efficient state upload is required
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