Abstract
Based on photon-phonon nonlinear interaction, a scheme of controllable photon-phonon converters is proposed at single-quantum level in a composed quadratically coupled optomechanical system. With the assistance of the mechanical oscillator, the Kerr nonlinear effect between photon and phonon is enhanced so that the single-photon state can be converted into the phonon state with high fidelity even under the current experimental condition that the single-photon coupling rate is much smaller than mechanical frequency (g ≪ ωm). The state transfer protocols and their transfer fidelity are discussed analytically and numerically. A multi-path photon-phonon converter is designed by combining the optomechanical system with low frequency resonators, which can be controlled by experimentally adjustable parameters. This work provides us a potential platform for quantum state transfer and quantum information.
Highlights
The radiation pressure in optomechanical system provides an excellent interaction between optical cavity mode and microcosmic or macroscopic mechanical mode [1, 2]
We show that the composed optomechanical system can work as a photon-phonon control phase-flip gate based on the cross-Kerr nonlinearity shown in the third term of the effective Hamiltonian in Eq (3)
If the photon counting is one, the mechanical oscillator will collapse to the state α|0 2 − β|1 2
Summary
The radiation pressure in optomechanical system provides an excellent interaction between optical cavity mode and microcosmic or macroscopic mechanical mode [1, 2]. Considering the realization, we use an auxiliary mechanical oscillators to enhance the quantum nonlinear effects in the system, and achieve an ultra-strong cross-Kerr nonlinearity (geff /ωeff ≫ 1). The second term in Hsys describes the quadratic optomechanical coupling between the original cavity and the mechanical membrane with strength g. By eliminating the rapid evolution mode b1 due to large frequency ωm, we obtain the effective interaction between the optomechanical cavity and the auxiliary oscillator mode b2, under the condition ωm1 ≫ {ωm, V, g} (Details are in APPENDIX). The effective frequency of the mechanical oscillator, coupling strength, and dumpling rates are described by ωef f. Similar with the quantum control schemes based on cross-Kerr nonlinearity [12, 27], the key factor of the controlling realization is the weight of nonlinear coupling rate geff in the Hamiltonian, i.e. geff ∼ ∆′, ωeff , γeff. It is possible for us to achieve an ultra-strong cross-Kerr nonlinearity in the system
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