Non-Markovian frequency conversion between optical and microwave photons with magnetomechanical transduction

As the main medium of quantum information, the frequency difference between optical and microwave photons is five orders of magnitude. Therefore, we generally improve the transmission efficiency of optical and microwave photons through coherent and bidirectional measures. The studies of the frequency conversion of optical and microwave photons in recent decades are all limited to Markovian approximations. In this paper we propose a scheme to achieve a two-stage frequency conversion between optical and microwave photons based on a hybrid of magnetic and mechanical excitations in non-Markovian environments. We estimate the interacting strengths under the optimal conditions of yttrium iron garnet and derive the conversion efficiency of optical and microwave photons through the scattering matrix. In all resonance modes, adjusting the defined complex cooperativities can get the conversion efficiency close to unity. The frequency conversion efficiency demonstrates a transition from Markovian to non-Markovian regimes by controlling the environmental spectral widths. This transition leads to enhancements of both the frequency conversion efficiency and conversion bandwidths, which originates from the excitation backflow obtained through the interaction between the systems and non-Markovian environments. In non-Markovian regimes, we predict that in areas with a large order of magnitude of optical pump power, the conversion bandwidths can be increased, but at the cost of a decrease in conversion efficiency, while decreasing the spectral widths can also achieve the same maximum conversion efficiency as in Markovian environments without requiring such a large optical pump power in non-Markovian regimes. Our scheme may provide an opportunity for the investigation of long-distance quantum communication for other non-Markovian quantum systems in quantum optics.