Magnon-assisted photon-phonon conversion in the presence of structured environments

Abstract

Quantum conversion or interface is one of the most prominent protocols in quantum information processing and quantum state engineering. We propose a photon-phonon conversion protocol in a hybrid magnomechanical system comprising a microwave optical mode, a driven magnon mode, and a mechanical-vibrating mode, which has attracted much interest and is expected to become a building block of the future quantum information network due to its controllability in coupling strengths. The microwave photons in the optical cavity are coupled to the magnons by the Zeeman interaction, and the latter are coupled to the mechanical phonons by the magnetostrictive interaction. With a strong photon-magnon interaction and a strong driving on the magnon, an effective Hamiltonian is constructed to describe the conversion between photons and phonons near their resonant point. The cavity-magnon system can then play the role of quantum memory. Moreover, the faithfulness of the photon-phonon conversion is estimated in terms of fidelities for state evolution and state-independent transfer. The former is discussed in the Lindblad master equation, taking account of the leakages of photons, phonons, and magnons into consideration. The latter is derived by the Heisenberg-Langevin equation considering the non-Markovian noise from the structured environments for both optical and mechanical modes. The state-evolution fidelity is found to be robust to the weak leakage. The transfer fidelity can be maintained by the Ohmic and sub-Ohmic environments of the photons and is insensitive to the $1/f$ noise of the phonons. Our work thus provides an interesting application for the magnon system as a photon-phonon converter in the microwave regime.