Magnon-assisted photon-phonon conversion in the presence of the 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. The microwave photons in the optical cavity are coupled to the magnons by the magnetic-dipole interaction, and the latter are coupled to the mechanical phonons by the magnetostrictive interaction. With strong photon-magnon interaction and strong driving on magnon, an effective Hamiltonian is constructed to describe the conversion between photons and phonons nearby their resonant point. The cavity-magnon system can then play the role of a 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 the leakages of photon, phonon and magnon 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.