Abstract

In a hybrid scheme, consisting of a three-level atom-cavity-oscillator system, we show that synchronization [J. Czartowski, R. Muller, K. Zyczkowski, and D. Braun, Phys. Rev. A 104, 012410 (2021)] and transfer of nonclassical states between the mechanical oscillator and the cavity field is possible. In this framework, we show that an initially thermalized mechanical oscillator, when connected to a squeezed bath, evolves to a squeezed state which in steady state is synchronized with the cavity mode. On the other hand, if the mechanical oscillator is initially prepared in a nonclassical state, e.g., squeezed and Schrodinger's cat states, while the cavity is in a thermal state, then a periodic transfer between the mechanical oscillator and cavity mode occurs for given interaction times. As qualitative results, we prove that the synchronization and transfer of the quantum states are feasible with high fidelity.