Realizing a mechanical dynamical Casimir effect with a low-frequency oscillator

We propose to realize a mechanical dynamical Casimir effect (MDCE) in a hybrid optomechanical system consisting of a cavity mode, a low-frequency mechanical oscillator, and a two-level atomic system. Described by the effective Hamiltonian, the mechanical energy is directly converted to the photons through a three-wave-mixing mechanism. It is not a quantum simulation of a parametric DCE such as in superconducting circuits. Using a master-equation approach, we analyze the system dynamics in various regimes with respect to the ratio of the effective coupling strength and the loss rate of the system. The dynamics under the strong-coupling regime confirms various three-wave-mixing processes for creating photons by annihilation of mechanical and atomic excitations. Under the weak-coupling regime, a continuous production of photons can be demonstrated by driving both the mechanical oscillator and atom. By virtue of an atom of tunable frequency, our method avoids using the high-frequency mechanical oscillator, which is required for the conventional DCE in optomechanical systems under the double-photon resonance yet is out of reach of experiment. It is found that the mechanical frequency can be about two orders smaller than the cavity mode in yielding a remarkable flux of DCE photons.