Dynamics of two levitated nanospheres nonlinearly coupling with non-Markovian environment**Project supported by the National Natural Science Foundation of China (Grant Nos. 11874099, 11605022, 11775040, 11747317, and 11474044).

Abstract

The dynamics of two nanospheres nonlinearly coupling with non-Markovian reservoir is investigated. A master equation of the two nanospheres is derived by employing quantum state diffusion method. It is shown that the nonlinear coupling can improve the non-Markovianity. Due to the sharing of the common non-Markovian environment, the state transfer between the two nanospheres can be realized. The entanglement and the squeezing of the individual mode, as well as the jointed two-mode are analyzed. The present system can be realized by trapping two nanospheres in a wideband cavity, which might provide a method to study adjustable non-Markovian dynamics of mechanical motion.