Quantum Dynamics of Bosonic Squeezing Under Multi-Tone Driving in an Optomechanical System

The squeezing of a mechanical mode can break through the “standard quantum limit”, which has significant applications in high-precision measurement. In this paper, we employ a full quantum stochastic method to investigate the dynamics of an optomechanical system under multi-tone driving. Previous method usually sets the classical mean value as a constant. For the dynamic process, this mean value should be time dependent, especially under the multi-tone driving. Here, we use the full quantum stochastic method, and we find that the mechanical squeezing exhibits nonmonotonic behavior with the enhancement of blue-sideband driving, which declines after reaching its maximum value; meanwhile, this system requires a longer time to evolve into a steady state. Moreover, the nonmonotonic trend of squeezing can also be observed by enhancing the strengths of both red- and blue-sideband driving simultaneously, and a shorter time is required to reach the steady state. This work provides valuable insights into the dynamics of an optomechanical system under multi-tone driving for the first time, which is of significant importance for improving the sensitivity of quantum precision measurement.