Optimized sideband cooling with initial system correlations in non-Markovian regime

An optimized sideband cooling in the presence of initial system correlations is investigated for a standard optomechanical system coupled to a general mechanical non-Markovian reservoir. We study the evolution of phonon number by incorporating the effects of initial correlations into the time-dependent coefficients in the Heisenberg equation. We introduce the concept of cooling rate and define an average phonon reduction function to describe the sideband cooling effect in non-Markovian regime. Our results show that the instantaneous phonon number can be significantly reduced by introducing either the parametric-amplification type or the beam-splitter type initial correlations. In addition, the ground state cooling rate can be accelerated by enhancing the initial correlation of beam-splitter type. By optimizing the initial state of the system and utilizing Q-modulation technology, a stable mechanical ground state can be obtained in a very short time. Our optimized cooling protocol provides an appealing platform for phonon manipulation and quantum information processing in solid-state systems.