Quantum Correlations Established During Non-Markovian Optimal Sideband Cooling

Optimal control theory is applied to sideband cooling of nano-mechanical resonators. The formulation described here makes use of exact results derived by means of the path-integral approach of quantum dynamics, so that no approximation is invoked. It is demonstrated that the intricate interplay between time-dependent fields and structured thermal bath may lead to improve results of the sideband cooling by an order of magnitude. Cooling is quantified by means of the mean number of phonons of the mechanical modes as well as by the von Neumann entropy. Quantum correlations established during the optimal sideband cooling are discused.