  We propose a scheme in which the cooling of a mechanical resonator is
achieved by exposing the optomechanical system to a non-Markovian environment.
Because of the backflow from the non-Markovian environment, the phonon number
can go beyond the conventional cooling limit in a Markovian environment.
Utilizing the spectrum density obtained in the recent experiment [Nature
Communications 6, 7606 (2015)], we show that the cooling process is highly
effective in a non-Markovian environment. The analysis of the cooling mechanism
in a non-Markovian environment reveals that the non-Markovian memory effect is
instrumental to the cooling process.
