Laser cooling of high temperature oscillator by multi-level system

We study the laser cooling of a mechanical oscillator through the coupling with a dissipative three-level system. Under a background temperature beyond the Lamb-Dicke regime, we extend the standard cooling analysis by separately studying the classical motion and the quantum dynamics of the oscillator. In Ladder-system cooling, the cooling rate degrades by orders of magnitude at large classical motion. This phenomenon causes a critical transition of the final temperature at a hot background. In stark contrast, electromagnetic-induced-transparency (EIT) cooling with a $\Lambda$-system produces significant negative cooling rate at high motional excitation. At steady state, the oscillator could exhibit both cooling and lasing behaviours. We argue that a successful EIT cooling requires either a poor quality oscillator to suppress the lasing effect, or terminating the cooling process at a transient stage.