  We consider a quantum Otto refrigerator cycle of a time-dependent harmonic
oscillator. We investigate the coefficient of performance at maximum figure of
merit for adiabatic and nonadiabatic frequency modulations. We obtain
analytical expressions for the optimal performance both in the high-temperature
(classical) regime and in the low-temperature (quantum) limit. We moreover
analyze the breakdown of the cooling cycle for strongly nonadiabatic driving
protocols and derive analytical estimates for the minimal driving time allowed
for cooling.
