We analyse a quantum Otto refrigerator based on a superconducting qubit coupled to two LC-resonators each including a resistor acting as a reservoir. We find various operation regimes: nearly adiabatic (low driving frequency), ideal Otto cycle (intermediate frequency), and non-adiabatic coherent regime (high frequency). In the nearly adiabatic regime, the cooling power is quadratic in frequency, and we find substantially enhanced coefficient of performance $epsilon$, as compared to that of an ideal Otto cycle. Quantum coherent effects lead invariably to decrease in both cooling power and $epsilon$ as compared to purely classical dynamics. In the non-adiabatic regime we observe strong coherent oscillations of the cooling power as a function of frequency. We investigate various driving waveforms: compared to the standard sinusoidal drive, truncated trapezoidal drive with optimized rise and dwell times yields higher cooling power and efficiency.
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