Optimal performance of an asymmetric quantum harmonic otto engine and refrigerator

We study a quantum Otto cycle that operates with a time-dependent harmonic oscillator as its working material. We consider the presence of an asymmetry between the two adiabatic processes of the Otto cycle, resulting in scenarios involving a sudden compression and a sudden expansion. We analytically derive the expressions for the efficiency and the coefficient of performance of this asymmetric quantum Otto cycle by employing the Omega function, which represents a balance between the maximum useful energy and the minimum lost energy. Notably, our findings reveal that the efficiency (coefficient of performance) of an asymmetric engine (refrigerator) is higher in the sudden compression case than in the sudden expansion case. Furthermore, we derive results for the maximum work efficiency and observe that the efficiency at the maximum Omega function consistently exceeds the maximum work efficiency. We also analyze the effect of the oscillator frequency and the bath temperatures on the efficiency of an asymmetric quantum Otto engine using contour plots. Finally, we calculate the fractional loss of work for both cases to comprehensively examine the performance of an asymmetric Otto engine.