Quantum Stirling heat engine with squeezed thermal reservoir

We analyze the performance of a quantum Stirling heat engine (QSHE), using a two level system and the harmonic oscillator as the working medium, that contacts with a squeezed thermal reservoir and a cold reservoir. First, we derive closed-form expressions for the produced work and efficiency which strongly depends on the squeezing parameter $r_h$. Then, we prove that the effect of squeezing heats the working medium to a higher effective temperature which leads to better overall performance. In particular, the efficiency increases with the degree of squeezing surpassing the standard Carnot limit, when the ratio of temperatures of hot and cold reservoir is small. Furthermore, we derive the analytical expressions for the efficiency at maximum work and the maximum produced work in the high and low temperature regime and we find that at extreme temperatures the squeezing parameter $r_h$ does not affect the performance of the QSHE. Finally, the performance of the QSHE depends on the nature of the working medium.