Impurity reveals distinct operational phases in quantum thermodynamic cycles

Abstract: We analyze the effect of impurity on the work output and efficiency of quantum Otto and quantum Carnot heat cycles, modeled as a single quantum particle in an infinite square well (ISW) potential, which is the working substance. We solve this quantum mechanical system perturbatively up to first and second order in strength of the impurity for strong and weak coupling regimes, respectively. We derive the analytical expressions of work and efficiency for the strong coupling regime to the first order in the strength parameter. The threshold value of the strength parameter in weak coupling is obtained up to which the numerical result agrees with the perturbative result for a repulsive and attractive impurity. To our surprise, an embedded impurity unlocks new operational phases in the system, such as a quantum heat engine, quantum refrigerator, and quantum cold pump. In addition, the efficiency of the quantum Otto heat engine is seen to reach Carnot efficiency for some parameter regimes. The cooling power and coefficient of performance of the quantum refrigerator and quantum cold pump are non-trivially affected by the impurity.