Impurity reveals distinct operational phases in quantum thermodynamic cycles

TL;DR

This paper investigates how impurity influences the operational phases, work output, and efficiency of quantum thermodynamic cycles modeled as a particle in an infinite well, revealing new phases and conditions for optimal performance.

Contribution

It provides analytical and numerical analysis of impurity effects on quantum Otto and Carnot cycles, uncovering new operational phases and conditions for maximum efficiency.

Findings

Impurity induces new operational phases like quantum heat engine, refrigerator, and cold pump.

Efficiency can reach Carnot limit under certain impurity conditions.

Impurity significantly affects cooling power and performance metrics.

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.