Optimal Performance of a Three-level Quantum Refrigerator

TL;DR

This paper analyzes the optimal performance of a three-level quantum refrigerator, deriving bounds for its efficiency and showing how it can be optimized under different objective functions, with connections to classical models.

Contribution

It provides general expressions for COP bounds, compares optimization strategies for cooling power and $hi$-function, and links quantum refrigeration to classical mesoscopic heat engines.

Findings

Cooling power is optimizable only locally with respect to one control frequency.

$hi$-function can be optimized globally with respect to two control frequencies.

In low-temperature regimes, the quantum refrigerator maps to Feynman's ratchet and pawl model.

Abstract

We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and $\chi$-function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power is optimizable only in the local region with respect to one control frequency, while $\chi$-function can be optimized globally with respect to two control frequencies. Additionally, we show that in the low-temperatures regime, our model of refrigerator can be mapped to Feynman's ratchet and pawl model, a classical mesoscopic heat engine. In the parameter regime where both cooling power and $\chi$-function can be optimized, we compare the cooling power of the quantum refrigerator at maximum $\chi$-function with the optimum cooling power.