Optimization of inverse one-qubit refrigerators

We study several optimal working regimes of one-qubit quantum refrigerators having one qubit at their cold side. We demonstrate that they can be optimized using the techniques of finite-time thermodynamics on the solutions of the Lindblad equation. Our results show that differently to what happens in classic refrigerators, in our quantum ones the optimization of the cooling power does not lead to an optimal working regime but that using the \(\Omega\) function we can find it. Then, we generalize the study using a family of target functions defined by powers of the coefficient of performance times the cooling power to carry out a more general optimization. These last optimizations reveal the importance that every parameter defining the refrigerator has on the performance of the refrigerators when they work optimally.