Employing Non-Markovian effects to improve the performance of a quantum Otto refrigerator

High-precision control over quantum systems has been providing many proof-of-principle experiments in quantum thermodynamics. The proper extension of thermal machines description to the quantum domain may has important implications to the design of quantum technologies. In general, the stroke-operating Markovian machines consider a complete thermalization of the system in the strokes where heat is exchanged between either the hot or the cold Markovian heat reservoirs. However, current advances in structured thermal reservoir designs have considered the inclusion of memory effects associated to non-Markovian dynamics, which have been receiving special attention in quantum thermodynamics. Here we consider a quantum Otto refrigerator with a particular choice of engineered cold reservoir and discuss its performance providing explicit expressions for the coefficient of performance, injected power, and cooling rate as well as associating these quantities to the total entropy production along the cycle. These relations are general and do not depend on the particular choice of the quantum refrigerant substance. Finally, we also consider a numerical simulation of a spin quantum refrigerator with experimentally feasible parameters to illustrate our results, showing that non-Markovian effects induced by the structured cold reservoir may improve the performance of a quantum Otto refrigerator.