Solids can be cooled by driving impurity ions with lasers, allowing them to transfer heat from the lattice phonons to the electromagnetic surroundings.This exemplifies a quantum thermal machine, which uses a quantum system as a working medium to transfer heat am22 pro model between reservoirs.We review the derivation of the Bloch-Redfield equation for a quantum system coupled to a reservoir, and its extension, using counting fields, to calculate heat currents.
We use the full form of this equation, which makes only the weak-coupling and Markovian approximations, to calculate the cooling power for a simple vegemite pop art model of laser cooling.We compare its predictions with two other time-local master equations: the secular approximation to the full Bloch-Redfield equation, and the Lindblad form expected for phonon transitions in the absence of driving.We conclude that the full Bloch-Redfield equation provides accurate results for the heat current in both the weak- and strong- driving regimes, whereas the other forms have more limited applicability.
Our results support the use of Bloch-Redfield equations in quantum thermal machines, despite their potential to give unphysical results.