Laser Cooling Beyond Rate Equations: Approaches From Quantum Thermodynamics

TL;DR

This paper explores advanced quantum thermodynamic models for laser cooling of solids, demonstrating that the full Bloch-Redfield equation offers accurate heat current predictions across various regimes, surpassing simpler approximations.

Contribution

It introduces the application of the full Bloch-Redfield equation to laser cooling, comparing its effectiveness with other master equations and establishing its broader applicability.

Findings

Full Bloch-Redfield equation accurately predicts heat currents in laser cooling.

Secular and Lindblad approximations have limited validity in certain regimes.

Full equation remains reliable even in strong-driving conditions.

Abstract

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 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 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, in spite of their potential to give unphysical results.