Thermodynamics of coherent energy exchanges between lasers and two-level systems

Abstract

We study the quantum thermodynamics of a coherent macroscopic electromagnetic field (laser) coupled to a two-level system (qubit) near resonance, from weak to strong driving regimes. This combined system is, in turn, weakly coupled to a thermal radiation field, and can be described by an autonomous quantum master equation. We show that the laser acts as an autonomous work source and that, in the macroscopic limit, the work produced is independent of the phase of the laser. Using the dressed qubit approach, we show that the variation of energy in the laser is not the work transferred to the dressed qubit, which is instead obtained from the ''dressed laser'' -- a coherent superposition of the laser and the qubit. Using a two-point measurement technique with counting fields, we obtain the full counting statistics for the work of the laser and dressed laser, and show that they satisfy Crooks fluctuation theorems. We then use these theorems as criteria to investigate the thermodynamic consistency of quantum master equations, first in the autonomous setup for the combined system, then in the non-autonomous setup where the coherent field is eliminated and effectively described by a time dependent external field. Treating the laser as an external field in known to yield expressions for the work which are in contradiction with quantum thermodynamics predictions in the strong drive regime. We show that these inconsistencies stem from a confusion between the laser and dressed laser, and show how to correct them. We also derive a new master equation, thermodynamically consistent at all driving regimes, from which the Bloch and Floquet master equations can be obtained using additional approximations (of which we also examine the consistency).