Thermodynamics of autonomous optical Bloch equations

Abstract

Optical Bloch Equations (OBEs) are canonical equations describing the dynamics of a classically driven atom coupled to a thermal bath. Their thermodynamics is highly relevant to establish fundamental energetic bounds of key quantum processes. A consistent framework is available in the regime where the drives and baths can be treated classically, i.e. remains insensitive to the coupling with the atom. This regime, however, is not adapted to explore minimal energy costs, nor to measure atom-induced energy variations inside drives and baths -- a key ability to directly measure and optimize work and heat exchanges. This calls for a new framework accounting for atomic back-actions on drives and baths. Here we build such a framework by describing the atom, the drive and the bath as a joint autonomous system, the drive and the bath being parts of the same electromagnetic field. Our approach captures atom-field correlations at fundamental timescales, as well as the atomic back-action on the field, allowing us to define work-like (heat-like) flows as energy flows stemming from effective unitary dynamics induced by one system on the other (non-unitary correlating dynamics). Time-integrated work-like and heat-like flows are directly measurable in the field, as changes of the mean field and fluctuations, respectively. Our approach differs from standard analyses by identifying an additional unitary contribution in the atom's dynamics, the self-drive, and its energetic counterpart, the self-work, yielding a tighter expression of the second law. We relate this tightening to the extra knowledge about the field state, as well as the potential of the interacted driving field to be recycled. Our autonomous framework deepens the current understanding of thermodynamics in the quantum regime and its potential for energy management at quantum scales.