Optical Bloch Equations (OBEs) are canonical equations of quantum open systems, that describe 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 drives and baths can be treated classically, i.e. remain 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 where the atomic back-action on drives and baths would be accounted for. Here we build such a framework suitable to analyze the situation where the atom, the drive and the bath form 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. This allows 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 dynamics induced by correlations). Time-integrated work-like and heat-like flows are shown to be directly measurable in the field, as changes of energy locked in the mean field and fluctuations, respectively. Our approach differs from standard open analyses by identifying an additional unitary contribution in the atom’s dynamics, the self-drive, and its energetic counterpart, the self-work, which yields a tighter expression of the second law. We quantitatively relate this tightening to the extra-knowledge about the field state as compared with usual treatments of the atom as an open system. Our autonomous framework deepens the current understanding of thermodynamics in the quantum regime and its potential for energy management at quantum scales. Its predictions can be probed in state-of-the-art quantum hardware, such as superconducting and photonic circuits.
Prasad et al. (Wed,) studied this question.