Laboratoire de Physique Théorique
Toulouse - UMR 5152

Recently, much attention was paid to the thermodynamic description of open quantum systems, looking for signatures of quantum properties like coherences or entanglement in thermodynamic quantities such as the heat flow exchanged witht a thermal environment. Motivation include the design of quantum heat engines exhibiting better performances with respect to their classical counterparts and the search of new insights in the fundamental limitations on the manipulation of quantum systems.

In this context, a quasi-resonantly driven two level atom coupled to a thermal environment is the simplest situation allowing to grasp the impact of coherent superpositions on thermodynamic quantities. Despite it is a ubiquitous process in quantum protocols (e.g. single qubit quantum gates in presence of an environment), a thermodynamic interpretation of fluorescence is still missing, or available only for timescales much longer than a single Rabi oscillation where the dynamics of the system can be described by a Floquet master equation (i.e. a rate equation between dressed states of the qubit). In contrast, shorter time-scales, e.g. corresponding to a single quantum gate, are captured by the Optical Bloch Equations (OBE), whose compatibility with thermodynamics has been questioned untill recently.

Starting with the exact description of the energy and entropy balances for a microscopic model of the driven qubit and its environment, we derive different expressions for the first and the second law of thermodynamics associated either with the optical Bloch equations (valid in shorter timescales) or with the Floquet mast equation (valid on longer timescales only). In the regime where Bloch equations are valid, we single out signatures of quantum coherences in the heat flows and in the entropy production, related to the competition between the creation of coherent superpositions of atomic energy eigenstates by the driving field and the decoherence induced by the bath. Our findings carry the seeds for future thermodynamic analyzes of quantum gates and the design of quantum engines in the strong coherent driving regime.