Work extraction from a quantum emitter subjected to control fields

The amount of extractable work from a quantum emitter, specifically a two-level quantum system (TLS) interacting with a photonic environment, is investigated under the control of an external driving field. In the Markovian regime under the classical control field, a TLS functions as a quantum battery, where interaction with the photonic bath leads to energy dissipation while the driving field replenishes it. The extractable work is quantified through ergotropy, a measure of the maximum work that can be extracted from a quantum state using the optimal unitary transformation. We systematically explore the evolution of ergotropy under the influence of either a continuous driving field or a periodic pulse sequence. Our analysis includes both coherent and incoherent contributions to the total ergotropy for different initial states of the TLS. Additionally, we examine how the detuning between the driving field and the emission frequency of the TLS, as well as the initial state of the system, affect work extraction for both continuous and periodic pulse driving fields.