  Semiconductor quantum dots operated dynamically are the basis of many quantum
technologies such as quantum sensors and computers. Hence, modelling their
electrical properties at microwave frequencies becomes essential to simulate
their performance in larger electronic circuits. Here, we develop a
self-consistent quantum master equation formalism to obtain the admittance of a
quantum dot tunnel-coupled to a charge reservoir under the effect of a coherent
photon bath. We find a general expression for the admittance that captures the
well-known semiclassical (thermal) limit, along with the transition to lifetime
and power broadening regimes due to the increased coupling to the reservoir and
amplitude of the photonic drive, respectively. Furthermore, we describe two new
photon-mediated regimes: Floquet broadening, determined by the dressing of the
QD states, and broadening determined by photon loss in the system. Our results
provide a method to simulate the high-frequency behaviour of QDs in a wide
range of limits, describe past experiments, and propose novel explorations of
QD-photon interactions.
