  We develop a microscopic theory for the relaxation dynamics of an optically
pumped two-level system (TLS) coupled to a bath of weakly interacting Bose gas.
Using Keldysh formalism and diagrammatic perturbation theory, expressions for
the relaxation times of the TLS Rabi oscillations are derived when the boson
bath is in the normal state and the Bose-Einstein condensate (BEC) state. We
apply our general theory to consider an irradiated quantum dot coupled with a
boson bath consisting of a two-dimensional dipolar exciton gas. When the bath
is in the BEC regime, relaxation of the Rabi oscillations is due to both
condensate and non-condensate fractions of the bath bosons for weak TLS-light
coupling and dominantly due to the non-condensate fraction for strong TLS-light
coupling. Our theory also shows that a phase transition of the bath from the
normal to the BEC state strongly influences the relaxation rate of the TLS Rabi
oscillations. The TLS relaxation rate is approximately independent of the pump
field frequency and monotonically dependent on the field strength when the bath
is in the low-temperature regime of the normal phase. Phase transition of the
dipolar exciton gas leads to a non-monotonic dependence of the TLS relaxation
rate on both the pump field frequency and field strength, providing a
characteristic signature for the detection of BEC phase transition of the
coupled dipolar exciton gas.
