Time-resolved physical spectrum in cavity quantum electrodynamics

The time-resolved physical spectrum of luminescence is theoretically studied for a standard cavity quantum electrodynamics system. In contrast to the power spectrum for the steady state, the correlation functions up to the present time are crucial for the construction of the time-resolved spectrum, while the correlations with future quantities are inaccessible because of the causality, i.e., the future quantities cannot be measured until the future comes. We find that this causality plays a key role in understanding the time-resolved spectrum, in which the Rabi doublet can never be seen during the time of the first peak of the Rabi oscillation. Furthermore, the causality can influence the transient magnitude of the Rabi doublet in some situations. We also study the dynamics of the Fano antiresonance, where the difference from the Rabi doublet can be highlighted.