  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 to understand 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 on the
transient magnitude of the Rabi doublet in some situations. We also study the
dynamics of the Fano anti-resonance, where the difference from the Rabi doublet
can be highlighted.
