  We employ the Dirac-Frenkel variational principle and multiple Davydov ansatz
to study time-dependent fluorescence spectra of a driven qubit in the weak- to
strong qubit-reservoir coupling regimes, where both the Rabi frequency and
spontaneous decay rate are comparable to the transition frequency of the qubit.
Our method agrees well with the time-local master-equation approach in the
weak-coupling regime, and offers a flexible way to compute the spectra from the
bosonic dynamics instead of two-time correlation functions. While the
perturbative master equation breaks down in the strong-coupling regime, our
method actually becomes more accurate due to the use of bosonic coherent states
under certain conditions. We show that the counter-rotating coupling between
the qubit and the reservoir has considerable contributions to the photon number
dynamics and the spectra under strong driving conditions even though the
coupling is moderately weak. The time-dependent spectra are found to be
generally asymmetric, a feature that is derived from photon number dynamics. In
addition, it is shown that the spectral profiles can be dramatically different
from the Mollow triplet due to strong dissipation and/or multiphoton processes
associated with the strong driving. Our formalism provides a unique perspective
to interpret time-dependent spectra.
