  We present explicit evaluations of quantum speed limit times pertinent to the
Markovian dynamics of an open continuous-variable system. Specifically, we
consider the standard setting of a cavity mode of the quantum radiation field
weakly coupled to a thermal bosonic reservoir. The evolution of the field state
is ruled by the quantum optical master equation, which is known to have an
exact analytic solution. Starting from a pure input state, we employ two
indicators of how different the initial and evolved states are, namely, the
fidelity of evolution and the Hilbert-Schmidt distance of evolution. The former
was introduced by del Campo {\em et al.} who derived a time-independent speed
limit for the evolution of a Markovian open system. We evaluate it for this
field-reservoir setting, with an arbitrary input pure state of the field mode.
The resultant formula is then specialized to the coherent and Fock states. On
the other hand, we exploit an alternative approach that employs both indicators
of evolution mentioned above. Their rates of change have the same upper bound,
and consequently provide a unique time-dependent quantum speed limit. It turns
out that the associate quantum speed limit time built with the Hilbert-Schmidt
metric is tighter than the fidelity-based one. As apposite applications, we
investigate the damping of the coherent and Fock states by using the
characteristic functions of the corresponding evolved states. General
expressions of both the fidelity and the Hilbert-Schmidt distance of evolution
are obtained and analyzed for these two classes of input states. In the case of
a coherent state, we derive accurate formulas for their common speed limit and
the pair of associate limit times.
