  In this work, we obtain an analytical representation of the density operator
of an atom in dissipative cavity when the reservoir is at zero temperature and
the total number of excitation is N=1. We also investigated the quantum speed
limit time(QSLT) of the atom and the non-Markovianity in the dynamics process.
The results show that the QSLT and the non-Markovianity can be effectively
manipulated by the atom-cavity coupling and the reservoir parameters. Both of
the atom-cavity coupling and the detuning can induce a sudden transition from
Markovian to non-Markovian dynamics and this transition is the main physical
reason of the quantum speed-up process. The critical value of sudden transition
from no speed-up to speed-up depends the atom-cavity coupling and the reservoir
parameters. The corresponding physical explanation is also provided for our
results.
