  The initial state of a quantum system can significantly influence its future
dynamics, especially in non-Markovain quantum processes due to the
environmental memory effects. Based on a previous work of ours, we propose a
method to quantify the memory effects of a non-Markovian quantum process
conditioned on a particular system initial state. We apply our method to study
the early-time dynamics of a superradiance model where $N$ atoms (the system)
interacting with a single-mode vacuum cavity (the environment) with several
types of initial states. We find that the value of the memory effects in the
early-time regime is half the environmental photon number for the (dephased)
Dicke states. Besides, the memory effects, the environmental photon number and
the degree of superradiance can be simultaneously enhanced by the coherence or
entanglement of some initial states. In our study, the transitions from
non-superradiant initial states to superradiant ones are always accompanied by
the enhancement of memory effects, showing the importance of memory effects in
superradiance.
