  In this paper, we show how to generate the multiple single-photon wavepackets
of arbitrary temporal shape from an optical cavity coupled with $N$ three-level
atoms driven by a driving field in the non-Markovian regime. We derive an exact
analytical expression of the optimal driving field for generating such
wavepackets, which depends on two detunings of the cavity and driving field
with respect to the three-level atoms. The cavity we used consists of two
mirrors facing each other, where one is perfect and the other exists the
dissipation (one-sided cavity), which couples with the corresponding
non-Markovian input-output fields. If the first single-photon wavepacket
generated by the Markovian system is the same as the non-Markovian case, the
Markovian system cannot generate the same multiple single-photon wavepackets as
the non-Markovian one when the spectral widths of the other environments taking
values different from the spectral width of the first environment, while
setting the equal spectral widths for the different environments can generate
this. The generated multiple different single-photon wavepackets are not
independent of each other, which satisfy certain relations with non-Markovian
spectral parameters. We analyse the transition from Markovian to non-Markovian
regimes and compare the differences between them, where the cavity interacts
simultaneously with the multiple non-Markovian environments. Finally, we extend
the above results to a general non-Markovian quantum network involving many
cavities coupled with driven three-level atoms.
