  We simulate the pump-probe experiments of lasing in molecular nitrogen ions
with particular interest on the effects of rotational wave-packet dynamics. Our
computations demonstrate that the coherent preparation of rotational wave
packets in N$_2^+$ by an intense short non-resonant pulse results in a
modulation of the subsequent emission from $B^2\Sigma_u^+ \rightarrow
X^2\Sigma_g^+$ transitions induced by a resonant seed pulse. We model the
dynamics of such pumping and emission using density matrix theory to describe
the N$_2^+$ dynamics and the Maxwell wave equation to model the seed pulse
propagation. We show that the gain and absorption of a delayed seed pulse is
dependent on the pump-seed delay, that is, the rotational coherences excited by
the pump pulse can modulate the gain and absorption of the delayed seed pulse.
Further, we demonstrate that the coherent rotational dynamics of the nitrogen
ions can cause lasing without electronic inversion.
