  By employing the time-dependent exact diagonalization method, we investigate
the photoexcited states of the excitonic insulator in the extended
Falicov-Kimball model (EFKM). We here show that the pulse irradiation can
induce the interband electron-electron pair correlation in the photoexcited
states, while the excitonic electron-hole pair correlation in the initial
ground state is strongly suppressed. We also show that the photoexcited states
contains the eigenstates of the EFKM with a finite number of interband
electron-electron pairs, which are responsible for the enhancement of the
electron-electron pair correlation. The mechanism found here is due to the
presence of the internal SU(2) pairing structure in the EFKM and thus it is
essentially the same as that for the photoinduced $\eta$-pairing in the
repulsive Hubbard model reported recently [T. Kaneko et al., Phys. Rev. Lett.
${\bf 122}$, 077002 (2019)]. This also explains why the nonlinear optical
response is effective to induce the electron-electron pairs in the photoexcited
states of the EFKM. Furthermore, we show that, unlike the $\eta$-pairing in the
Hubbard model, the internal SU(2) structure is preserved even for a
nonbipartite lattice when the EFKM has the direct-type band structure, in which
the pulse irradiation can induce the electron-electron pair correlation with
momentum ${\it {\bf q}}$ = ${\textbf 0}$ in the photoexcited states. We also
discuss briefly the effect of a perturbation that breaks the internal SU(2)
structure.
