  We theoretically investigate the dynamical Franz-Keldysh effect in
femtosecond time resolution, that is, the time-dependent modulation of a
dielectric function at around the band gap under an irradiation of an intense
laser field. We develop a pump-probe formalism in two distinct approaches:
first-principles simulation based on real-time time-dependent density
functional theory and analytic consideration of a simple two-band model. We
find that, while time-average modulation may be reasonably described by the
static Franz-Keldysh theory, a remarkable phase shift is found to appear
between the dielectric response and the applied electric field.
