  Rapidly changing the refractive index of a medium in space and time
(space-time photonic crystal, STPC) has been a challenging task. Such a rapid
change can be achieved by carrier-wave Rabi flopping. We show that it can be
realized when a train of half-cycle light pulses collide in a simple
three-level atomic medium. We found the formation of Bragg microcavities and
demonstrated their ultrafast control in this case. The proposed approach is a
convenient way to control medium properties on the sub-cycle time scale. It is
a demonstration of the formation of STPCs and their ultrafast control in a
simple atomic medium, which has been a difficult task until now.
