  A new frontier in optics research has been opened by the recent developments
in non-perturbative optical modulation in both time and space that creates
temporal boundaries generating ``time-reflection'' and ``time-refraction'' of
light in the medium. The resulting formation of a Photonic Time Crystal within
the modulated optical material leads to a broad range new phenomena with a
potential for practical applications, from non-resonant light amplification and
tunable lasing, to the new regime of quantum light-matter interactions.
However, the formation of the temporal boundary for light relies on optical
modulation of the refractive index that is both strong and fast even on the
time scale of a single optical cycle. Both of these two problems are extremely
challenging even when addressed independently, leading to conflicting
requirements for all existing methods of optical modulation. However, as we
show in the present work, an alternative approach based on virtual interband
transition excitation, solves this seemingly insurmountable problem. Being
fundamentally dissipation-free, optical modulation by virtual excitation does
not face the problem of heat accumulation and dissipation in the material,
while the transient nature of the excited virtual population that modifies the
material response only on the time scale of a single optical cycle, ensures
that the resulting change in the refractive index is inherently ultrafast. Here
we develop the theoretical description of the proposed modulation approach, and
demonstrate that it can be readily implemented using already existing optical
materials and technology.
