  In recent years, strong-field physics in condensed-matter was pioneered as a
novel approach for controlling material properties through laser-dressing, as
well as for ultrafast spectroscopy via nonlinear light-matter interactions
(e.g. harmonic generation). A potential controversy arising from these
advancements is that it is sometimes vague which band-picture should be used to
interpret strong-field experiments: the field-free bands, the adiabatic
(instantaneous) field-dressed bands, Floquet bands, or some other intermediate
picture. We here try to resolve this issue by performing 'theoretical
experiments' of time- and angle-resolved photoelectron spectroscopy (Tr-ARPES)
for a strong-field laser-pumped solid, which should give access to the actual
observable bands of the irradiated material. To our surprise, we find that the
adiabatic band-picture survives quite well, up to high field intensities
(~10^12 W/cm^2), and in a wide frequency range (driving wavelengths of 4000 to
800nm, with Keldysh parameters ranging up to ~7). We conclude that to first
order, the adiabatic instantaneous bands should be the standard blueprint for
interpreting ultrafast electron dynamics in solids when the field is highly
off-resonant with characteristic energy scales of the material. We then discuss
weaker effects of modifications of the bands beyond this picture that are
non-adiabatic, showing that by using bi-chromatic fields the deviations from
the standard picture can be probed with enhanced sensitivity. Our work outlines
a clear band picture for the physics of strong-field interactions in solids,
which should be useful for designing and analyzing strong-field experimental
observables and also to formulate simpler semi-empirical models.
