  Ponderomotive energy shifts experienced by Rydberg atoms in optical fields
are known to be well approximated by the classical quiver energy of a free
electron. We examine such energy shifts quantum mechanically and elucidate how
they relate to the ponderomotive shift of a free electron in off-resonant
fields. We derive and evaluate corrections to the ponderomotive free electron
polarizability in the length and velocity (transverse or Coulomb) gauges, which
agree exactly as mandated by the gauge invariance. We also show how the free
electron value emerges from the Dirac equation through summation over the Dirac
sea states. We find that the free-electron AC Stark shift comes as an
expectation value of a term proportional to the square of the vector potential
in the velocity gauge. On the other hand, the same dominant contribution can be
obtained to first order via a series expansion of the exact energy shift from
the second order perturbation theory in the length gauge. Finally, we
numerically examine the validity of the free-electron approximation. The
correction to the free-electron value becomes smaller with increasing principal
quantum number, and it is well below a per cent for 60s states of Rb and Sr
away from the resonances.
