  We demonstrate that strong-field ionization of atoms driven by circularly
polarized light becomes an adiabatic process when described in the frame
rotating with the laser field. As a direct consequence, a conservation law
emerges: in the rotating frame the energy of the tunneling electron is
conserved for rotationally invariant potentials. This conservation law, arising
from a classical picture, is retrieved through a proper classical-quantum
correspondence when considering the full quantum system, beyond the Strong
Field Approximation.
