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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.

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