Symmetry breaking of Kramers-Henneberger atoms by ponderomotive force

It was believed that Kramers-Henneberger (KH) atoms in a linearly polarized superintense laser field exhibit the structure of “dichotomy.” At large quiver amplitude, the two lowest-lying eigenstates are degenerated and both have a dichotomous symmetric structure. However, this is not a common structure for KH atoms because KH atoms practically can only exist in the focused laser field. However, in a focused laser, KH state electrons usually experience the ponderomotive force, which will lift the degeneracy and break the symmetry.