Models of Two-Level Atoms in Quasiperiodic External Fields

We prove that the spectrum of the generalized quasienergy operator of a plane-polarized two-level atom in a strong external quasiperiodic electromagnetic field with nonzero constant Fourier component is pure point, under Diophantine conditions on the frequency ratio, and excluding a small subset of resonant values. The widespread belief that there may be only pure point spectrum in such models is briefly discussed in Section 2 and the circularly polarized case—a well-known soluble model—is revisited from the point of view of the quasienergy operator..