Algebraic solution for a two-level atom in radiation fields and the Freeman resonances

Abstract

Using techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasi-energies is obtained, which shows that the Bloch-Siegert shift is always finite, regardless of whether the original or the shifted level spacing is an integral multiple of the driving frequency, ω. We also find that the wave functions, though finite when the original level spacing is an integral multiple of ω, become divergent when the intensity-dependent shifted energy spacing is an integral multiple of the photon energy. This result provides, for the first time in the literature, an ab-initio theoretical explanation for the occurrence of the Freeman resonances observed in above-threshold ionization experiments. PACS number(s): 32.80. Rm, 42.65.Ky, 12.20Ds, 03.65.Nk

Precise calculation of quasienergies of a driven two-level atom based on the Guo–Wu–Van Woerkom solution

“…(3) The technique developed for obtaining accurate numerical solutions to the idealized two-level model may be generalized to obtain accurate numerical quasienergies and wavefunctions for a driven N-level system. Not long ago, the first analytically exact solution to the Bloch equation was obtained by Guo, Wu, and Van Woerkom (GWV) [12]. The solution of GWV made accurate numerical calculations possible.…”

“…Our results can be used in treating a resonance, such as the Freeman resonance [12]. When it appears, the transitions between the ground state and other excited states that are not resonant can be ignored.…”

“…From the above relations we see that the accuracy of the wavefunctions Y AE depends on the accuracy of the quasienergies E. The expression for the quasienergies is given in terms of infinite determinants [12]. When the original energy spacing is an integer, i.e., 2D ¼ n ðn ¼ 1; 2; 3; .…”

“…In the generic case, where the original energy spacing is not an integer, the quasienergies can be calculated with all r n from Eq. (12). The coefficients for the case of n > 100, beyond the cutoff of the table, can be calculated with the same method developed in the current paper.…”

“…In the current paper, we start with a brief review of previous results [12,16,17], then show the calculational procedures to produce quasienergies in all cases by using the data table. The main formulas for producing the data table are described in the second section.…”