A solution for the time-dependent Schrödinger equation is given for an N-level system interacting with a sinusoidal field of arbitrary amplitude E, frequency v and phase 8, in the presence of an applied static field of arbitrary strength E°. The solution is obtained by a modification of a previous exact method of solution for E° = 0 and retains the essential analytic features of the exact wavefunction for the problem. The Floquet form of the solution yields (a) the location and the widths of allowed transitions and the location of forbidden transitions, by use of characteristic exponent plots, but without evaluating the spectrum, and (b) convenient expressions for the steady-state induced transition probabilities, including the effects of a uniform relaxation mechanism, that only require the solution of the wave equation over the initial period of the hamiltonian. The approach is equally applicable to Stark (or Zeeman) frequency sweep or tuning problems. The ability to incorporate the effects of static fields in the solution is important since a variety of problems (e.g. anti-crossing spectroscopy) involve the application of such fields to a level configuration interacting with a sinusoidal field. As a detailed specific example, the multi-photon steady-state induced transition probabilities and characteristic exponents are studied, as a function of frequency v, for the unperturbed (E° ≠ 0) and the perturbed (E°=0) two-level system under saturating conditions. It is also demonstrated, for the coupling strengths of interest in multi-photon calculations, that the method of solution discussed here is a viable unified alternative to dressed-atom techniques.
ASJC Scopus subject areas
- Molecular Biology
- Condensed Matter Physics
- Physical and Theoretical Chemistry