TY - JOUR

T1 - Multi-photon spectra in the presence of strongly saturating oscillating and static fields

AU - Moloney, J. V.

AU - Meath, William J.

N1 - Funding Information:
1. INTRODUCTION The two-level system, in the dipole approximation, has provided the basis for the study of a wide variety of linear and non-linear interactions between radiation and matter \[1-3\]. Much of the discussion in the literature has been confined to the study of the important spin-89 atom in the presence of a strong radio-frequency field, in which the spin-i-states are tuned by sweeping with a static transverse Zeeman field \[3, 4\] ; apparently little attention has been given to the analogous frequency-sweep problem (see, however, \[5\]). The theoretical approaches to the problem usually involve either continued fraction expansions and/or hamiltonian matrix techniques \[5-9\]. Some of the practical limitations of these methods have been discussed previously \[5, 8\], as a function of the strength of the coupling between the states of the system, and these approaches t This research was supported by a grant from the National Research Council of Canada. J~ Present address : Fakultiit fiir Physik, Universitiit Bielefeld, Bielefeld, Germany. wA ssociated with the Center for Interdisciplinary Studies in Chemical Physics.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1978/4

Y1 - 1978/4

N2 - 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.

AB - 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.

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U2 - 10.1080/00268977800100841

DO - 10.1080/00268977800100841

M3 - Article

AN - SCOPUS:5844368729

VL - 35

SP - 1163

EP - 1175

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 4

ER -