A previously developed exact semiclassical method is used to evaluate multi-photon spectra and Floquet characteristic exponents (dressed-atom energies) for several multi-level systems interacting with both strong oscillating and static fields under varying degrees of saturation. The usefulness of characteristic exponent plots in extracting the physically significant features of the spectrum, without the necessity of evaluating portions of the complete spectrum, is demonstrated for a number of model three-level systems which are not directly amenable to study by the often used rotating-wave approximation. The effect of neighbouring non-resonant states on two-photon resonance profiles is also discussed using three to six level systems (H and Na atoms) as models.
A previously developed exact semiclassical method is used to evaluate multi-photon spectra and Floquet characteristic exponents (dressed-atom energies) for several multi-level systems interacting with both strong oscillating and static fields under varying degrees of saturation. The usefulness of characteristic exponent plots in extracting the physically significant features of the spectrum, without the necessity of evaluating portions of the complete spectrum, is demonstrated for a number of model three-level systems which are not directly amenable to study by the often used rotating-wave approximation. The effect of neighbouring non-resonant states on two-photon resonance profiles is also discussed using three to six level systems (H and Na atoms) as models.
A solution for the time-dependent Schrödinger equation is given for an N-level system interacting with a sinusoidal field of arbitrary amplitude , frequency v and phase δ, in the presence of an applied static field of arbitrary strength . The solution is obtained by a modification of a previous exact method of solution for 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 and the perturbed 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.
An analytic expression for the absorption spectra of a two-level molecule or atom is derived, within the rotating wave approximation (RWA), which includes the effects of permanent dipole moments and static electric fields. The derivation is for the interaction of the system with a plane-polarized sinusoidal electromagnetic field (EMF) in the semi-classical electric dipole approximation. The RWA resonance profile, and a series of exactly calculated two-level model spectra, are used to investigate some single- and multi-photon spectral effects due to permanent dipoles and static fields, relative to the atomic problem (no permanent dipoles). These effects include the occurrence of even as well as odd photon transitions. Permanent dipole moments can cause narrowing of the resonances, oscillatory fringes around the resonances as a function of frequency, and decreases in the molecule-EMF coupling, relative to the atomic results. Comparisons with exact two-level model spectra are used to study the validity of the RWA results and indicate that several features, such as dynamic backgrounds and shifts of the resonance frequencies from the weak EMF limits of {dollar}\\omega\\sbsp{lcub}\\rm res{rcub}{lcub}\\rm N{rcub}{dollar} = {dollar}\\Delta{dollar}E/N, N = 1,2,3, dots, are missing in the RWA spectra as the coupling increases.;Perturbative corrections to the RWA absorption spectra and the full widths at half maxima for the resonances are derived, neglecting static fields, and used to investigate and explain the effects missing in the RWA; the RWA resonance profile is a zeroth plus first order result obtainable from a time-independent Floquet Hamiltonian secular equation. The usefulness and validity of the perturbative corrections are investigated and it is concluded that these corrections are not useful computationally past second order. However, the corrections are useful in understanding some of the deficiencies of the RWA. These include the shifts of the N-photon resonance positions to low frequency, with respect to {dollar}\\Delta{dollar}E/N, that can occur for molecules with non-zero permanent dipoles; the shift is always to high frequency for atoms. A series of exact model calculations, for "giant dipole" molecules, is also used to discuss the effects of permanent dipole moments on spectra and to establish comparisons with the recent literature on the subject.
The authors present an exact treatment of two- and multiquantum transitions in three-level systems driven by two intense linearly polarised monochromatic fields based on the semiclassical many-mode Floquet theory developed recently. Further they extend the almost degenerate perturbation theory of Salwen (1955-6) to the two-mode Floquet Hamiltonian and obtain approximate analytical formulae for multiphoton transition probabilities, resonance bichromatic shifts and widths, and absorption lineshapes beyond the conventional rotating-wave approximation (RWA). Detailed comparison of the analytical, the RWA, and the exact results is given. Several novel features of multiphoton lineshape characteristics are pointed out.
For pt.I see Chem. Phys. Lett. vol.96, p.464 (1983). The non-linear multiphoton excitation dynamics of two-level systems under the influence of two strong linearly polarised monochromatic fields is studied exactly for the first time along the semiclassical many-mode Floquet theory. The present approach relaxes the restrictions of the conventional generalised rotating-wave approximation (GRWA) and allows correct treatment of various non-linear features such as power broadening, resonance shift, asymmetry in absorption lineshape, etc. By extending the nearly degenerate perturbative method of Salwen (1955), approximate analytical expressions for transition probabilities are obtained for multiphoton resonance processes for which (n+1) photons of one field are absorbed, whereas n photons of the other field are emitted, where n is an arbitrary integer. Detailed comparison of the analytical, the GRWA and the numerically exact results is given. Also presented is a case study of the time evolution of spin 1/2 systems in multi-quantum NMR transitions driven by pulsed bichromatic radiofrequency fields.
A five-level model molecule consisting of a ground and four nearly degenerate excited states, where the excited states arise, via static couplings, from the interaction of a doorway state with three background states, is used to investigate neighbouring-level effects and the validity of the generalized rotating-wave or quasi-resonant approximation for such systems. Calculations are performed to determine the (single-photon) absorption spectra associated with the model, and the underlying temporal behaviour of the molecular states, using both RWA and (exact) Floquet techniques, as functions of the frequency and field strength of the applied sinusoidal electric field. For the field strengths studied, corresponding to ground-doorway-state transition coupling strengths (E d - E g) < 0·04, the RWA results for the overall absorption spectra and for the resonance profiles associated with the individual excited states are generally in excellent agreement with exact calculations, although some interesting subtle differences do occur for the largest considered. On the other hand, the temporal development of the molecular states is well represented by the RWA only for small times. The spectral results, as a function of , are used to discuss some of the interesting features, due to neighbouring-level effects involving the nearly degenerate excited states, that occur during the transition from weak to strong molecule-EMF coupled problems. These include intensity stealing by off-resonance molecular states and inversions of the order of resonance frequencies relative to those corresponding to the weak-field limits.
For pt.II see ibid., vol.9, p.1221 (1976). Discusses the steady-state response of a three-level atom in two-photon absorption. The applied laser fields can have arbitrary intensities (within the rotating-wave approximation (RWA)). A general expression is derived for the population excited on the uppermost energy level. Two special cases which allow a trivial Doppler averaging are treated in detail. For an off-resonant intermediate state the two-photon spectrum is a simple Lorentzian showing a power shift and modest cross power broadening. The same features are retained when several off-resonance intermediate levels are assumed. For very strong laser fields the Doppler shifts can be neglected in the first approximation. The corresponding spectra are analysed.