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.
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.
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 spectral and dynamic effects associated with a non-zero difference, d, between the permanent dipole moments of two molecular states involved in a transition, are investigated for a variety of electromagnetic field-molecule interactions. Both analytical and exact numerical techniques are used to solve the time-dependent Schrodinger equation and to obtain the temporal populations of the molecular states and the associated absorption spectra, for molecular interactions with a Gaussian pulsed, or one or two continuous wave (CW), laser(s).;Analytical rotating wave approximation results are derived for a single CW laser interacting with a two-level d {dollar}\\ne{dollar} 0 molecule with an excited state lifetime, and for a two-level d {dollar}\\ne{dollar} 0 molecule interacting with two CW lasers. A symmetry-adapted Riemann product integral method for exact calculations of pulsed laser-molecule interactions is developed and applied to specific problems. The Floquet technique for the treatment of periodic Hamiltonians is extended to accommodate the interaction of a molecule with two CW lasers.;The one-field RWA results are used to predict and interpret the effects of permanent dipoles on the temporal behaviour of the molecular states for a decaying two-level system interacting with a CW laser, and for a non-decaying two-level system interacting with a pulsed laser. It is shown that the excited state lifetime and the pulse duration can act as internal and external probes, respectively, of the temporal effects of permanent dipoles, relative to the often-studied d = 0 problem. The two-field analytical RWA solutions are used to help discuss and predict the effects of permanent dipole moments in two-laser multi-photon transitions. Several examples of multi-photon, two-colour, two-level resonance profiles, calculated in the RWA and by using exact Floquet techniques, are used to demonstrate how particular multi-photon transitions can be optimized, and to help quantify the conditions for the validity of the two-colour RWA. The effects of neighbouring energy levels on the transition of interest, for both probe and pump-probe laser-molecule interactions, are investigated using a series of three- to seven-level model molecular systems.
Perturbative corrections are derived for the rotating-wave approximation (RWA) for the single-photon and multiphoton resonance profiles due to the interaction between a two-level molecule, with nonzero permanent dipoles, and a sinusoidal time-dependent electric field. The derivation is carried out through the use of a Floquet secular equation that introduces the effects of the permanent dipole moments into the problem through the argument, d\ensuremath{\cdot}e^scrE/\ensuremath{\omega}, of Bessel functions contained in molecule-laser coupling parameters; here d=${\ensuremath{\mu}}_{22}$-${\ensuremath{\mu}}_{11}$, where ${\ensuremath{\mu}}_{\mathrm{ii}}$ is the permanent dipole of molecular state i, and scrE, e^, and \ensuremath{\omega} are the field strength, direction of polarization unit vector, and the circular frequency of the electromagnetic field (EMF). Expansions for the N-photon resonance profiles and the associated resonance frequencies and full widths at half maximum, in powers of the couplings between the transition and permanent dipole moments and the applied EMF, are obtained by expanding the Bessel functions in the perturbative results and are compared with those in the literature (available mostly for d=0 only). The perturbative results, and a series of exactly calculated two-level model absorption spectra, are used to discuss (1) the ability of the explicit perturbative corrections to the RWA to explain the differences between exact and RWA resonance profiles (for example, the positive or negative Bloch-Siegert shifts and dynamic backgrounds absent in the RWA), (2) the usefulness of the perturbative corrections in general, and (3) the effects of permanent dipoles on single-photon and multiphoton absorption spectra.
A rotating-wave approximation (RWA) for the single-photon and multiphoton resonance profiles for a two-level molecule interacting with both sinusoidal and static electric fields is derived. Included is a useful expression for the coupling between the molecule and the applied sinusoidal field which exhibits the effects of both diagonal dipole matrix elements (permanent dipole moments) and the applied static electric field. Comparisons of the RWA results with exact two-level calculations provide qualitative information concerning the validity of the RWA as a function of molecular and field parameters. These examples are also used to illustrate the interpretive nature of the RWA results for the resonance profiles and some of the effects of permanent dipoles and static fields on the profiles. Of particular interest are examples involving Boltzmann rotationally averaged spectra as a function of temperature where it is shown that minima in the spectra occurring for high temperatures can be reduced or removed completely if the temperature or applied static field is reduced.
The interaction is studied of a Gaussian pulsed or a continuous wave (CW) electric field with a molecule that has a nonzero difference d between the permanent dipoles of the ground and excited states involved in a transition. The unusual spectral effects associated with the transition with d ≠ 0, relative to the often studied case with d = 0, have been investigated previously in the two-level approximation and for continuous wave lasers. The observation of these effects, including markedly increased periods of excited state populations and negative Bloch-Siegart shifts, will often require the intense fields associated with pulsed rather than purely continuous wave electric fields. Transitions induced by continuous wave and pulsed laser-‘permanent dipole molecule’ interactions, for high field intensities and varying pulse durations, are investigated with model calculations carried out using exact Floquet and symmetry-adapted Riemann product integral methods. These calculations illustrate how the increased period of the excited state populations for dipolar molecules, and the associated molecule-field couplings, can be probed by sampling the time-dependent populations of the excited states using ultrashort to short pulses. The discussion illustrates the predictive and interpretive importance of the analytical expression for the molecule-EMF coupling provided by the rotating wave approximation (RWA) with d ≠ 0. The examples considered show, for example, temporal beating effects between the field and the RWA or Rabi frequencies and their dependence on d.
The interaction of two continuous wave electric fields (lasers) with a two-level molecule, that has a nonzero difference d, between the permanent dipoles of the two states involved in a multiphoton two-color transition, is studied in the rotating wave approximation and by using exact methods. Analytical rotating wave approximation results for the time-dependent populations of the molecular states and for the resonance profiles are derived and used to help discuss the effects of permanent dipole moments in the two-color absorption problem. Several examples of multiphoton, two-color, two-level resonance profiles calculated in the rotating wave approximation and by using exact techniques, are employed for illustrative purposes. They are used to help quantify the conditions for the validity of the two-color rotating wave approximation, which are considerably more restrictive than the analogous conditions for the one-color rotating wave approximation with d≠0, and to illustrate the interpretive and predictive nature of the rotating wave approximation results. For example, there are many multiphoton, two-color transitions that are available if a molecule possesses permanent dipoles (d≠0). The analytic rotating wave approximation expression for the molecule-two laser coupling can often be used to reliably estimate the field parameters of the two lasers that are required to optimize a given transition relative to others.