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Physical Review A

Linear susceptibility of a three-level system driven by an intense multimode laser field

V. Yu. Finkel'Shteǐn

Published Feb 1, 1983• 4 citations
Publisher

Abstract

A theory of ac Stark splitting at double resonance in a three-level system is presented, the upper and lower transitions being coupled to a near-resonant intense multimode field and a weak monochromatic field, respectively. Linear response to a weak field is considered. The analytical treatment calling into action a diagram technique and the quasistationary-states method is carried out beyond the limits of perturbation theory and the nonresonant approximation. The multimode structure of the radiation spectrum results in a quasi-periodicity of the field-correlation function. It leads to a strong modulation of the absorbtion line shape with a period $\frac{1}{2}\ensuremath{\Delta}{\ensuremath{\nu}}_{0}$ where $\ensuremath{\Delta}{\ensuremath{\nu}}_{0}$ is the intermode interval. The role of different weakening effects such as spontaneous decay of the levels, the finite pulse duration, and instrumental and natural fluctuations of a single mode is studied. The last effect is shown to be the most important, and a possible method of direct measurement of the natural-fluctuations' correlation function is proposed.

DOI
10.1103/physreva.27.961

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A theory of ac Stark splitting at double resonance in a three-level system is presented, the upper and lower transitions being coupled to a near-resonant intense multimode field and a weak monochromatic field, respectively. Linear response to a weak field is considered. The analytical treatment calling into action a diagram technique and the quasistationary-states method is carried out beyond the limits of perturbation theory and the nonresonant approximation. The multimode structure of the radiation spectrum results in a quasi-periodicity of the field-correlation function. It leads to a strong modulation of the absorbtion line shape with a period 12\ensuremathΔ\ensuremathν0\frac{1}{2}\ensuremath{\Delta}{\ensuremath{\nu}}_{0}21​\ensuremathΔ\ensuremathν0​ where \ensuremathΔ\ensuremathν0\ensuremath{\Delta}{\ensuremath{\nu}}_{0}\ensuremathΔ\ensuremathν0​ is the intermode interval. The role of different weakening effects such as spontaneous decay of the levels, the finite pulse duration, and instrumental and natural fluctuations of a single mode is studied. The last effect is shown to be the most important, and a possible method of direct measurement of the natural-fluctuations' correlation function is proposed.
In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.
A three-level cascade system coupled to two pulsed, fluctuating multimode laser fields is studied with numerical Monte Carlo simulations. Laser noise is modeled by introducing abrupt, random variations into the field parameters. We show that both phase and amplitude fluctuations may increase the signal through the ac Stark effect, and we demonstrate how noise can change the whole spectral structure of the transitions. As a result that is conveniently produced with simulations but that is often difficult to attain analytically, we also present on- and off-resonance signal distributions at various saturation levels and in different noise scenarios.
Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.
The parametric resonances and the quasi-level structure of an atom strongly driven by a near-resonant amplitude-modulated optical field are studied theoretically. An approximate analytical solution of the density-matrix equations of motion is obtained for two-level and three-level atoms. Based on this solution the quasi-level shifts are analyzed, and the conditions for the quasi-levels to cross each other are derived. Expressions are given for the probe-wave absorption/gain spectrum near the parametric resonance and far from it. It is pointed out that the parametric resonances appear when the pumping field sidebands are tuned to resonance with some transitions among the quasi-levels.
In a helium glow discharge, the A. C. Stark shift of the 4 3S 1 → 2 3P0,1,2 transition (λ ≅ 4 713 Å) induced by nonresonant interaction of the 4 3S and 4 3P levels with a multimode CO2 laser field is measured as a function of laser intensity in the range IL < 35 MW/cm 2. Departure from the linear intensity dependence given by second order perturbation theory is observed for IL > 2 MW/cm2. A three-level atom model taking into account the interaction with the laser field in a non perturbative way agrees with the experiment. Strong broadening is also detected for IL > 1 MW/cm2. This broadening grows with IL until a quasi-continuum spreading over 50 Å is observed for IL = 33 MW/cm2. This broadening results from amplitude and phase fluctuations of the laser field modes during interaction. For IL = 33 MW/cm2 the recorded 4 713 Å spectral line shape reflects the statistical distribution of the mode amplitudes.
The resonant multiphoton resonances shifts and widths and ionization cross-sections for multielectron atoms in a intense laser radiation field are studied. It is carried out a new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation. In relativistic theory, the Gell-Mann and Low adiabatic formula for energy shift is connected with electrodynamical scattering matrice, which includes interaction with as a laser field as a photon vacuum field (radiative decay). The optimized basis of the relativistic orbitals is generated with using a minimization procedure for the gauge-non-invariant contribution (the fourth-order of the QED perturbation theory) to the radiation width of atomic state. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction “atom- multimode laser pulse” is greater than the corresponding shift and width for a case of the “atom- single-mode pulse” (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.