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Physical Review A

Effect of strong electromagnetic fields on dilute-gas spectra: The three-level system

Lewis S. Klein, Michel Giraud, A. Ben‐Reuven

Published Aug 1, 1974• 24 citations
Publisher

Abstract

The effect of a strong perturbing radiation field on spectral lines is studied using an extension of the Kubo-Zwanzig-Fano relaxation formalism. The problem of a dilute gas interacting with a strong perturbing field and a weak probe field is solved, assuming a separation of collisional and radiative processes, by introducing a classical-field renormalization technique. The solution is formulated entirely in terms of linear-response functions. This method is applied to the problem of the three-level absorber perturbed by a strong field and probed by a weak field. Multiphoton transitions, double resonance, and dynamic Stark effects can be treated as manifestations of this three-level problem.

DOI
10.1103/physreva.10.682

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Physical Review A•Jul 1, 1982•17 citations
The effect of a strong perturbing radiation field on spectral lines is studied using an extension of the Kubo-Zwanzig-Fano relaxation formalism. The problem of a dilute gas interacting with a strong perturbing field and a weak probe field is solved, assuming a separation of collisional and radiative processes, by introducing a classical-field renormalization technique. The solution is formulated entirely in terms of linear-response functions. This method is applied to the problem of the three-level absorber perturbed by a strong field and probed by a weak field. Multiphoton transitions, double resonance, and dynamic Stark effects can be treated as manifestations of this three-level problem.
The Kubo-Zwanzig-Fano relaxation method is extended to the problem of a homogeneous dilute system interacting with arbitrarily strong fields composed of several monochromatic modes, neglecting breakdown and spatial correlations. The Von Neumann equation for the density matrix is solved for classical fields, using a procedure in which the harmonics numbers are treated as the classical analog (in Liouville space) of the quantum fields occupation-number representation. This solution is adapted to the case where memory effects during the absorption or emission of a photon can be neglected. Two examples illustrate the method, which is generally applicable in such problems as saturation, double resonance, and frequency mixing involving the nonlinear response of independent molecules.
We investigate theoretically the spectrum of weak probe field absorption by three-level atoms with the Λ configuration of levels in the field of a strong electromagnetic wave acting on an adjacent transition and colliding with buffer gas atoms. Analysis is carried out for the general case of arbitrary collisional relaxation of low-frequency coherence at a transition between two lower levels. It is shown that, in the absence of collisional relaxation of low-frequency coherence, the probe field spectrum always exhibits clearly manifested anisotropy with respect to mutual orientation of wavevectors of the strong and probe radiation (even under small Doppler broadening). It is found that the probe field spectrum may acquire under certain conditions supernarrow resonances with a width proportional to the diffusion coefficient for atoms interacting with radiation. This fact may form the basis for a spectroscopic method for measuring transport frequencies of collisions between absorbing and buffer particles. A large-amplitude supernarrow resonance (with an amplitude much larger than the amplitude of the resonance near the line center), which is observed in the far wing of the absorption line, exhibits collisional narrowing (a nonlinear spectroscopic analog of the Dicke effect) at collision frequencies several orders of magnitude lower that the Doppler linewidth. Simple working equations proposed for describing the probe field spectrum are convenient for experimental data processing.
A previously developed diagrammatic method for calculating the nonlinear response of a dilute gas at near resonance with strong classical radiation fields is extended to include velocity-dependent homogeneous and inhomogeneous broadening phenomena. The method is applied to two-level saturated-absorption (Lamb-dip) spectroscopy. Expressions are obtained for the collision-broadened Lamb dip probed by a weak field in the presence of an arbitrarily strong saturating field and are compared to the usual infinite-Doppler-width, weak-saturation expression. We study the effects of velocity and momentum transfer on the line-shape parameters and discuss the effect of phase-changing and strong inelastic collisions on the intensity.
Abstract The interaction of three and two-level atomic systems with two electromagnetic fields, a weak near resonant high-frequency and a strong off-resonant low-frequency ones, is analyzed by applying the method of multiple-scale perturbation theory. We consider two examples: (1) a three-level Λ system interacting with a weak XUV field at the high-energy transition and a strong IR field at the adjacent low-energy transition. The IR field will periodically Stark modulate the energy of the most excited state, which will result in generation of sidebands of the XUV field at the frequencies multiple of the IR field modulation frequency; (2) a two-level atom interacting with a weak near-resonant high-frequency and an off-resonant low-frequency field, which is related to the quantum amplification by superradiant emission of radiation problem.
The spectrum of weak probe field absorption (amplification) by two-level atoms experiencing collisions with buffer gas atoms in a strong resonance laser field is studied theoretically. Analysis is carried out for systems with a weak Doppler broadening under relatively mild constraints on the strong field intensity for the general case of an arbitrary change in the phase of the radiation-induced dipole moment in elastic collisions of gas particles. It is shown that, in spite of uniform broadening of the absorption line, the probe field spectrum exhibits a clearly manifested anisotropy to mutual orientation of the wavevectors of strong and probe radiation. It is found that the width of resonances in the probe field spectrum under definite conditions (that can easily be created in experiments) is proportional to the diffusion coefficient for atoms interacting with radiation. This fact can form the basis of the spectroscopic method for measuring the transport frequencies of collisions between particles absorbing radiation and buffer particles. It is shown that phase memory effects in collisions strongly modify the probe field spectrum both qualitatively and quantitatively. Simple operative formulas proposed for the probe field spectrum are convenient for experimental data processing.
We develop an expansion for the resonance Raman line shape of a three-level system ∣a〉|a〉∣a〉, ∣b〉|b〉∣b〉, and ∣c〉|c〉∣c〉 in an arbitrary strong radiation field, being perturbed by dephasing collisions with foreign gas particles. The microscopic information relevant to the line broadening is expresssed in terms of a hierarchy of nnn-time correlation functions of the transition dipole operator (n=2,4,6,…n=2,4,6,\dots{}n=2,4,6,…). To lowest order (n=2n=2n=2) the spectrum is expressed in terms of the three ordinary line-shape functions corresponding to the ab\mathrm{ab}ab, bc\mathrm{bc}bc, and ac\mathrm{ac}ac transitions. The present theory is not restricted to the impact limit and, depending on the collision time scale, may yield very different results from the well-known impact spectra. Explicit calculations of the predicted spectra are presented for a model system.