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Journal of Physics B Atomic and Molecular Physics

Resonance fluorescence and resonance Raman lineshapes in strong radiation fields

Yitzhak Rabin, A. Ben‐Reuven

Published May 28, 1980• 25 citations
Publisher

Abstract

Lineshapes of three-level resonance Raman scattering and two-level resonance fluorescence, homogeneously broadened by collisions, in the presence of arbitrarily strong coherent radiation, are studied by means of a tetradic (density-matrix) scattering theory. In the case of medium coupling strength V L to the radiation field (where T 2 -1 <or=V L << tau c -1 , with T 2 and tau c being the coherence damping and collision times, respectively) the Mollow lineshape (1977) for resonance fluorescence is rederived, with proper T 2 and population cross-relaxation effects included. In particular it is shown that relaxation through intermediate non-resonant levels can considerably alter the lineshape in resonance fluorescence. In the case of strong coupling (V L >or approximately= tau c -1 ) the collision rates are modified by the applied field (optical collisions). It is shown that, whereas in self attenuation spectra optical collision rates can be obtained only from line intensity or line wing measurements, in resonance scattering these rates are directly obtained from linewidth measurements.

DOI
10.1088/0022-3700/13/10/009

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Lineshapes of three-level resonance Raman scattering and two-level resonance fluorescence, homogeneously broadened by collisions, in the presence of arbitrarily strong coherent radiation, are studied by means of a tetradic (density-matrix) scattering theory. In the case of medium coupling strength V L to the radiation field (where T 2 -1 <or=V L << tau c -1 , with T 2 and tau c being the coherence damping and collision times, respectively) the Mollow lineshape (1977) for resonance fluorescence is rederived, with proper T 2 and population cross-relaxation effects included. In particular it is shown that relaxation through intermediate non-resonant levels can considerably alter the lineshape in resonance fluorescence. In the case of strong coupling (V L >or approximately= tau c -1 ) the collision rates are modified by the applied field (optical collisions). It is shown that, whereas in self attenuation spectra optical collision rates can be obtained only from line intensity or line wing measurements, in resonance scattering these rates are directly obtained from linewidth measurements.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.
The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.
The influence of phase memory effects on the spectrum of resonance Raman scattering by three-level atoms with the Λ configuration of levels experiencing collisions with buffer gas atoms in a strong monochromatic radiation field is studied theoretically. Systems with a small Doppler broadening compared to the collision frequency (large buffer gas pressures) are analysed in the general case of an arbitrary change (from complete change to complete preservation) in the phase memory at any of three transitions in the Λ system. It is shown that in the absence of the collision relaxation of the low-frequency coherence at the transitions between two lower levels of the Λ system, the radiation scattering spectrum has a spectrally narrow component at the Raman frequency, which, despite the homogeneous broadening of the absorption line, exhibits a strongly pronounced anisotropy. In the direction, close to the propagation direction of exciting radiation, this line maximally narrows down. It is significant that upon optical pumping to the level unaffected by a strong field the resonance Raman spectrum noticeably differs from the spectrum in the case of the probe field. A simple expression is proposed for calculating the degree of the phase memory preservation in collisions from the relative amplitude of the Raman resonance.
The resonant response of a multilevel atomic system to strong coherent radiation is analyzed using an extension of the methods of time-independent scattering theory, adapted to the density-matrix formalism in order to include thermal bath effects. General steady-state expressions are derived for self-attenuation and resonance scattering rates in strong saturating fields, as functions of the coupling strengths, relaxation parameters, and frequency detunings. Formal expressions are given for radiative-damping and collision-broadening relaxation parameters, relating the latter to scattering amplitudes. Modifications of collision-broadening parameters by the presence of very strong fields are discussed. The Bloch equations are derived by transformation to the time domain, under specified conditions.
The effect of binary collisions on the fluorescence spectrum of an atom in a nearly resonant monochromatic radiation fievd is evaluated in terms of formal relaxation and correlation operators that refer to a single collision. The driving field can be included in the atomic Hamiltonian, and its time dependence is transformed away, giving rise to a modified atom. The authors relate the strengths and the widths of line occurring in the fluorescence spectrum to the rate of optical collisions, and to other elements of the scattering matrix of the modified atom.
The resonant Raman scattering in a three level system produces an optical pumping of molecules from the initial to the final states which are radiatively coupled to the intermediate resonant state. We consider the pumping that is produced by an intense, pulsed, monochromatic radiation field that is near-resonant with the initial resonance frequency. The Heitler–Ma damping theory is solved exactly for the case when the resonance fluorescence is weak compared to the Raman scattering, or any other processes which might cause irreversible decay of the resonant state. In particular, we examine the usefulness of dressed states to describe the intense field limit. The spectral line shape for the Raman scattering is obtained. The transient behavior following the onset of the laser pulse is examined and a careful analysis of the pumping rate and its relationship to both weak and strong field theories is presented.