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Physical Review A

Zeeman degeneracy effects in collisional intense-field resonance fluorescence

J. Cooper, R. J. Ballagh, Keith R. Burnett

Published Aug 1, 1980• 27 citations
Publisher

Abstract

Resonance fluorescence due to intense laser fields from a Zeeman degenerate atom being perturbed by collisional interactions is calculated in the impact regime by using the quantum-fluctuation-regression theorem. Various interesting effects are found. For example, the scattered intensity spectrum for a $J=0$ to $J=1$ transition for polarization parallel to the laser polarization is essentially an asymmetric triplet, whereas for a perpendicular polarization due to collisions the spectrum is essentially a doublet (whose frequencies do not correspond with any of those of the triplet). Further, the width of the fluorescent component (whose frequency is close to the unperturbed frequency) actually decreases with increasing laser power.

DOI
10.1103/physreva.22.535

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Resonance fluorescence due to intense laser fields from a Zeeman degenerate atom being perturbed by collisional interactions is calculated in the impact regime by using the quantum-fluctuation-regression theorem. Various interesting effects are found. For example, the scattered intensity spectrum for a J=0J=0J=0 to J=1J=1J=1 transition for polarization parallel to the laser polarization is essentially an asymmetric triplet, whereas for a perpendicular polarization due to collisions the spectrum is essentially a doublet (whose frequencies do not correspond with any of those of the triplet). Further, the width of the fluorescent component (whose frequency is close to the unperturbed frequency) actually decreases with increasing laser power.
The time-dependent theory of Courtens and Sz\"oke is generalized using the approach of Burnett et al. to derive time-dependent spectral intensities of resonance fluorescence from atoms driven by a pulsed laser in the presence of collisions. These results are valid both for laser detunings inside and outside the usual impact region of the spectrum, including Zeeman degeneracy effects. We apply this theory to a simple but important example (J=0J=0J=0 to J=1J=1J=1) to obtain quantitative predictions for the observable scattered-light spectrum which can be directly compared with recent experiments.
Effects of the atomic Zeeman degeneracy on the resonance fluorescence spectrum of a closed two-level atom with arbitrary ground-state angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​ and excited-state, angular momentum Je{\mathit{J}}_{\mathit{e}}Je​ are studied in detail. Especially interesting are the narrow structures due to the spontaneous Raman scattering and the incoherent Rayleigh scattering. Results for the cycling transition of a Cs atom are presented as part of the examples.
The theory of the collisional and radiative relaxation of an atom perturbed by foreign-gas atoms in the presence of an intense monochromatic laser beam is developed. The spatial degeneracy of the levels and the reorientation effects of the collisions are included. The impact approximation is not made, but the Doppler effect is neglected. The spectrum of the fluorescent and scattered light is obtained from an eigenvalue problem in Liouville space using the dressed-atom approach and rotationally irreducible tensors. Minimal symmetry-adapted bases in Liouville space are constructed for linear, circular and elliptical incident polarisation. The method is illustrated for S 0 -P 1 transitions.
The effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.
The general method developed in a previous paper (see ibid., vol.10, p.345 (1977)) is applied to the problem of resonance Raman scattering in very intense laser fields. At very low intensities the spectrum consists of three monochromatic lines (Rayleigh, Raman Stokes and anti-Stokes) which split into a triplet and two doublets when the laser light, tuned on one of the two transitions connecting the upper state to the two lower sublevels, has a sufficiently high intensity to saturate this transition but not the second one. The Raman and Rayleigh lines are completely mixed when the intensity becomes so high that both transitions are saturated. The corresponding evolution of the spectrum is determined. Optical-pumping effects leading to asymmetries in the fluorescence spectrum are taken into account.