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Physical Review A

Theory of time-dependent intense-field collisional resonance fluorescence

Paul D. Kleiber, J. Cooper, Keith R. Burnett, C. V. Kunasz, Michael G. Raymer

Published Jan 1, 1983• 26 citations
Publisher

Abstract

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 ($J=0$ to $J=1$) to obtain quantitative predictions for the observable scattered-light spectrum which can be directly compared with recent experiments.

DOI
10.1103/physreva.27.291

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Journal of Physics B Atomic Molecular and Optical Physics•Jan 28, 1988•14 citations
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.
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.
We extend the theory of light scattering from an atom undergoing collisions to the case of strong laser fields, where the expansion in powers of $\ensuremath{\Omega}{\ensuremath{\tau}}_{c}$ that was used formerly in a series of papers by Burnett et al. breaks down. In particular we consider in detail the conditions necessary to relate the observable quantities to intense-field collisional rate constants in a dressed-state basis (such as those calculated by Light and Sz\"oke). We also show (following Rabin and Ben-Reuven) that by studying the spectrum emitted by the atoms in the presence of a strong field one may measure the collisional rates for transfer between the dressed states of atom plus radiation field.
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.
We have studied the problem of a collisionally perturbed two-level atom in an intense driving field by developing a method which allows us to calculate the field-dependent collision operator in terms of the low intensity field-independent line-broadening function arising in the usual unified theory of pressure broadening. Our relations are exact to all orders in the field in the limiting case of weak collisions, but they are exact also in the complementary case of strong collisions and weak fields. We apply our results to derive explicit expressions for the rate of optical collisions, the fluorescence spectrum in the case of well-separated components, and the absorption during an adiabatic square pulse.
The time-dependent spectrum of the light scattered by a collisionally damped two-level atom weakly excited off resonance by a partially coherent laser field is evaluated. Both the collisional and the laser noise are treated as classical Markovian, Gaussian processes while, in addition, the atom is assumed to experience damping and fluctuations that are due to its coupling to an unspecified exterior reservoir. The scattered-field spectra are determined both at steady state and at times following the abrupt turn off of the laser field (the delayed spectrum). The distinct contributions to these spectra arising from the various noise sources as well as the finite bandwidth of the detecting interferometer are investigated in each case. Where appropriate, comparisons are made with related work of Saari [ Light Scattering in Solids ( Plenum, New York, 1979)]. A general inequality is also found that must be satisfied by the longitudinal and the transverse decay rates induced by the exterior reservoir. Finally, the inverse detuning of the laser is found to provide a limit on the time in which the undressing of the atom could be observed to occur following the turn off of the laser.
The resonance fluorescence of a two-level atom interacting with a laser pulse is studied, following the short-pulse approximation. The authors demonstrate that an explicit expression of the energy spectrum in terms of atomic-state amplitudes holds also for an off-resonance excitation. Some analytically solvable cases are studied in detail, showing that the main spectral properties of the fluorescence emitted under adiabatic and non-adiabatic pulsed excitation can be easily described. For the first time the continuous dependence of the fluorescence spectrum on laser detuning is reported for a smooth pulse.