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Journal of Physics B Atomic and Molecular Physics

Resonant Stark effect for a sequence of fluorescent decays

E Smithers, Helen S. Freedhoff

Published Dec 21, 1975• 32 citations
Publisher

Abstract

A fully quantum-mechanical treatment is presented of the interaction of a two-level atom with an intense applied field. The resonant Stark effect spectrum is calculated for a single decay process in the case of an arbitrarily detuned applied field, and for a sequence of many fluorescent decays in the case of a resonant applied field. The results of these calculations agree with recent experimental observations, and with previous theoretical calculations using different methods. In addition, a misinterpretation contained in a previous letter by the present authors (see ibid., vol.7, L.432 (1974)) is pointed out.

DOI
10.1088/0022-3700/8/18/008

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Journal of Physics B Atomic and Molecular Physics•Sep 14, 1984•1 citation
A fully quantum-mechanical treatment is presented of the interaction of a two-level atom with an intense applied field. The resonant Stark effect spectrum is calculated for a single decay process in the case of an arbitrarily detuned applied field, and for a sequence of many fluorescent decays in the case of a resonant applied field. The results of these calculations agree with recent experimental observations, and with previous theoretical calculations using different methods. In addition, a misinterpretation contained in a previous letter by the present authors (see ibid., vol.7, L.432 (1974)) is pointed out.
For pt.I see ibid., vol.14, p.4171 (1981). Semiclassical and quantal time-dependent results are presented for a model of N identical two-level atoms occupying the same site (the Dicke model) and driven by a CW off-resonance laser field. The exact semiclassical time-dependent solutions are derived from an analysis of the Fokker-Planck equation for the system in the atomic coherent states representation. Steady-state behaviour predicted by these solutions is in agreement with that obtained from the exact quantal steady-state analysis in the thermodynamic limit N to infinity . The semiclassical theory predicts (in the steady state) one type of fluorescent spectrum, which is a single sharp line ( delta function) centered at the driving field frequency. This is like the case at exact resonance and below threshold. Quantum mechanically, analytical results are obtained in the strong-field limit and within the secular approximation of the master equation: the fluorescence spectrum is the usual dynamical Stark triplet, apart from a cooperative factor N 2 . The absorption spectrum and the second-order intensity autocorrelation function are also calculated. Numerical results are also presented for finite N(N<or approximately=5). The effect of detuning on the additional sidebands (occurring at higher harmonics) in both the fluorescent and adsorption spectrum are examined.
For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.
We present calculations of the spontaneous-emission spectrum from a two-photon two-level system in the presence of an arbitrarily intense monochromatic field at half of the two-photon transition frequency. The single-photon counterpart to this is called resonance fluorescence. Because of the complexity of the two-photon two-level model, many effects arise that are absent in the one-photon problem. In particular, we show how the Rayleigh scattering from this system is markedly different and discuss the role of Stark shifts on the emission spectrum.