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Journal of Physics B Atomic and Molecular Physics

Detuning effects in the phaseshift measurement of lifetimes using monochromatic light

W A McClean, S. Swain

Published Aug 21, 1976• 17 citations
Publisher

Abstract

The model of Armstrong and Feneuille (1975) for phaseshift measurements of atomic lifetimes using monochromatic excitation is solved for the case where the laser frequency is not necessarily on resonance with the atomic transition. It is found that even quite small detunings (of the order of those which may be difficult to avoid in practice) produce significant changes in the phaseshifts and strength of the modulated component.

DOI
10.1088/0022-3700/9/12/013

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Physical Review Letters•Jul 28, 1997•32 citations
The model of Armstrong and Feneuille (1975) for phaseshift measurements of atomic lifetimes using monochromatic excitation is solved for the case where the laser frequency is not necessarily on resonance with the atomic transition. It is found that even quite small detunings (of the order of those which may be difficult to avoid in practice) produce significant changes in the phaseshifts and strength of the modulated component.
It is shown that, if one uses an essentially monochromatic but weakly modulated light source to excite atoms or molecules in a resonant way, the phase shift of the scattered light is strongly dependent on the strength of the excitation. However, for low values of the excitation strength, this dependence disappears but a result which differs by a factor of two from the result obtained for broad-band light excitation is found. In addition, the strength of the modulated component of the scattered light displays a resonant behaviour in the modulation frequency, this response being directly related to the well-known Autler-Townes effect.
In a recent publication1 the question of the possibility of observing directly the quantum jumps associated with the excitation and deexcitation of an atomic electron in a three-level transition was considered. While the analysis of Ref. 1 reveals the manner in which the fluorescence from a strong transition of a lifetime T1 is modulated by the absorption and emission processes of a weak transition of lifetime T2 (T1 ≪ T2), it was restricted to the case of incoherent excitation of the two transitions. The purpose of the present work is to reconsider this problem for monochromatic excitation in which a variety of coherent effects come into play. The analysis proceeds in a straightforward fashion in the Heisenberg representation to yield expressions for field and atomic correlation functions representing probabilities for the detection of successive photons from the same transition as well as for cross correlations of emission probabilities. In the limit of T1 ≪ T2, a coarse graining of time with respect to the strong transition produces expressions analogous to those presented in Ref. 1. The roles of Autler-Townes splitting, frequency detuning, and saturation of the weak transition are discussed.
The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.
Abstract The effect of detuning from the centre of the Doppler-broadened profile of a transition is studied by use of the rate of change of a modified density matrix. The variation of population density of the two energy levels involved in the transition is obtained under transient conditions. Two values of the ratio of the damping parameters 2γ and γ' for the on-diagonal and off-diagonal matrix elements are considered; γ' = γ corresponds to very low gas pressures and y' = 10y to conditions for which phase-destroying collisions predominate. While these considerations apply both in the visible and infra-red spectral regions, and equally to atoms and molecules, they are at present of special interest in connection with excitation of transitions of importance in laser photochemistry.
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.