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Spectrochimica Acta Part B Atomic Spectroscopy

Some considerations on the saturation parameter for 2- and 3-level systems in laser excited fluorescence

Nicolo’ Omenetto, Cornelius A. van Dijk, James D. Winefordner

Published Jan 1, 1982• 21 citations
Publisher
DOI
10.1016/0584-8547(82)80082-7

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In this paper we analyse the effect of coherent saturation in the laser-induced fluorescence (LIF) of molecules. We develop an earlier model introduced by Billy et al. in 1987 of this coherent effect and propose a simple formula predicting the line shape and the line intensity for a laser-molecule interaction time considerably longer than the excited-state radiative lifetime. The predictions of this formula are tested on a LIF experiment in which a Na2 molecular beam is excited with a continuous-wave single-frequency dye laser. Considerable spectral broadening, up to two hundred times the natural linewidth is observed, in good agreement with the model.
A model is presented, based on rate equations for a two-level system, which describes both the temporal and time-integrated dependence of the fluorescence signal due to saturation by a broad band and spatially homogeneous laser beam in an optically thin medium. In particular, we discuss the processing of the fluorescence signal by a gated integrator and relations between gate width, laser pulse length, and decay rate constant of the two-level system. It is shown that, even in the relatively simple case of a fully saturating, rectangular laser pulse, the integrated signal is still dependent on atomic and collisional parameters. On the other hand, this dependency can be used to measure these parameters. The only case in which the integrated signal becomes independent of these parameters is the case of a perfectly rectangular portion being sliced out of the time dependent fluorescence signal. An experimental method, which is expected to result in a better approximation of the saturation parameter in the case of the integrated signals, is suggested.
In this paper, we present a method to measure transient fluorescent dynamics with single trapped ions in a Paul trap. We use 40 Ca + ions that exhibit a Λ-type three-level system and measure the characteristic optical pumping times between the ground S 1/2 and the meta-stable D 3/2 levels. We prepare one of these states and then pump it to the opposite via the excited P 1/2 state. By measuring the scattered photons of the ion, we retrieve transient curves of the atomic fluorescence. These curves provide fundamental information about the atomic system, such as branching fractions and excited-state lifetimes, as well as experimental parameters like the efficiency of the detection system and the saturation parameter of one of the transitions. Finally, we study the time-dependent fluorescence as a function of optical power and detuning of the lasers and find a very good agreement with simulating the dynamics via a three-level open quantum system through a set of optical Bloch equations. Being able to record time-dependent fluorescence is of particular interest as it contains information about the temperature, cooling, and heating dynamics of the ion.