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Physical Review A

Nonlinear radiation imprisonment in magneto-optical vapor traps

Nikolai N. Bezuglov, A. F. Molisch, F. Fuso, M. Allegrini, Aigars Ekers

Published Jun 13, 2008• 1 citation
Publisher

Abstract

We analyze nonlinear radiation imprisonment (RI) effects in an optically thick vapor in different temperature regimes. An analytical approach is proposed to treat nonlinear decay problems. Special attention is paid to vapor samples having curvilinear geometries (cylinder, sphere) and being excited by a strong laser pulse. We derive a number of new formulas for different radiative trapping factors as functions of opacity and propose a general approach for RI evaluation allowing us to deal with samples both at room and low, or very low, temperatures, such as those customarily achieved in magneto-optical trap (MOT) experiments. As a result, we predict a ``subnatural'' decay of radiation escaping from cold vapors, which can be envisioned as the basis for a sensitive and reliable MOT diagnostic tool.

DOI
10.1103/physreva.77.063414

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We investigate radiation trapping in an atomic vapor which has been excited by a strong short laser pulse. Since the saturation of the vapor by the pulse leads to a decrease in the effective absorption coefficient, the radiation trapping becomes nonlinear. We derive approximate analytical expressions for the excited-state density in the directly excited region, the fluorescence-excited region, and the density averaged over the whole cell. Starting out from fairly simple approximate expressions based on a prescribed distribution of excited atoms, we then develop physically motivated correction factors that drastically improve the accuracy. All these expressions are given for three important cell geometries: the plane-parallel slab, the infinite cylinder, and the sphere. We compare our results to accurate numerical solutions, and find agreement within 5--10%. We then derive the decay time of the emergent radiation, and find that it can be smaller than the natural lifetime of the excited atoms, in agreement with recent experimental results obtained for sodium vapors.
We investigate radiation-imprisonment (RI) phenomena in a system of cold atoms trapped in magneto-optical traps (MOTs) when cooling lasers are switched off for a short period. The problem is formulated within the framework of the Streater-Cooper-Sandle equation that belongs to the Markov class and accounts for photon frequency redistribution in multiple scattering processes. On the basis of a semiclassical approach, we derive explicit analytical solutions for the spectral problem of the RI equation neglecting Doppler effects. The analysis reveals peculiarities in emission profiles under initial partial saturation of the resonance transition by the probe laser pulse. Comparison between theoretical and experimental data on effective radiative lifetimes obtained in Cs and Rb MOTs confirms the validity of the discussed nonstationary model of RI in cold samples. For small detunings, the Streater-Cooper-Sandle equation agrees with the experimental data, while in the case of large detunings, the theory does not agree, probably due to non-Markovian effects.
We have successfully trapped sp7\\sp7sp7Li in a vapor cell magneto-optical trap (MOT). The trap is studied in detail and the parameters are measured from the experiment. The trapping mechanism has been understood in terms of the radiation force and a simple one dimensional model is used in interpreting and predicting the experimental results. The cold-cold atom collision rate coefficient is measured in a beam MOT. The two collision mechanisms, fine structure changing and radiative escape, are discussed in a molecular picture. One of the channels, the fine structure changing channel, can be turned on and off by the experimental conditions, namely the laser intensity in this experiment. The rate coefficient for each mechanism has been determined from the experiment.
We solve the Holstein equation describing radiation trapping in an atomic vapor by the geometric quantization technique. The treatment is based on studying the integral trapping equation as a wave equation for an associated quasiparticle with a complicated form of its dispersion law. The latter is determined by the spectral properties of the vapor medium. Extending our previous work, which dealt with one-dimensional (1D) geometries, we consider here more realistic two- and three-dimensional (2D and 3D) vapor cell geometries. For this, an explicit representation of the phase factors is derived when the quasiparticle is reflected under arbitrary angles from the surface of the cell confining the vapor. We give closed-form equations to obtain analytically the complete 3D spectrum of escape factors in finite cylinder, sphere, parallelepiped, and finite prismlike geometries for all practically occurring line shapes and opacities. In addition, the relevant semiclassical variational method is applied to develop a perturbation theory for the evaluation of escape factors in more complicated geometries that are sometimes adopted in experiments, including infinite (or finite) elliptical cylinders, prolate and oblate ellipsoids. Comparisons with numerical calculations show that results are accurate within 55%5 for the ground modes and even better for higher-order modes.
Imprisonment of resonant radiation in gases on the basis of the numerical solution of the rate balance equation for the excited atoms and the transfer resonant radiation equation is investigated. Calculations of the escape factor for the slab, cylinder and sphere at Doppler and Lorentz forms of absorption and scattering profiles are executed. Calculation results of the escape factor for the cylinder and slab are compared with Holsten's asymptotical solutions. The numerical data for time dependence of a spectrum, the intensity of resonant radiation and the spatial distribution of the excited atomic concentration in a regime of afterglow are also considered.
We solve the Holstein equation of radiation trapping in an atomic vapor cell by the geometric quantization technique (GQT). In the GQT, the rate equation for the excited-state density is transformed into an ``equivalent'' Schr\"odinger equation for an associated quasiparticle. The problem of finding the complete set of radiation escape factors is thus reduced to searching quantized energy values for the quasiparticle locked into the vapor cell. We combine already known solutions for the trapping factors at high opacities with new results for the phase jump at the vapor cell boundary to arrive, within the framework of the GQT technique, at solutions that are valid at all opacities. The phase factors are independent of geometry, and we derive an explicit representation for them by the Wiener-Hopf technique in the most simple geometry, a half-space. Our approach enables an analytical computation of the trapping factors in all practically occurring line shapes (including Voigt lines and hyperfine-split lines), all opacities, and all modes in one-dimensional (1D), 2D, and 3D geometries allowing for variable separation. We present results obtained in 1D geometries at all opacities that show discrepancies within 5% for the lowest-order trapping factor and even less (at the level of approximately 0.1%) for higher-order modes, in agreement with the predictions of the GQT theory that has been developed.