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Journal of Physics B Atomic and Molecular Physics

Effective two-state behaviour of a collisionally perturbed Zeeman degenerate atomic transition and its application to optical bistability

R. J. Ballagh, J. Cooper, Weston J. Sandle

Published Oct 28, 1981• 10 citations
Publisher

Abstract

In real atoms, levels connected by a dipole transition contain a number of degenerate Zeeman states. Thus in practice, the phenomena of optical pumping and collisional transfer amongst states severely restrict the application of a simple two-state model. There are a number of cases, however, where the macroscopic dipole induced in an atomic gas has the same general form as predicted by the two-state model, and these are presented here. The effects of optical pumping and collisional transfer, and the implications for the description of optical bistability, are discussed. In particular, ground-state optical pumping can, under certain conditions of low perturber density, considerably reduce the power necessary to achieve bistability.

DOI
10.1088/0022-3700/14/20/012

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In real atoms, levels connected by a dipole transition contain a number of degenerate Zeeman states. Thus in practice, the phenomena of optical pumping and collisional transfer amongst states severely restrict the application of a simple two-state model. There are a number of cases, however, where the macroscopic dipole induced in an atomic gas has the same general form as predicted by the two-state model, and these are presented here. The effects of optical pumping and collisional transfer, and the implications for the description of optical bistability, are discussed. In particular, ground-state optical pumping can, under certain conditions of low perturber density, considerably reduce the power necessary to achieve bistability.
We have observed a sudden reversal in the direction of population transfer between nearly degenerate Zeeman sublevels during optical pumping of the cesium 6S1/2{\mathit{S}}_{1/2}S1/2​(F=4)\ensuremath{\rightarrow}6P3/2{\mathit{P}}_{3/2}P3/2​(F'=5) cycling transition. As a result of the reversal, the number of atoms in an atomic beam, with quantum numbers 6S1/2{\mathit{S}}_{1/2}S1/2​ (F=4; mF{\mathrm{m}}_{\mathit{F}}mF​=-4), is a function of laser frequency and has a sharp dispersive shape. A rate-equation model indicates that similar dispersive shapes for the population can be expected in the optical pumping of any nondegenerate system with more than two levels, if the level spacing is much smaller than the laser linewidth.
We have investigated atomic coherence changes caused by optical pumping applied to electromagnetically induced absorption (EIA) occurring at the open system, which consists of the transition between the F g = 2 ground state and the F e = 3 excited state in the 85 Rb D1-line. For optical pumping, another laser resonantly tuned to the transition between the F g = 3 ground state and the F e = 2 excited state was used. We found that the atomic coherence for EIA can be changed not by increasing the pumping rate but by pumping differently populations into the Zeeman sublevels in the F g = 2 ground state, which is realized by changing the polarization of the pumping laser. The experimental results were able to be analysed by density matrix equations in the simple model system.
The theory of several experiments involving optical pumping is presented in a simplified form. Vector methods are employed to discuss the hyperfine energy levels of an atom in a weak magnetic field, and, for the purposes of considering relaxation time, the system is assumed to have only two effective levels. The Breit-Rabi equation for the ground-state hyperfine Zeeman energy levels of an alkali atom is derived from the Schrödinger equation to facilitate the interpretation of the quadratic Zeeman effect. A number of suggestions for practical optical pumping experiments are made.
We discuss the optical bistable behavior of a system of N two-level atoms pumped by a coherent input field and coupled to a squeezed vacuum field by treating the optical bistability of such a system as an input-output problem. We consider the equation of motion for atomic dipole moments, coupled to the cavity field and the squeezed vacuum, and the boundary condition connecting the input and output fields with the atomic lowering operator. A simple analytical expression for the influence of the squeezed vacuum input on the bistable behavior of the output field is derived by this method. The results indicate a strong influence of the squeezed vacuum input on optical bistability. The squeezed (stretched) vacuum input field tends to increase (decrease) the range of optical bistability.
Optical pumping performed with a quasi monochromatic laser beam in an atomic gas introduces a redistribution of Zeeman populations selectively in a single velocity class. In the limit of low pumping intensity the rate theory is valid for a description of velocity-selective optical pumping (V.S.O.P.). Well-defined atomic observables (population, orientation, alignment) and their velocity-correlated collisional relaxation can be studied. Also, a modified scheme for the detection of second order effects of optical pumping allows one to observe light shift induced signals. In particular, V.S.O.P. and its combination with modulated pumping, magnetic depolarization (level crossing), and magnetic resonance techniques provide information about the atomic collision characteristics such as collision rates and kernels for velocity-changing collisions.