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Physical Review A

Light Propagation in Optically Pumped Alkali Vapors

B.S. Mathur, Haoqin Tang, W. Happer

Published Sep 1, 1970• 47 citations
Publisher

Abstract

The propagation of light in an optically pumped vapor is determined semiclassically by the expectation value of a dielectric susceptibility operator. We present explicit formulas for the dielectric susceptibility of a vapor of alkali atoms. The qualitative features of the susceptibility are illustrated for the specific case of ${\mathrm{Rb}}^{87}$. The theory of this paper is essential for a clear understanding of phenomena such as the birefringence of alkali vapors and the microwave modulation of light by alkali vapors. Some experimental observations of birefringence in rubidium vapor are interpreted with the semiclassical theory.

DOI
10.1103/physreva.2.648

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Journal of the Optical Society of America B•Apr 24, 2025•1 citation
The propagation of light in an optically pumped vapor is determined semiclassically by the expectation value of a dielectric susceptibility operator. We present explicit formulas for the dielectric susceptibility of a vapor of alkali atoms. The qualitative features of the susceptibility are illustrated for the specific case of Rb87{\mathrm{Rb}}^{87}Rb87. The theory of this paper is essential for a clear understanding of phenomena such as the birefringence of alkali vapors and the microwave modulation of light by alkali vapors. Some experimental observations of birefringence in rubidium vapor are interpreted with the semiclassical theory.
Real and virtual absorption of weak monochromatic light is analyzed with semiclassical radiation theory. The influence of the light on the atoms is described by an effective ground-state Hamiltonian operator, and the effect of the atoms on the light is described by a dielectric susceptibility operator. These operators are expressed explicitly in terms of familiar ground-state observables, angular factors, oscillator strengths, and plasma dispersion functions. The theory gives a comprehensive description of optical pumping, light shifts, and light modulation due to real and virtual absorption of light, and several new effects are predicted. Repopulation of the atomic ground state from a polarized excited state is not considered in this paper.
This paper reports an investigation of parametric frequency conversion in a vapor of Rb87{\mathrm{Rb}}^{87}Rb87 atoms in which nearly resonant optical waves are coupled with microwaves at the ground-state hyperfine-structure (hfs) frequency of Rb87{\mathrm{Rb}}^{87}Rb87 by the nonlinear susceptibilities of Rb87{\mathrm{Rb}}^{87}Rb87 vapor. These nonlinear susceptibilities are greatly enhanced by optical pumping of the ground-state hfs levels of Rb87{\mathrm{Rb}}^{87}Rb87 and by using nearly resonant light. The frequency-conversion process generates optical sideband waves which are separated in frequency from the carrier light waves by the ground-state hfs frequency of Rb87{\mathrm{Rb}}^{87}Rb87 (6.835 GHz). These sidebands have been directly observed in the spectral profiles of Rb85{\mathrm{Rb}}^{85}Rb85 resonance light which had passed through Rb87{\mathrm{Rb}}^{87}Rb87 vapor. The conversion efficiency of power from the carrier waves to the sideband waves in a 45-cm length of vapor was greater than 1%. The observed behavior of the sidebands is in excellent qualitative agreement with the predictions of a semiclassical theory.
Narrowing of magnetic-resonance lines in a dense optically pumped alkali-metal vapor (87{(}^{87}(87Rb) has been observed. This observation is shown to be a result of optical pumping with a monochromatic light source tuned such that the real part of the vapor polarizability, which is responsible for light shifts, is essentially zero. A model based on the Bloch equations is used to describe the observed narrowing effect, and results of numerical calculations based on this model are presented. The results agree qualitatively with observations, and show correctly the disappearance of the effect at low light levels. This narrowing effect is of importance to the development of precision frequency standards and magnetometers utilizing monochromatic light sources (such as semiconductor lasers).
A generalized model for the magnetic resonance signal corresponding to the 0-0 hyperfine transition in an optically pumped alkali-metal vapor is presented. Under conditions of microwave power broadening, the model predicts ``anomalous'' light broadening and ``anomalous'' relaxation narrowing of the magnetic resonance linewidth. Good agreement between theory and experiment was obtained in an experiment that confirmed the prediction of anomalous light broadening. These results show that the 0-0 hyperfine transition cannot be described as a simple two-level system; rather, the alkali-atom's nuclear spin plays an important role in determining the magnetic resonance linewidth.
We have developed a simple heuristic method for determining the polarization of an optically pumped alkali-metal vapor. A linearly polarized probe beam traverses a vapor cell perpendicular to the pump-beam propagation direction, and the transmitted beam intensity is monitored for orthogonal linear polarizations. As the probe beam is scanned in frequency across the D1{D}_{1}D1​ transition, its linear-polarization-dependent transmission can be used as a measure of the atomic orientation of the vapor. We analyze these transmission differences and their dependence on the alkali-metal number density in the vapor.
Rubidium vapor cells play a key role in contemporary quantum optics since they have strong nonlinear interactions with a low-power incident laser light. The simplest nonlinear interaction is the Kerr effect. Although most calculations concentrate on the unsaturated Kerr effect, the saturated Kerr effect has been measured in many materials including 85Rb and 87Rb vapor. Moreover, entanglement-generating vapor cells often operate in the saturated regime. Here, the calculation of the saturated Kerr effect for rubidium vapor at the D2 line uses a density matrix formulation that includes two hyperfine-split levels and all magnetic sublevels in each of the ground and excited states to account for incomplete optical pumping: the transit time of the atoms through the beam is too short to reach a final population distribution. The calculation shows a rapid qualitative change at low optical power, in semiquantitative agreement with experimental data.