Physical Review A

Quantitative investigation of the resonant nonlinear Faraday effect under conditions of optical hyperfine pumping

S. I. Kanorsky, Antoine Weis, James Wurster, Theodor W. Hänsch

Published Feb 1, 1993• 92 citations

Abstract

We extend our previous discussion of the resonant nonlinear Faraday effect in terms of the precession of an induced quadrupole moment to the realistic experimental situations where depopulation, repopulation, and hyperfine optical pumping contribute. We derive, to lowest order in the light intensity, an analytical expression for the magnetorotation angle near an electric-dipole resonance in an atomic medium of arbitrary spins. We find excellent quantitative agreement with absolute measurements performed on the Cs ${\mathit{D}}_{2}$ line.

DOI: 10.1103/physreva.47.1220

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Physical Review A

Quantitative investigation of the resonant nonlinear Faraday effect under conditions of optical hyperfine pumping

S. I. Kanorsky, Antoine Weis, James Wurster, Theodor W. Hänsch

Published Feb 1, 1993• 92 citations

Publisher

Abstract

{\mathit{D}}_{2}

line.

DOI: 10.1103/physreva.47.1220

Related papers

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{\mathit{D}}_{2}

line.

We have performed quantitative measurements of the variation of the on-resonance absorption coefficients ${\ensuremath{\kappa}}_{0}$ of the four hyperfine components of the Cs

{D}_{1}

transition as a function of laser power

P

, for pumping with linearly and with circularly polarized light. Sublevel populations derived from rate equations assuming isotropic population relaxation (at a rate ${\ensuremath{\gamma}}_{1}$) yield algebraic ${\ensuremath{\kappa}}_{0}(P)$ dependences that do not reproduce the experimental findings from Cs vapor in a paraffin-coated cell. However, numerical results that consider spin-exchange relaxation (at a rate ${\ensuremath{\gamma}}_{\mathrm{se}}$) and isotropic relaxation fit the experimental data perfectly well. The fit parameters, viz., the absolute value of ${\ensuremath{\kappa}}_{0}$, the optical pumping saturation power

{P}_{\mathrm{sat}}

, and the ratio ${\ensuremath{\gamma}}_{\mathrm{se}}/{\ensuremath{\gamma}}_{1}$, are well described by the experimental conditions and yield absolute values for ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{\mathrm{se}}$. The latter is consistent with the previously published Cs-Cs spin-exchange relaxation cross section.

By photoionizing hyperfine (HF) levels of the Cs state

6{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}

in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around $180\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s})$ spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of ``dark'' and ``bright'' resonances leading to power-dependent branching coefficients.