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arXiv:physics/0309061 · Physical Review A

Nonlinear magneto-optical rotation of frequency-modulated light resonant with a low-Jtransition

Yu. P. Malakyan, Simon Rochester, Dmitry Budker, Derek F. Jackson Kimball, Valeriy V. Yashchuk

Published Jan 26, 2004• 34 citations
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Abstract

A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a $J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0$ transition is presented. The theory is developed for a Doppler-free transition and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium $D1$ line.

DOI
10.1103/physreva.69.013817

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A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a J=1\ensuremath→J\ensuremath′=0J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0J=1\ensuremath→​J\ensuremath′=0 transition is presented. The theory is developed for a Doppler-free transition and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium D1D1D1 line.
Experimental signals of nonlinear magneto-optical resonances at D1{D}_{1}D1​ excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1{D}_{1}D1​ transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=2$ transition of 87Rb^{87}\text{R}\text{b}87Rb has been observed. A bright resonance was observed at the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 85Rb^{85}\text{R}\text{b}85Rb, but displaced from the exact position of the transition due to the influence of the nearby ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=2$ transition, which is a dark resonance whose contrast is almost 2 orders of magnitude larger than the contrast of the bright resonance at the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.
We present experimental and numerical studies of nonlinear magneto-optical rotation (NMOR) in rubidium vapor excited with resonant light tuned to the $5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ absorption line (421 nm). Contrary to the experiments performed to date on the strong D1{D}_{1}D1​ or D2{D}_{2}D2​ lines, in this case, the spontaneous decay of the excited state 62P1/26{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}62P1/2​ may occur via multiple intermediate states, affecting the dynamics, magnitude, and other characteristics of NMOR. Comparing the experimental results with the results of modeling based on Auzinsh et al. [Phys. Rev. A 80, 053406 (2009)], we demonstrate that despite the complexity of the structure, NMOR can be adequately described with a model, where only a single excited-state relaxation rate is used.
We present experimental and numerical studies of nonlinear magneto-optical rotation (NMOR) in rubidium vapor excited with resonant light tuned to the 52 ⁣S1/2→62 ⁣P1/25^2\!S_{1/2}\rightarrow 6^2\!P_{1/2}52S1/2​→62P1/2​ absorption line (421~nm). Contrary to the experiments performed to date on the strong D1D_1D1​ or D2D_2D2​ lines, in this case, the spontaneous decay of the excited state 62 ⁣P1/26^2\!P_{1/2}62P1/2​ may occur via multiple intermediate states, affecting the dynamics, magnitude and other characteristics of NMOR. Comparing the experimental results with the results of modelling based on Auzinsh et al., Phys. Rev. A 80, 1 (2009), we demonstrate that despite the complexity of the structure, NMOR can be adequately described with a model, where only a single excited-state relaxation rate is used.
Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the D2{D}_{2}D2​ line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser-induced fluorescence was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87{}^{87}87Rb and near to the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85{}^{85}85Rb. The bright resonance became dark as the laser power density was increased above 0.6 mW/cm2{}^{2}2 or 0.8 mW/cm2{}^{2}2, respectively. When the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87{}^{87}87Rb was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50${}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}$C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.
Application of nonlinear magneto-optical (Faraday) rotation to magnetometry is investigated. Our experimental setup consists of a modulation polarimeter that measures rotation of the polarization plane of a laser beam resonant with transitions in Rb. Rb vapor is contained in an evacuated cell with antirelaxation coating that enables atomic ground-state polarization to survive many thousand wall collisions. This leads to ultranarrow features $(\ensuremath{\sim}{10}^{\ensuremath{-}6} \mathrm{G})$ in the magnetic-field dependence of optical rotation. The potential sensitivity of this scheme to sub-$\ensuremath{\mu}\mathrm{G}$ magnetic fields as a function of atomic density, light intensity, and light frequency is investigated near the D1D1D1 and D2D2D2 lines of 85Rb.{}^{85}\mathrm{Rb}.85Rb. It is shown that through an appropriate choice of parameters the shot-noise-limited sensitivity to small magnetic fields can reach $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$