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Physical Review A

Nonlinear electro- and magneto-optical effects related to Bennett structures

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

Published Jan 31, 2002• 26 citations
Publisher

Abstract

Optical pumping of an atomic sample with narrow-band light can create sub-Doppler features, known as Bennett structures, in the velocity distribution of state populations. In the presence of static magnetic or electric fields, the corresponding sub-Doppler features in the index of refraction can cause nonlinear optical rotation and induced ellipticity of resonant light propagating through the atomic medium. Physical mechanisms causing Bennett-structure-related nonlinear electro- and magneto-optical effects are discussed in detail for transitions involving states with low angular momenta. Measurements of Bennett-structure-related nonlinear magneto-optical rotation and electric-field-induced ellipticity for the Rb $D2$ line are performed and compared to density-matrix calculations. The latter effect can be used for measuring electric fields applied to atoms.

DOI
10.1103/physreva.65.033401

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Optical pumping of an atomic sample with narrow-band light can create sub-Doppler features, known as Bennett structures, in the velocity distribution of state populations. In the presence of static magnetic or electric fields, the corresponding sub-Doppler features in the index of refraction can cause nonlinear optical rotation and induced ellipticity of resonant light propagating through the atomic medium. Physical mechanisms causing Bennett-structure-related nonlinear electro- and magneto-optical effects are discussed in detail for transitions involving states with low angular momenta. Measurements of Bennett-structure-related nonlinear magneto-optical rotation and electric-field-induced ellipticity for the Rb D2D2D2 line are performed and compared to density-matrix calculations. The latter effect can be used for measuring electric fields applied to atoms.
The nonlinear interaction between an optical medium and an electro-magnetic field can induce gradients in the index of refraction distribution, leading to patterns or filamentation in the most diverse nonlinear materials: solids, anisotropic soft matter (liquid crystals), cells containing thermal vapors, etc. One common difficulty in interpreting the results of these experiments and in comparing them to models is that the details of the interaction in these media are very complex. Cold atomic systems have well known linear and nonlinear optical properties, as illustrated in experiments on four wave mixing, electro-magnetic induced transparency or slow light propagation. Such samples are thus an excellent candidate for improving the comparison between theory and experiments, but so far to our knowledge no investigations on patterns have been performed in such systems.
A precise, accurate, and relatively straightforward in situ method to measure and control the ellipticity of light resonantly interacting with an atomic vapor is described. The technique can be used to minimize vector light shifts. The method involves measurement of ellipticity-induced resonances in the magnetic-field dependence of nonlinear magneto-optical rotation of frequency-modulated light. The light propagation direction is orthogonal to the applied magnetic field B\mathbf{B}B and the major axis of the light polarization ellipse is along B\mathbf{B}B. When the light modulation frequency matches the Larmor frequency, elliptically polarized light produces a precessing atomic spin orientation transverse to B\mathbf{B}B via synchronous optical pumping. The precessing spin orientation causes optical rotation oscillating at the Larmor frequency by modulating the atomic vapor's circular birefringence. Based on this technique's precision, in situ nature (which avoids systematic errors arising from optical interfaces) and independent control of the most important systematic errors, it is shown that the accuracy of light ellipticity measurements achievable with this technique can exceed that of existing methods by orders of magnitude.
An experiment on nonlinear laser spectroscopy and magneto-optics at the Advanced Undergraduate Laboratory at Berkeley is described. The experiment consists of three parts. In the first part, students learn to operate a diode laser system and characterize its performance using a Fabry–Perot spectrum analyzer. In the second part, Doppler-broadened laser-induced fluorescence and Doppler-free saturated absorption spectra of the rubidium D2 line (780 nm) are recorded and analyzed. Finally, in the third part of the experiment, which we describe in greater detail, the near-resonant magneto-optical rotation is investigated. Nonlinear light-atom interaction leads to spectacular manifestations of the resonant Faraday effect—polarization plane rotation in a magnetic field applied along the direction of light propagation radically different from the linear case. In particular, narrow (∼30 Hz) effective line widths are observed in this experiment corresponding to a rotation enhancement by some seven orders of magnitude compared to the linear Faraday rotation.
We predict theoretically and demonstrate experimentally an ellipticity-dependent nonlinear magneto-optic rotation of elliptically polarized light propagating in a medium with atomic coherence. We show that this effect results from hexadecapole and higher-order moments of the atomic coherence, and is associated with an enhancement of Kerr and higher-order nonlinearities accompanied by suppression of the other linear and nonlinear susceptibility terms of the medium. These nonlinearities might be useful for quantum signal processing. In particular, we report an observation of enhancement of the polarization rotation of elliptically polarized light resonant with the ${5S}_{1/2}F=\stackrel{\ensuremath{\rightarrow}}{2}{5P}_{1/2}F=1$ transition of 87Rb.{}^{87}\mathrm{Rb}.87Rb.
Large Faraday rotations can be generated by circular birefringence of atomic samples in an axial magnetic field in the vicinity of atomic resonance lines. More generally, magneto-optical effects in atomic samples include circular dichroism in addition to birefringence, resulting in a modification of the ellipticity as well as the polarization alignment. Usually such effects are investigated for homogeneous linear polarizations, but the mechanisms apply also to polarization structures such as vector vortices. We investigate the effect of optical activity of a rubidium vapor in the hyperfine Paschen–Back regime along the D2 line, for the example of azimuthally polarized input light. We show that for low atomic densities, circular birefringence dominates over dichroism, and azimuthal polarization is rotated toward radial polarization. The rotation angle increases with increasing optical densities. At high vapor temperatures, dichroism becomes more and more relevant, leading to intricate variations of both alignment and ellipticity. Our results shine new light on the interplay between different magneto-optic effects at strong magnetic fields. Their highly sensitive response to detuning may find applications in spectroscopy and quantum sensing.
We theoretically investigate magneto-optical rotation (MOR) of a linearly polarized probe field in the four-level N-type cold atoms. By applying a static magnetic field and a weak coupling field, it is shown that the birefringence enhancement is induced in the system. Moreover, we show that the static magnetic field has a major role in switching the dichroism to enhanced birefringence in the system. We also obtain a large intensity for the output field with nearly perpendicular MOR angle by 88 degrees with subnatural width. It is demonstrated that Doppler broadening has a destructive effect on the MOR of the polarization direction of the probe field. The results of our study can be used for selecting narrow band of wavelengths and polarization converter for efficient switching of TM/TE polarization modes in optical communication, the depolarization backscattering lidar, polarization spectroscopy and precision measurements.