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arXiv:physics/0203077 · Reviews of Modern Physics

Resonant nonlinear magneto-optical effects in atoms

Dmitry Budker, Wojciech Gawlik, Derek F. Jackson Kimball, Simon Rochester, Valeriy V. Yashchuk, Antoine Weis

Published Nov 20, 2002• 807 citations
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Abstract

The authors review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. They begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances. These effects are then contrasted with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultranarrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.

DOI
10.1103/revmodphys.74.1153

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The authors review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. They begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances. These effects are then contrasted with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultranarrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.
Several dispersionlike features in the magnetic field dependence of the nonlinear magneto-optic effect were observed in an experiment performed on rubidium atoms contained in a vapor cell with antirelaxation coating. The narrowest feature has effective resonance width $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g\ensuremath{\mu}\ensuremath{\Delta}{B}_{z}\ensuremath{\approx}2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}1.3\mathrm{Hz}$, where $\ensuremath{\Delta}{B}_{z}\ensuremath{\approx}2.8\ensuremath{\mu}\mathrm{G}$ is the peak-to-peak separation. The observed nontrivial dependence of the magneto-optic effect on transverse magnetic fields is discussed. The results of this work may be applied to low-field magnetometry, to parity and time reversal invariance violation experiments, etc.
Nonlinear in laser power, near-resonant light-atom interaction leads to a number of spectacular modifications of a well-known effect -polarization plane rotation in a magnetic field applied along the direction of light propagation.In particular, the rotation can be enhanced by up to nine orders of magnitude compared to the linear case.Faraday effect [ 1 ] is the rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation.In 1898, Macaluso and Corbino eJ, studying absorption spectra of the alkali atoms in the presence of magnetic fields, discovered that the Faraday effect in the vicinity of resonance absorption lines also had a distinct resonant character.The essence of the Macaluso-Corbino effect can be illustrated by considering a simple case of a F= 1 ~ F'=O transition (Fig. 1 ).Linearly polarized light incident on the sample can be resolved into two counter-rotating circular components ( cr~.In the absence of a magnetic field, the M=±l sublevels are degenerate and the optical resonance
Magneto-optical (Faraday) rotation is a process in which the plane of light polarization rotates as light propagates through a medium along the direction of a magnetic field. In atomic vapors where ground state atomic polarization relaxes very slowly (relaxation rates ≳1 Hz), there arise ultranarrow, light-power-dependent (nonlinear) features in the magnetic field dependence of Faraday rotation. The shot-noise-limited sensitivity of a magnetometer based on nonlinear Faraday rotation can exceed 10−11 G/Hz, corresponding to a sensitivity of ∼10−6 Hz/Hz to Zeeman sublevel shifts. Here we discuss recent progress in magnetometry based on nonlinear optical rotation and consider the application of these methods to searches for fundamental-symmetry-violating interactions.
Nonlinear magneto-optical processes are a rich source of interesting and useful phenomena, with both practical and fundamental-physics applications. Theoretical modeling is helpful for understanding and visualizing the mechanisms for nonlinear magneto-optical effects (NMOE), and for analyzing and optimizing devices based on these effects. Part I of this Thesis describes Bloch-equation methods and visualization techniques that can be used to model a wide variety of NMOE in atomic vapors. Part II presents several applications of the methods, including the investigation and visualization of a specific effect involving radio-frequency fields, a study of the general consequences of hyperfine structure on NMOE, and modeling and optimization of systems for laser guide stars. Appendices present additional mathematical material and describe a Mathematica package used for density-matrix calculations.
Nonlinear magneto-optical effects, originated from atomic coherence, are studied both theoretically and experimentally in thermal Rb vapor. The analytical description of the fundamental properties of coherent media are based on the simplified three- and four-level systems, and then verified using numerical simulations and experimental measurements. In particular, we analyze the modification of the long-lived atomic coherence due to various physical effects, such as reabsorption of \nspontaneous radiation, collisions with a buffer gas atoms, etc. We also discuss the importance of the high-order nonlinearities in the description of the polarization rotation for the elliptically polarized light. The effect of self-rotation of the elliptical polarization is also analyzed. \nPractical applications of nonlinear magneto-optical effects are considered in precision metrology and magnetometery, and for the generation of non-classical states of electromagnetic field.