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Physical Review Letters

Nonlinear Magneto-optic Effects with Ultranarrow Widths

Dmitry Budker, Valeriy V. Yashchuk, Max S. Zolotorev

Published Dec 28, 1998• 239 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.81.5788

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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 \ensuremathγ=g\ensuremathμ\ensuremathΔBz\ensuremath≈2\ensuremathπ\ifmmode×\else\texttimes\fi1.3Hz\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}\ensuremathγ=g\ensuremathμ\ensuremathΔBz​\ensuremath≈2\ensuremathπ\ifmmode×\else\texttimes\fi1.3Hz, where \ensuremathΔBz\ensuremath≈2.8\ensuremathμG\ensuremath{\Delta}{B}_{z}\ensuremath{\approx}2.8\ensuremath{\mu}\mathrm{G}\ensuremathΔBz​\ensuremath≈2.8\ensuremathμG 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.
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 $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$
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.
This work presents new methods of optical magnetometry developed in the Center for Magneto-Optical Research at the Jagiellonian University. Using rubidium atoms contained in cm-long glass cells and amplitude-modulated laser we have recorded magneto-optical signals of extremely small widths. These signals allow measurements of magnetic fields with a sensitivity comparable to that achieved with magnetometers based on Superconducting Quantum Interference Devices (SQUIDs). Full Text: PDF References: M. Faraday,Experimental Researches in Electricity. Nineteenth Series, Trans. R. Soc. London 136, 1 (1846). [CrossRef] K. Barczak and S. Pustelny,Magnetooptic properties of special optical type D fibers, J. Phys. IV 137, 15 (2006). [CrossRef] W. Gawlik, J. Kowalski, R. Neumann, and F. Trager, Observation of the electric hexadecapole moment of free Na atoms in a forward scattering experiment, Opt. Commun. 12, 400 (1974). [CrossRef] W. Gawlik, S. Pustelny, in New Trends in Quantum Coherence and Optics, R. Drampyan Ed., 47 (New York, Nova Publishers, 2009). D. W. Gawlik, D. F. Kimball, S. M. Rochester, A. Weis, and V. V. Yashchuk,Resonant nonlinear magneto-optical effects in atoms, Rev. Mod. Phys. 74, 1153 (2002). [CrossRef] D. V.V. Yashchuk, and M. Zolotorev,Nonlinear Magneto-optic Effects with Ultranarrow Widths, Phys. Rev. Lett. 81(26), 5788 (1998). [CrossRef] D. D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev,Sensitive magnetometry based on nonlinear magneto-optical rotation, Phys. Rev. A 62, 043403 (2000). [CrossRef] G. Wąsik, W. Gawlik, J. Zachorowski, and W. Zawadzki, Laser frequency stabilization by Doppler-free magnetic dichroism, Appl. Phys. B 75, 613 (2002). [CrossRef] W. Gawlik, L. Krzemien, S. Pustelny, D. Sangla, J. Zachorowski, M. Graf, A. O. Sushkov, and D. Budker, magneto-optical rotation with amplitude modulated light, Appl. Phys. Lett. 88 131108 (2006). [CrossRef] D. D. F. Kimball, V. V. Yashchuk, M. Zolotorev,Nonlinear magneto-optical rotation with frequency-modulated light, Phys. Rev. A 65, 055403 (2002). [CrossRef] J. M. Higbie, E. Corsini, and D. Robust, high-speed, all-optical atomic magnetometer, Rev. Sci. Instr. 77, 113106 (2006). [CrossRef] S. Pustelny, A. Wojciechowski, M. Kotyrba, K. Sycz, J. Zachorowski, W. Gawlik, A. Cingoz, N. Leefer, J. M. Higbie, E. Corsini, M. P. Ledbetter, S. M. Rochester, A. O. Sushkov, and D. All-optical atomic magnetometers based on nonlinear magneto-optical rotation with amplitude modulated light, Proc. of SPIE 6604, 660404 (2007). [CrossRef] S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, W. Gawlik, Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light, J. Appl. Phys. 103, 063108 (2008). [CrossRef] S. Pustelny, S. M. Rochester, D. F. Jackson Kimball, V. V. Yashchuk, D. and W. Gawlik, Nonlinear magneto-optical rotation with modulated light in tilted magnetic fields, Phys. Rev. A 74, 063420 (2006). [CrossRef]
The dynamics of resonant light propagation in rubidium vapor in a cell with antirelaxation wall coating are investigated. We change the polarization of the input light and measure the time dependence of the polarization after the cell. The observed dynamics are shown to be analogous to those in electromagnetically induced transparency. Spectral dependence of light pulse delays is found to be similar to that of nonlinear magneto-optic rotation. Delays up to $\ensuremath{\approx}13\mathrm{ms}$ are observed, corresponding to a 8m/s8\mathrm{m}/\mathrm{s}8m/s group velocity. Fields of a few microgauss are used to control the group velocity.
We observe a narrow secondary dispersive feature nested within conventional nonlinear magneto-optical rotation (NMOR) signals obtained with a laser-cooled rubidium vapor. A similar feature has been previously named a "twist" by Budker et. al., in the context of warm vapor optical magnetometry [Phys. Rev. A. 81, 5788-5791 (1998)], and was ascribed to simultaneous optical pumping through multiple nearby hyperfine levels. In this work the twist is observed in a cold atom vapor, where the hyperfine levels are individually addressable, and thus is due to a different mechanism. We experimentally and numerically characterize this twist in terms of magnetic field strength, polarization, and optical intensity and find good agreement between our data and numerical models. We find that the twist width is proportional to the magnetic field in the transverse direction, and therefore two independent directions of the magnetic field can be measured simultaneously. This technique is useful as a simple and rapid in-situ method for nulling background magnetic fields.
Larmor precession of laser-polarized atoms contained in antirelaxation-coated cells, detected via nonlinear magneto-optical rotation (NMOR), is a promising technique for a new generation of ultrasensitive atomic magnetometers. For magnetic fields directed along the light propagation direction, resonances in NMOR appear when linearly polarized light is frequency or amplitude modulated at twice the Larmor frequency. Because the frequency of these resonances depends on the magnitude but not the direction of the field, they are useful for scalar magnetometry. Additional NMOR resonances at the Larmor frequency appear when the magnetic field is tilted away from the light propagation direction in the plane defined by the light propagation and polarization vectors. These resonances, studied both experimentally and with a density matrix calculation in the present work, offer a convenient method of achieving additional information about a direction of the magnetic field.