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arXiv:physics/0602109 · Physical Review A

Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range

Víctor M. Acosta, M. P. Ledbetter, Simon Rochester, Dmitry Budker, Derek F. Jackson Kimball, D. C. Hovde, Wojciech Gawlik, Szymon Pustelny, Jerzy Zachorowski, Valeriy V. Yashchuk

Published May 17, 2006• 125 citations
arXivHTMLPDF

Abstract

Recent work investigating resonant nonlinear magneto-optical rotation (NMOR) related to long-lived $({\ensuremath{\tau}}_{\mathrm{rel}}\ensuremath{\sim}1\mathrm{s})$ ground-state atomic coherences has demonstrated potential magnetometric sensitivities exceeding ${10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}\mathrm{G}∕\sqrt{\mathrm{Hz}}$ for small $(\ensuremath{\lesssim}1\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{G}$) magnetic fields. In the present work, NMOR using frequency-modulated light (FM NMOR) is studied in the regime where the longitudinal magnetic field is in the geophysical range$(\ensuremath{\sim}500\mathrm{mG})$, of particular interest for many applications. In this regime a splitting of the FM NMOR resonance due to the nonlinear Zeeman effect is observed. At sufficiently high light intensities, there is also a splitting of the FM NMOR resonances due to ac Stark shifts induced by the optical field, as well as evidence of alignment-to-orientation conversion type processes. The consequences of these effects for FM-NMOR-based atomic magnetometry in the geophysical field range are considered.

DOI
10.1103/physreva.73.053404

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Recent work investigating resonant nonlinear magneto-optical rotation (NMOR) related to long-lived (\ensuremathτrel\ensuremath∼1s)({\ensuremath{\tau}}_{\mathrm{rel}}\ensuremath{\sim}1\mathrm{s})(\ensuremathτrel​\ensuremath∼1s) ground-state atomic coherences has demonstrated potential magnetometric sensitivities exceeding 10\ensuremath−11G∕Hz{10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}\mathrm{G}∕\sqrt{\mathrm{Hz}}10\ensuremath−11G∕Hz​ for small (\ensuremath≲1\ensuremathμG(\ensuremath{\lesssim}1\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{G}(\ensuremath≲1\ensuremathμG) magnetic fields. In the present work, NMOR using frequency-modulated light (FM NMOR) is studied in the regime where the longitudinal magnetic field is in the geophysical range(\ensuremath∼500mG)(\ensuremath{\sim}500\mathrm{mG})(\ensuremath∼500mG), of particular interest for many applications. In this regime a splitting of the FM NMOR resonance due to the nonlinear Zeeman effect is observed. At sufficiently high light intensities, there is also a splitting of the FM NMOR resonances due to ac Stark shifts induced by the optical field, as well as evidence of alignment-to-orientation conversion type processes. The consequences of these effects for FM-NMOR-based atomic magnetometry in the geophysical field range are considered.
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.
Atomic spin polarization of alkali atoms in the ground-state can survive thousands of collisions with paraffin-coated cell walls. The resulting long spin-relaxation times achieved in evacuated, paraffin-coated cells enable precise measurement of atomic spin precession and energy shifts of ground-state Zeeman sublevels. In the present work, nonlinear magneto-optical rotation with frequency-modulated light (FM NMOR) is used to measure magnetic field-induced spin precession for rubidium atoms contained in a paraffin-coated cell. The magnetometric sensitivity of FM NMOR for the rubidium D2 line is studied as a function of light power, detuning, frequency-modulation amplitude, and rubidium vapor density. For a 5-cm-diameter cell at temperature T≈35 °C, the optimal shot-noise-projected magnetometric sensitivity is found to be 2×10−11 G/Hz (corresponding to a sensitivity to spin precession frequency of ≈10 μHz/Hz or a sensitivity to Zeeman sublevel shifts of ≈4×10−20 eV/Hz).
We report on investigations of nonlinear magneto-optical rotation (NMOR) in rubidium vapor subjected to a modulated magnetic field and continuous-wave (cw) laser-light illumination. By superimposing modulation and a static (dc) magnetic field, we demonstrate the appearance of resonances at both small and large (compared to the ground-state relaxation rate) values of the static field. Since in conventional NMOR there is no rotation at high fields, this suggests an existence of an alternative mechanism generating anisotropy in the considered case, which we identify as parametric resonance. The experiments are performed using light of small ellipticity, and rotation signals are significantly enhanced by combining atom-induced polarization rotation with a passive rotation induced with a wave plate. All the observations are supported with theoretical simulations. The density-matrix formalism and angular-momentum probability surfaces are used to provide an intuitive explanation of the observed signals.
Optical pumping in an alkali metal vapour produces long-standing coherences of ground state Zeeman sub-levels. These coherences produce large nonlinear magneto-optic rotation (NMOR). Techniques using optical coherences for sensitive magnetometry have been in vogue for a long time. However, the sensitivity achieved has been three orders of magnitude lower than that of a SQUID magnetometer. The NMOR technique has yielded signals having a very narrow width of a few micro-Gauss. In principle, it has been demonstrated that with NMOR magnetometers one can obtain a sensitivity matching, or better than the sensitivity of a Squid magnetometer. There are still many problems to be resolved before these magnetometers can be put to use in geomagnetic and biological applications, where small magnetic fields need to be measured.
Precise magnetometry is vital in numerous scientific and technological applications. At the forefront of sensitivity, optical atomic magnetometry, particularly techniques utilizing nonlinear magneto-optical rotation (NMOR), enables ultraprecise measurements across a broad field range. Despite their potential, these techniques reportedly lose sensitivity in higher magnetic fields, which is attributed to the alignment-to-orientation conversion (AOC) process. In our study, we utilized light with continuously rotating linear polarization to avoid the AOC, which produced robust optical signals and achieving high magnetometric sensitivity over a dynamic range nearly three times greater than Earth's magnetic field. We demonstrated that employing rotating polarization surpasses other NMOR techniques that use modulated light. Our findings also indicate that the previously observed signal deterioration was not due to the AOC, suggesting an alternative cause for this decline.
We study the possibility of creating quantum superposition states in alkali atoms. Our methodology is based on the phenomenon of nonlinear magneto-optical rotation (NMOR). The effect of magneto-optical rotation occurs whenever the resonant light propagates through the medium immersed in a longitudinal magnetic field and manifests itself as a rotation of the polarization plane of light. The effect is strongly enhanced by the nonlinearity of light-atom interaction and allows state-of-the art atomic magnetometry. On the other hand, the nonlinear magneto-rotation provides means to controllably affect and detect atom's quantum state. We present the work on this topic and report on some characteristics of superposition quantum states such as lifetimes or efficiency of it's creation in various conditions.