Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Nonlinear Magneto-optical Rotation via Alignment-to-Orientation Conversion

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

Published Sep 4, 2000• 120 citations
Publisher

Abstract

Nonlinear magneto-optical rotation is investigated at high light powers where the rotation is significantly modified by ac Stark shifts. These shifts are shown to change the overall sign of rotation for closed F-->F+1 transitions compared to the low light power limit. The effect is demonstrated by measurements in rubidium and density matrix calculations. The results are important for applications of nonlinear optical rotation such as sensitive magnetometry.

DOI
10.1103/physrevlett.85.2088

Related papers

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

Víctor M. Acosta, M. P. Ledbetter, Simon Rochester +7 more

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.

arXiv:physics/0602109•Physical Review A•May 17, 2006•125 citations

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

Yu. P. Malakyan, Simon Rochester, Dmitry Budker +2 more

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.

arXiv:physics/0309061•Physical Review A•Jan 26, 2004•34 citations

Sensitive magnetometry based on nonlinear magneto-optical rotation

Dmitry Budker, Derek F. Jackson Kimball, Simon Rochester +2 more

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 $D1$ and $D2$ lines of ${}^{85}\mathrm{Rb}.$ It is shown that through an appropriate choice of parameters the shot-noise-limited sensitivity to small magnetic fields can reach $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$

Physical Review A•Sep 11, 2000•335 citations

Rotating Polarization Magnetometry

Szymon Pustelny, Przemysław Włodarczyk

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.

arXiv:2412.20044•Sensors•Apr 24, 2025•1 citation

Nonlinear magneto-optical rotation in optically thick media

Simon Rochester, Dmitry Budker

Nonlinear magneto-optical rotation is a sensitive technique for measuring magnetic fields. Here, the shot-noise-limited magnetometric sensitivity at high light power is analysed for optically thick media. Such media have been the subject of recent experimental and theoretical investigations.

arXiv:physics/0202071•Journal of Modern Optics•Nov 1, 2002•14 citations

Compensation of ac Stark shifts in optical magnetometry

Irina V. Novikova, Andrey B. Matsko, Vladimir L Velichansky +2 more

The ac Stark shift of the resonance frequency of the nonlinear magneto-optic effect (NMOE) results in a fundamental broadening of this resonance which limits the precision of optical magnetometry based on NMOE. We have studied the dependence of the ac Stark shift versus frequency of the probing laser for the ${D}_{1}$ and ${D}_{2}$ lines of ${}^{87}\mathrm{Rb},$ and have shown that there exists a frequency where the shifts from different hyperfine components of the upper level cancel each other. This holds promise for an in-principle increase in the sensitivity of optical magnetometers. The influence of buffer gas on Faraday rotation and ac Stark shifts is also considered.

Physical Review A•May 7, 2001•47 citations
Nonlinear magneto-optical rotation is investigated at high light powers where the rotation is significantly modified by ac Stark shifts. These shifts are shown to change the overall sign of rotation for closed F-->F+1 transitions compared to the low light power limit. The effect is demonstrated by measurements in rubidium and density matrix calculations. The results are important for applications of nonlinear optical rotation such as sensitive magnetometry.
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.
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 D1D1D1 line.
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 $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$
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.
The ac Stark shift of the resonance frequency of the nonlinear magneto-optic effect (NMOE) results in a fundamental broadening of this resonance which limits the precision of optical magnetometry based on NMOE. We have studied the dependence of the ac Stark shift versus frequency of the probing laser for the D1{D}_{1}D1​ and D2{D}_{2}D2​ lines of 87Rb,{}^{87}\mathrm{Rb},87Rb, and have shown that there exists a frequency where the shifts from different hyperfine components of the upper level cancel each other. This holds promise for an in-principle increase in the sensitivity of optical magnetometers. The influence of buffer gas on Faraday rotation and ac Stark shifts is also considered.