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arXiv:0810.2221 · Physical Review A

Cancellation of nonlinear Zeeman shifts with light shifts

Kasper Jensen, Víctor M. Acosta, James Higbie, M. P. Ledbetter, Simon Rochester, Dmitry Budker

Published Feb 4, 2009• 63 citations
arXivHTMLPDF

Abstract

Nonlinear Zeeman (NLZ) shifts arising from magnetic-field mixing of the two hyperfine ground states in alkali-metal atoms lead to splitting of magnetic-resonance lines. This is a major source of sensitivity degradation and the so-called ``heading errors'' of alkali-metal-vapor atomic magnetometers operating in the geophysical field range $(B\ensuremath{\approx}0.2--0.7\phantom{\rule{0.3em}{0ex}}\mathrm{G})$. Here, it is shown theoretically and experimentally that NLZ shifts can be effectively canceled by light shifts caused by a laser field of appropriate intensity, polarization, and frequency, a technique that can be readily applied in practical situations.

DOI
10.1103/physreva.79.023406

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Nonlinear Zeeman (NLZ) shifts arising from magnetic-field mixing of the two hyperfine ground states in alkali-metal atoms lead to splitting of magnetic-resonance lines. This is a major source of sensitivity degradation and the so-called ``heading errors'' of alkali-metal-vapor atomic magnetometers operating in the geophysical field range (B\ensuremath≈0.2−−0.7G)(B\ensuremath{\approx}0.2--0.7\phantom{\rule{0.3em}{0ex}}\mathrm{G})(B\ensuremath≈0.2−−0.7G). Here, it is shown theoretically and experimentally that NLZ shifts can be effectively canceled by light shifts caused by a laser field of appropriate intensity, polarization, and frequency, a technique that can be readily applied in practical situations.
The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear Zeeman effect and heading error based on spin locking. In an all-optical synchronously pumped magnetometer with separate pump and probe beams, we apply a radio-frequency field which is in phase with the precessing magnetization. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with ∼100 Hz width in the Earth-field range into a single peak with a width of 22 Hz, whose position is largely independent of the orientation of the sensor within a range of orientation angles. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude, decreasing its width, and removing the important and limiting heading-error systematic.
The nonlinear Zeeman effect can induce splittings and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. We demonstrate an all-optical scheme, based on spin locking, to suppress the nonlinear Zeeman effect. This scheme achieves spin locking via an effective oscillating magnetic field in the form of AC Stark shifts induced by an intensity- and polarization-modulated laser beam. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ width in the Earth-field range into a peak with a central component width of 25 Hz. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude and decreasing its width. An advantage of the all-optical approach is the absence of crosstalk between nearby sensors when they are used in a gradiometric or array arrangement.
We demonstrate an alignment-based 87Rb^{87}\mathrm{Rb}87Rb magnetometer that is immune to nonlinear Zeeman (NLZ) splitting, addressing an important problem in alkali-metal atomic magnetometry. In our scheme, there is a single magnetic resonance peak and well-separated hyperfine transition frequencies, making the magnetometer insensitive or even immune to NLZ-related heading errors. It is shown that the magnetometer can be implemented for practical measurements in geomagnetic environments, and the photon-shot-noise-limited sensitivity reaches 9  fT/Hz9\text{ }\text{ }\mathrm{fT}/\sqrt{\mathrm{Hz}}9  fT/Hz​ at $5\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}$ and remains at tens of fT/Hz\mathrm{fT}/\sqrt{\mathrm{Hz}}fT/Hz​ at $50\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}$ at room temperature.
The nonlinear Zeeman effect can induce splittings and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. We demonstrate a scheme to suppress the nonlinear Zeeman effect all optically based on spin locking. Spin locking is achieved with an effective oscillating magnetic field provided by the AC Stark-shift of an intensity-modulated and polarization-modulated laser beam. This results in the collapse of the multi-component asymmetric magnetic-resonance line with about 100 Hz width in the Earth-field range into a peak with a central component width of 25Hz. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude and decreasing its width. Advantage of an all-optical approach is the absence of cross-talk between nearby sensors when these are used in a gradiometric or in an array arrangement.
Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic field measurement, have become one of the most sensitive magnetic field detectors. Their application areas range from practical uses such as detections of NMR signals to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping and the collision between alkali atoms and between alkali atoms and the buffer gas. Starting from a full master equation containing both the ground and excited states, we adiabatically eliminate the excited states and obtain an effective master equation in the ground-state subspace that shows an intuitive picture and dramatically accelerates the numerical simulation. Solving this effective master equation, we find that in the light-narrowing regime, where the line width is reduced while the coherent precession signal is enhanced, the frequency-dependence of the light shift is largely reduced, which agrees with experimental observations in cesium magnetometers. Since this effective master equation is general and is easily solved, it can be applied to an extensive parameter regime, and also to study other physical problems in alkali-metal-vapor magnetometers, such as heading errors.
Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic-field measurement, have become one of the most sensitive magnetic-field detectors. Their application areas range from practical uses such as NMR signal detection to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping and the collision between alkali-metal atoms and between alkali-metal atoms and the buffer gas. Starting from a full master equation containing both the ground and excited states, we adiabatically eliminate the excited states and obtain an effective master equation in the ground-state subspace that shows an intuitive picture and dramatically accelerates the numerical simulation. Solving this effective master equation, we find that in the light-narrowing regime, where the linewidth is reduced while the coherent precession signal is enhanced, the frequency dependence of the light shift is largely reduced, which agrees with experimental observations in cesium magnetometers. Since this effective master equation is general and is easily solved, it can be applied to an extensive parameter regime, and also to study other physical problems in alkali-metal-vapor magnetometers, such as heading errors.