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Cambridge University Press eBooks

Optical magnetometry with modulated light

Derek F. Jackson Kimball, Szymon Pustelny, Valeriy V. Yashchuk, Dmitry Budker

Published Mar 7, 2013• 6 citations
Publisher

Abstract

Introduction Soon after the development of optical magnetometers based on the radio-optical double resonance method (see Chapter 4), it was realized by Bell and Bloom [1] that an alternative method for optical magnetometry was to modulate the light used for optical pumping at a frequency resonant with the Larmor precession of atomic spins. In a Bell-Bloom optical magnetometer, circularly polarized light resonant with an atomic transition propagates through an atomic vapor along a direction transverse to a magnetic field B . Atomic spins immersed in B precess at the Larmor frequency Ω L , and when the light intensity is modulated at Ω m = Ω L , a resonance in the transmitted light intensity is observed. The essential ideas of the Bell–Bloom optical magnetometer are reviewed in Chapter 1 (Section 1.2), and can be summarized in terms of what Bell and Bloom termed optically driven spin precession: in analogy with a driven harmonic oscillator, in a magnetic field B atomic spins precess at a natural frequency equal to Ω L and the light acts as a driving force oscillating at the modulation frequency Ω m . From another point of view, the Bell-Bloom optical magnetometer can be described in terms of synchronous optical pumping: when Ω m = Ω L , there is a “stroboscopic” resonance in which atoms are optically pumped into a spin state stationary in the frame rotating with Ω L . Depending on the details of the atomic structure, the spin state stationary in the rotating frame can be either a dark state that does not interact with the modulated light or a bright state for which the strength of the light–atom interaction is increased.

DOI
10.1017/cbo9780511846380.007

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Introduction Soon after the development of optical magnetometers based on the radio-optical double resonance method (see Chapter 4), it was realized by Bell and Bloom [1] that an alternative method for optical magnetometry was to modulate the light used for optical pumping at a frequency resonant with the Larmor precession of atomic spins. In a Bell-Bloom optical magnetometer, circularly polarized light resonant with an atomic transition propagates through an atomic vapor along a direction transverse to a magnetic field B . Atomic spins immersed in B precess at the Larmor frequency Ω L , and when the light intensity is modulated at Ω m = Ω L , a resonance in the transmitted light intensity is observed. The essential ideas of the Bell–Bloom optical magnetometer are reviewed in Chapter 1 (Section 1.2), and can be summarized in terms of what Bell and Bloom termed optically driven spin precession: in analogy with a driven harmonic oscillator, in a magnetic field B atomic spins precess at a natural frequency equal to Ω L and the light acts as a driving force oscillating at the modulation frequency Ω m . From another point of view, the Bell-Bloom optical magnetometer can be described in terms of synchronous optical pumping: when Ω m = Ω L , there is a “stroboscopic” resonance in which atoms are optically pumped into a spin state stationary in the frame rotating with Ω L . Depending on the details of the atomic structure, the spin state stationary in the rotating frame can be either a dark state that does not interact with the modulated light or a bright state for which the strength of the light–atom interaction is increased.
Introduction Shortly after the inception of atomic magnetometry, alkali-vapor magnetometers were being used to measure the Earth's magnetic field to unprecedented precision. During the same era, Bell and Bloom first demonstrated all-optical atomic magnetometry through synchronous optical pumping [1] (see Chapters 1 and 6). In this approach, optical-pumping light is frequency- or amplitude-modulated at harmonics of the Larmor frequency ω L to generate a precessing spin polarization within an alkali vapor at finite magnetic field [2, 3]. Although this technique received considerable attention from the atomic physics community for its applicability to optical pumping experiments, Earth's-field alkali-vapor atomic magnetometers continued to rely on radiofrequency (RF) field excitation for several decades (see Chapter 4). Upon the advent of diode lasers addressing alkali and metastable helium transitions, synchronously pumped magnetometers experienced a revival beginning in the late 1980s. In recent years, such magnetometers have found applications in nuclear magnetic resonance detection [4] (see also Chapter 14), quantum control experiments [5], and chip-scale devices intended for spacecraft use [6] (see also Chapters 7 and 15). All-optical magnetometers possess several advantages over devices that employ RF coils. RF-driven magnetometers can suffer from cross-talk if two sensors are placed in close proximity, since the AC magnetic field driving resonance in one vapor cell can adversely affect the other. All-optical magnetometers are free from such interference. When operated in self-oscillating mode [7], RF-driven magnetometers require an added ±90° electronic phase shift in the feedback loop to counter the intrinsic phase shift between the RF field and the probe-beam modulation.
We propose a scheme for a Bell–Bloom atomic magnetometer based on a single beam. In our approach, the light is periodically modulated synchronously with Larmor precession. As a result, the light that interacts with atoms is alternately polychromatic and monochromatic. When the light is polychromatic, the ±1st sidebands of the light are optically resonant with the atoms, and the atoms are polarized by pumping. When the light is monochromatic, a differential detection technique extracts the Faraday-rotation signal of the light, and the polarization of the light is probed. We demonstrate an experimental implementation of the Bell–Bloom magnetometer that achieves a sensitivity for magnetic-field detection of 0.25 pT/Hz1/2 at 1 Hz. Our scheme is suitable for developing compact, miniaturized magnetometers.
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.
A precise, accurate, and relatively straightforward in situ method to measure and control the ellipticity of light resonantly interacting with an atomic vapor is described. The technique can be used to minimize vector light shifts. The method involves measurement of ellipticity-induced resonances in the magnetic-field dependence of nonlinear magneto-optical rotation of frequency-modulated light. The light propagation direction is orthogonal to the applied magnetic field B\mathbf{B}B and the major axis of the light polarization ellipse is along B\mathbf{B}B. When the light modulation frequency matches the Larmor frequency, elliptically polarized light produces a precessing atomic spin orientation transverse to B\mathbf{B}B via synchronous optical pumping. The precessing spin orientation causes optical rotation oscillating at the Larmor frequency by modulating the atomic vapor's circular birefringence. Based on this technique's precision, in situ nature (which avoids systematic errors arising from optical interfaces) and independent control of the most important systematic errors, it is shown that the accuracy of light ellipticity measurements achievable with this technique can exceed that of existing methods by orders of magnitude.
In recent years diode laser sources have become widespread and reliable tools in magneto-optical spectroscopy. In particular, laser-driven atomic magnetometers have found a wide range of practical applications. More recently, so-called magnetically silent variants of atomic magnetometers have been developed. While in conventional magnetometers the magnetic resonance transitions between atomic sublevels are phase-coherently driven by a weak oscillating magnetic field, silent magnetometers use schemes in which either the frequency or the amplitude of the light beam is modulated. Here we present a theoretical model that yields algebraic expressions for the parameters of the multiple resonances that occur when either amplitude-, frequency-, or polarization-modulated light of circular polarization is used to drive the magnetic resonance transition in a transverse magnetic field. The relative magnitudes of the resonances that are observed in the transmitted light intensity at harmonic mmm of the Larmor frequency ${\ensuremath{\omega}}_{L}$ (either by DC or phase sensitive detection at harmonics qqq of the modulation frequency ${\ensuremath{\omega}}_{\mathrm{mod}}$) of the transmitted light are expressed in terms of the Fourier coefficients of the modulation function. Our approach is based on an atomic multipole moment representation that is valid for spin-oriented atomic states with arbitrary angular momentum FFF in the low light power limit. We find excellent quantitative agreement with an experimental case study using (square-wave) amplitude-modulated light.
A self-oscillating magnetometer based on nonlinear magneto-optical rotation using amplitude-modulated pump light and unmodulated probe light (AM-NMOR) in 87Rb has been constructed and tested towards a goal of airborne detection of magnetic anomalies. In AM-NMOR, stroboscopic optical pumping via amplitude modulation of the pump beam creates alignment of the ground electronic state of the rubidium atoms. The Larmor precession causes an ac rotation of the polarization of a separate probe beam; the polarization rotation frequency provides a measure of the magnetic field. An anti-relaxation coating on the walls of the atomic vapor cell results in a long lifetime of 56 ms for the alignment, which enables precise measurement of the precession frequency. Light is delivered to the magnetometer by polarization-maintaining optical fibers. Tests of the sensitivity include directly measuring the beat frequency between the magnetometer and a commercial instrument and measurements of Earth's field under magnetically quiet conditions, indicating a sensitivity of at least 5 pT/νHz. Rotating the sensor indicates a heading error of less than 1 nT, limited in part by residual magnetism of the sensor.