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arXiv:physics/0609196 · Physical Review A

Detection of radio-frequency magnetic fields using nonlinear magneto-optical rotation

M. P. Ledbetter, Víctor M. Acosta, Simon Rochester, Dmitry Budker, Szymon Pustelny, Valeriy V. Yashchuk

Published Feb 8, 2007• 67 citations
arXivHTMLPDF

Abstract

We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high-frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. Based on experimentally measured signal-to-noise ratio, we demonstrate a sensitivity of $100\phantom{\rule{0.3em}{0ex}}\mathrm{pG}∕\sqrt{\mathrm{Hz}}$ (rms) in a $3.5\text{\ensuremath{-}}\mathrm{cm}$-diameter paraffin coated cell. Assuming detection at the photon shot-noise limit, we project a sensitivity as low as $25\phantom{\rule{0.3em}{0ex}}\mathrm{pG}∕\sqrt{\mathrm{Hz}}$ (rms).

DOI
10.1103/physreva.75.023405

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We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high-frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. Based on experimentally measured signal-to-noise ratio, we demonstrate a sensitivity of 100pG∕Hz100\phantom{\rule{0.3em}{0ex}}\mathrm{pG}∕\sqrt{\mathrm{Hz}}100pG∕Hz​ (rms) in a 3.5\ensuremath-cm3.5\text{\ensuremath{-}}\mathrm{cm}3.5\ensuremath-cm-diameter paraffin coated cell. Assuming detection at the photon shot-noise limit, we project a sensitivity as low as 25pG∕Hz25\phantom{\rule{0.3em}{0ex}}\mathrm{pG}∕\sqrt{\mathrm{Hz}}25pG∕Hz​ (rms).
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.
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).
Here we demonstrate an atomic magnetometer that has a bandwidth of more than 100 kHz and a sensitivity of $180\phantom{\rule{0.2em}{0ex}}\mathrm{fT/}\ensuremath{\surd}\mathrm{Hz}$ at a Fourier frequency of 8 Hz, and $0.7\phantom{\rule{0.2em}{0ex}}\mathrm{nT/}\ensuremath{\surd}\mathrm{Hz}$ at 100 kHz. These sensitivity measurements are achieved at geophysically useful magnetic field magnitudes (approximately $50\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{T}$ inside a three-layer $\ensuremath{\mu}$-metal shield) and are limited by the photon shot noise for frequencies above 8 Hz. This device is based on a nonlinear magneto-optical rotation sensor that is operated with an active feedback to the pump modulation frequency. We present a theoretical description of the response functions of the components in the magnetometer. We show that the range of operation of atomic magnetometers can thus be expanded beyond the conventional high-sensitivity, low-bandwidth domain, to provide a high-linearity, high-bandwidth, and high-sensitivity sensor.
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 $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$
We describe an alkali-metal magnetometer for detection of weak magnetic fields in the radio-frequency (rf) range. High sensitivity is achieved by tuning the Zeeman resonance of alkali atoms to the rf frequency and partially suppressing spin-exchange collisions in the alkali-metal vapor. We demonstrate magnetic field sensitivity of 2 fT/Hz(1/2) at a frequency of 99 kHz with a resonance width of 400 Hz. We also derive a simple analytic expression for the fundamental limit on the sensitivity of the rf magnetometer and show that a sensitivity of about 0.01 fT/Hz(1/2) can be achieved in a practical system with a measurement volume of 200 cm3.
The detection of nonlinear magneto-optical rotation (NMOR) of polarized light through alkali atomic vapor is a highly sensitive technique for measuring magnetic fields. We demonstrate that when using frequency modulated light to excite the NMOR resonance, it is possible to cause the system to self-oscillate. The NMOR signal is not a simple replica of the sine wave modulation of the light, but rather contains many higher harmonics of the modulation frequency, and we implement two ways of processing the signal to recover the fundamental modulation frequency in the feedback loop and induce self-oscillation. Self-oscillation simplifies and reduces the power consumption of the electronics required to operate a magnetometer, making the NMOR technique attractive for commercialized magnetic sensors.