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arXiv:1706.08149 · Physical Review A

In situ measurement of light polarization with ellipticity-induced nonlinear magneto-optical rotation

Derek F. Jackson Kimball, Jordan Dudley, Yan Li, Dilan Patel

Published Sep 12, 2017• 14 citations
arXivHTMLPDF

Abstract

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 $\mathbf{B}$ and the major axis of the light polarization ellipse is along $\mathbf{B}$. When the light modulation frequency matches the Larmor frequency, elliptically polarized light produces a precessing atomic spin orientation transverse to $\mathbf{B}$ 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.

DOI
10.1103/physreva.96.033823

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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.
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 magnetometric technique is demonstrated that may be suitable for precision measurements of fields ranging from the submicrogauss level to above the earth field. It is based on resonant nonlinear magneto-optical rotation caused by atoms contained in a vapor cell with antirelaxation wall coating. Linearly polarized, frequency-modulated laser light is used for optical pumping and probing. If the time-dependent optical rotation is measured at the first harmonic of the modulation frequency, ultra-narrow (\ensuremath{\sim} a few hertz) resonances are observed at near-zero magnetic fields, and at fields where the Larmor frequency coincides with half the light modulation frequency. Upon optimization, the sensitivity of the technique is expected to exceed ${10}^{\ensuremath{-}11} G/\sqrt{\mathrm{Hz}}.$
We report on experimental and theoretical investigations of the polarization dependence of magnetic resonance generated by synchronous optical pumping. Magnetic resonances with narrow linewidth are generated experimentally using a rubidium vapor cell with octadecyltrichlorosilane antirelaxation coating on inner walls. We studied the effect of light ellipticity on the amplitudes and widths of magnetic resonances by matching the light modulation frequency with $2{\mathrm{\ensuremath{\Omega}}}_{L}$ (alignment) and ${\mathrm{\ensuremath{\Omega}}}_{L}$ (orientation) in a Bell-Bloom interaction geometry, where ${\mathrm{\ensuremath{\Omega}}}_{L}$ corresponds to the Larmor frequency. Both $2{\mathrm{\ensuremath{\Omega}}}_{L}$ and ${\mathrm{\ensuremath{\Omega}}}_{L}$ resonance amplitudes showed a strong dependence on the light ellipticity. In addition, we showed that the duty cycle of light modulation changes the slope of amplitude variations in $2{\mathrm{\ensuremath{\Omega}}}_{L}$ and ${\mathrm{\ensuremath{\Omega}}}_{L}$ resonances with light ellipticity. As a potential application, we showed that the difference between $2{\mathrm{\ensuremath{\Omega}}}_{L}$ and ${\mathrm{\ensuremath{\Omega}}}_{L}$ resonance amplitudes can be used for in situ measurement of light ellipticity. We also studied the dependence of $2{\mathrm{\ensuremath{\Omega}}}_{L}$ and ${\mathrm{\ensuremath{\Omega}}}_{L}$ resonance amplitudes on the polarization angle of linearly polarized light. These amplitudes oscillate periodically with the polarization angle. We found this oscillatory behavior to be sensitive to the tilt in magnetic field direction from the polarization plane. Such a property could be used to realize a vector magnetometer. A density matrix based theoretical model is developed to simulate the magnetic resonance spectrum for different light polarizations. Our theoretical model accurately reproduces the above-mentioned experimental observations.
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.
Abstract The polarization of light affected by the birefringence of optical elements, such as vapor cell walls, mirrors, and windows, may introduce systematic errors that can be minimized by precisely measuring and correcting the light polarization with a highly sensitive atomic polarimeter. In high precision measurements, it is necessary to measure the light polarization with a high precision where the light interacts with atoms. However, it is inconvenient or even impossible to use the presented method to measure the light polarization, for example, in a cell or cavity. We present a precise and relatively straightforward method to measure the light polarization based on a cesium (Cs) atomic magnetometer configuration. The pump-probe scheme is involved in our experiment. The pump light polarizes atomic spins and the probe light measures the spins polarization. The optical rotation of the probe light significantly depends on the pump light ellipticity, which can be used to measure the light polarization with a high precision. In our work, we present a method to measure the pump light ellipticity with a sensitivity of 2.1 × 10 −8 rad Hz −1/2 for linearly polarized light, which has approximately an order of magnitude improvement than previous research results.
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.