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arXiv:2003.12897 · Physical Review A

Light-ellipticity and polarization-angle dependence of magnetic resonances in rubidium vapor using amplitude-modulated light: Theoretical and experimental investigations

Raghwinder Singh Grewal, G. S. Pati, Renu Tripathi

Published Sep 2, 2020• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.033102

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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\ensuremathΩL2{\mathrm{\ensuremath{\Omega}}}_{L}2\ensuremathΩL​ (alignment) and \ensuremathΩL{\mathrm{\ensuremath{\Omega}}}_{L}\ensuremathΩL​ (orientation) in a Bell-Bloom interaction geometry, where \ensuremathΩL{\mathrm{\ensuremath{\Omega}}}_{L}\ensuremathΩL​ corresponds to the Larmor frequency. Both 2\ensuremathΩL2{\mathrm{\ensuremath{\Omega}}}_{L}2\ensuremathΩL​ and \ensuremathΩL{\mathrm{\ensuremath{\Omega}}}_{L}\ensuremathΩL​ 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\ensuremathΩL2{\mathrm{\ensuremath{\Omega}}}_{L}2\ensuremathΩL​ and \ensuremathΩL{\mathrm{\ensuremath{\Omega}}}_{L}\ensuremathΩL​ resonances with light ellipticity. As a potential application, we showed that the difference between 2\ensuremathΩL2{\mathrm{\ensuremath{\Omega}}}_{L}2\ensuremathΩL​ and \ensuremathΩL{\mathrm{\ensuremath{\Omega}}}_{L}\ensuremathΩL​ resonance amplitudes can be used for in situ measurement of light ellipticity. We also studied the dependence of 2\ensuremathΩL2{\mathrm{\ensuremath{\Omega}}}_{L}2\ensuremathΩL​ and \ensuremathΩL{\mathrm{\ensuremath{\Omega}}}_{L}\ensuremathΩL​ 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.
We report our investigations on the dependence of magnetic resonance spectrum on the light ellipticity and the polarization angle. A rubidium vapor cell with octade-cyltrichlorosilane (OTS) antirelaxation coating has been used in our experiment to produce narrow linewidth magnetic resonances. We show that excitation using elliptically polarized light can simultaneously produce the alignment and orientation resonances in a Bell-Bloom interaction geometry. We have developed a theoretical model to calculate the resonance spectrum using light with a varying degree of ellipticity. Amplitudes of the alignment and orientation resonances show a strong dependence on the light ellipticity. Our study shows that the duty cycle of light modulation can effectively control the amplitude variations of the alignment and orientation resonances with light ellipticity. We propose that the difference between the alignment and orientation resonance amplitudes can be used for in situ measurement of the light
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.
We investigate the polarization modulation between two linear orthogonal states of the laser beam that synchronously pumps time-dependent atomic alignment in caesium atoms exposed to a static magnetic field. Because of the atomic alignment symmetry two independent groups of resonances can be distinguished in the transmitted light: when modulation frequency matches either the Larmor frequency or its second harmonics, ${\ensuremath{\omega}}_{L}$ and $2{\ensuremath{\omega}}_{L}$, respectively. We report on our experiments, and discuss a model that perfectly reproduces the observed spectra. We have observed that the amplitudes and linewidths of resonances at ${\ensuremath{\omega}}_{L}$ and $2{\ensuremath{\omega}}_{L}$ show magnetic-field direction dependence. This peculiar behavior makes our approach interesting for future application to atomic magnetometry, in view of a dead-zone free high-sensitivity magnetometer.
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.
We present a combined theoretical and experimental study of magnetic resonance transitions induced by polarization-modulated light in cesium vapor exposed to a transverse magnetic field. Signals are obtained by phase-sensitive analysis of the light power traversing the vapor cell at six harmonics of the polarization modulation frequency. Resonances appear whenever the Larmor frequency matches an integer multiple of the modulation frequency. We have further investigated the modifications of the spectra when varying the modulation duty cycle. The resonance amplitudes of both in-phase and quadrature components are well described in terms of the Fourier coefficients of the modulation function. The background-free signals generated by the polarization modulation scheme have a high application potential in atomic magnetometry.
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.