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Physical Review A

High-order magnetic resonance in the presence of strong longitudinal radio-frequency magnetic field based on atomic alignment states

Tao Shi, Ge Jin, Sheng Zou

Published Apr 26, 2024• 10 citations
Publisher

Abstract

A longitudinal radio-frequency (rf) magnetic field resonating at the Larmor frequency along the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction in the presence of a static transverse magnetic field s investigated. Optical-radio-frequency double resonance in $^{85}\mathrm{Rb}$ characterizes the strength of an external magnetic field through the precession frequency of $^{85}\mathrm{Rb}$ atoms. The measurements are carried out in a paraffin-coated $^{85}\mathrm{Rb}$ cell with a spin alignment configuration. An intriguing discovery of magnetic resonance peaks is observed at subharmonics of the Larmor frequency, accompanied by the emergence of nonlinear effects in the vicinity of the resonance. Notably, when the Larmor frequency reaches zero, the optical rotation signals induced by the rf magnetic field demonstrate a superposition of high-order harmonics of the rf frequency. Based on the simplified density matrix formalism and perturbation treatment, analytical expressions for the optical rotation are consistent with experimental outcomes. These findings hold the potential of extending our understanding on unveiling the dynamics of population and coherence among Zeeman sublevels, thereby advancing our knowledge in the field of alignment magnetometry.

DOI
10.1103/physreva.109.043117

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A longitudinal radio-frequency (rf) magnetic field resonating at the Larmor frequency along the z\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}z\ifmmode^\elseˆ\fi direction in the presence of a static transverse magnetic field s investigated. Optical-radio-frequency double resonance in 85Rb^{85}\mathrm{Rb}85Rb characterizes the strength of an external magnetic field through the precession frequency of 85Rb^{85}\mathrm{Rb}85Rb atoms. The measurements are carried out in a paraffin-coated 85Rb^{85}\mathrm{Rb}85Rb cell with a spin alignment configuration. An intriguing discovery of magnetic resonance peaks is observed at subharmonics of the Larmor frequency, accompanied by the emergence of nonlinear effects in the vicinity of the resonance. Notably, when the Larmor frequency reaches zero, the optical rotation signals induced by the rf magnetic field demonstrate a superposition of high-order harmonics of the rf frequency. Based on the simplified density matrix formalism and perturbation treatment, analytical expressions for the optical rotation are consistent with experimental outcomes. These findings hold the potential of extending our understanding on unveiling the dynamics of population and coherence among Zeeman sublevels, thereby advancing our knowledge in the field of alignment magnetometry.
Abstract We have constructed a transverse modulated magnetometer based on spin alignment in a paraffin-coated 85 Rb cell operated in a geophysical magnetic field of 47.1 µT. When an orthogonal driving magnetic field ( x ^ axis) is resonant on the Larmor frequency ( z ^ axis), we have proposed a new method to zero the static residual magnetic fields in the transverse plane and achieved a sensitivity of 1.8 pT Hz − 1 with bandwidth of 200 Hz. The repump light ( F g = 2 → F e = 2 ) redistributes the populations in the ground state, rendering the state | F g = 2 ⟩ dark. This effect significantly amplifies the optical rotation signals nearly fourfold. The numerical solution of the Liouville equation is in good agreement with the experimental results. By using perturbation treatment and employing appropriate approximations, the derived analytical expressions for optical rotation are deduced to succinctly elucidate the dynamics of atomic alignment under parametric modulation. These outcomes could be extended for the advancement of an alignment magnetometer that has been designed to detect a weak magnetic signal in the geophysical range.
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 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 $3.5\text{\ensuremath{-}}\mathrm{cm}$-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).
Recent work investigating resonant nonlinear magneto-optical rotation (NMOR) related to long-lived $({\ensuremath{\tau}}_{\mathrm{rel}}\ensuremath{\sim}1\mathrm{s})$ ground-state atomic coherences has demonstrated potential magnetometric sensitivities exceeding ${10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}\mathrm{G}∕\sqrt{\mathrm{Hz}}$ for small $(\ensuremath{\lesssim}1\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{G}$) magnetic fields. In the present work, NMOR using frequency-modulated light (FM NMOR) is studied in the regime where the longitudinal magnetic field is in the geophysical range$(\ensuremath{\sim}500\mathrm{mG})$, of particular interest for many applications. In this regime a splitting of the FM NMOR resonance due to the nonlinear Zeeman effect is observed. At sufficiently high light intensities, there is also a splitting of the FM NMOR resonances due to ac Stark shifts induced by the optical field, as well as evidence of alignment-to-orientation conversion type processes. The consequences of these effects for FM-NMOR-based atomic magnetometry in the geophysical field range are considered.