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Physical Review A

Single magneto-optical resonance in a modulated RF field

Eugene A. Tsygankov, Sergei A. Zibrov, Alexander S. Zibrov, Maria I. Vaskovskaya, Dmitry S. Chuchelov, Vitali V. Vassiliev, Vladimir L Velichansky, Sergey Petropavlovsky, Valery P. Yakovlev

Published Jun 26, 2019• 5 citations
Publisher

Abstract

A symmetric magneto-optical resonance arising from the single two-quantum RF transition $|{F}_{g}=1,{m}_{{F}_{g}}=\ensuremath{-}1\ensuremath{\rangle}\ensuremath{\leftrightarrows}|{F}_{g}=1,\phantom{\rule{4pt}{0ex}}{m}_{{F}_{g}}=1\ensuremath{\rangle}$ in an optically aligned atomic ensemble is studied in the case when the quadratic Zeeman shift exceeds the width of the resonance. It is shown that the signal-to-noise ratio of the resonance can be significantly increased by applying the phase modulation to the RF field at a frequency close to the value of quadratic Zeeman shift. This theoretical prediction is corroborated by the experimental results with $^{87}\mathrm{Rb}$ atoms. The proposed technique can be used in magnetometers based on atomic alignment or by utilizing multiquantum RF resonances in optically oriented atomic ensembles.

DOI
10.1103/physreva.99.063835

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A symmetric magneto-optical resonance arising from the single two-quantum RF transition ∣Fg=1,mFg=\ensuremath−1\ensuremath⟩\ensuremath⇆∣Fg=1,mFg=1\ensuremath⟩|{F}_{g}=1,{m}_{{F}_{g}}=\ensuremath{-}1\ensuremath{\rangle}\ensuremath{\leftrightarrows}|{F}_{g}=1,\phantom{\rule{4pt}{0ex}}{m}_{{F}_{g}}=1\ensuremath{\rangle}∣Fg​=1,mFg​​=\ensuremath−1\ensuremath⟩\ensuremath⇆∣Fg​=1,mFg​​=1\ensuremath⟩ in an optically aligned atomic ensemble is studied in the case when the quadratic Zeeman shift exceeds the width of the resonance. It is shown that the signal-to-noise ratio of the resonance can be significantly increased by applying the phase modulation to the RF field at a frequency close to the value of quadratic Zeeman shift. This theoretical prediction is corroborated by the experimental results with 87Rb^{87}\mathrm{Rb}87Rb atoms. The proposed technique can be used in magnetometers based on atomic alignment or by utilizing multiquantum RF resonances in optically oriented atomic ensembles.
We report a new method for excitation of magnetic resonance in an optically aligned atomic ensemble. It employs a comb-like rf field acting on the end sublevels of the F g = 1 state separated by the doubled Zeeman frequency. This approach provides a resonance without substructures associated with the quadratic Zeeman shift. A theoretical explanation of the effect is given in terms of the two-quantum transition | F g = 1 , m F g = − 1 ⟩ ⇆ | F g = 1 , m F g = 1 ⟩ and is corroborated by an experiment with 87 R b atoms. Possible advantages of the approach and its range of applicability are discussed.
Parametric-resonance magnetometer is a high-sensitivity quantum sensor characterized by applying the non-resonant radio-frequency (RF) fields to the atomic ensemble. The RF fields lead to crosstalk in the multi-sensor design, thus disturbing the magnetic-field measurement results. We propose an optically modulated alignment-based 4He parametric-resonance magnetometer. By using the fictitious field generated by the modulated light shift, parametric resonance is realized, and crosstalk caused by the magnetic RF field is prevented. The relative intensity noise of the lasers is suppressed to optimize the sensitivity of the magnetometer. Our magnetometer experimentally demonstrates a magnetic-field noise floor of 130 fT/Hz1/2 in both open- and closed-loop operations and has the potential to reach 70 fT/Hz1/2 when compared with the optimized magnetic RF scheme. It provides near-zero magnetic-field measurements with a 2 kHz bandwidth at room temperature, which is useful for high-bandwidth measurements in biomagnetic applications.
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.
In radio frequency (RF) experiments on aligned atoms (e.g. optical double resonance) new phenomena can be found in the case of longitudinal excitation if a strong oscillating RF field is used: both the positions of the RF resonances (RF shift) and the widths (power broadening) depend on the direction of the light observed and on the state of its (linear) polarisation. This applies to the main (single-quantum) transitions as well as the (odd) multi-quanta transitions. These effects have been observed in an experiment on aligned mercury atoms in the metastable 6 3 P 2 state and have been confirmed by numerical calculations based on the semiclassical approach.
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.
Quantum information protocols utilizing atomic ensembles require preparation of a coherent spin state (CSS) of the ensemble as an important starting point. We investigate the magneto-optical resonance method for characterizing a spin state of caesium atoms in a paraffin coated vapour cell. Atoms in a constant magnetic field are subject to an off-resonant laser beam and an RF magnetic field. The spectrum of the Zeeman sub-levels, in particular the weak quadratic Zeeman effect, enables us to measure the spin orientation, the number of atoms, and the transverse spin coherence time. Notably the use of 894 nm pumping light on the D1 line, ensuring the state F = 4, m F = 4 is a dark state, helps us to achieve spin orientation of better than 98%. Hence we can establish a CSS with high accuracy, which is critical for the analysis of the entangled states of atoms.