Abstract
We present theoretical description of Voigt and Faraday effect based optically pumped magnetometers using the Floquet expansion. Our analysis describes the spin-operator dynamics of the first, $\hat{F}(t)$, and second, $\hat{F}^2(t)$, order moments and takes into account of different pumping profiles and decoherence effects. We find that the theoretical results are in good agreement with the experimental demonstrations over a wide range of fields and pumping conditions. Finally, the theoretical analysis presented here is generalized and can be extended to different magnetometry schemes with arbitrary pumping profiles and multiple radio-frequency fields.
Highlights
Atomic-vapor-based optically pumped magnetometers (OPMs) [1,2] have become state-of-the-art magnetic field sensors with numerous applications in very diverse areas, ranging from fundamental physics in searching for electric dipole moment (EDM) [3,4], to geophysical and space magnetometry, medicine, such as magnetoencephalography (MEG) [5,6] and magnetocardiography [7,8,9]
A number of d√ifferent OPM architectures have shown sensitivity of fT/ Hz, based on spin-exchange relaxation-free (SERF) magnetometers [10,11], radio-frequency excited spin with Mx and Mz magnetometers relying on a linear atomic response [12,13,14], and modulated light magnetometers producing nonlinear magneto-optical rotation (NMOR) [15,16] due to a nonlinear optical response of the atoms
Most of OPMs are based on a Faraday dispersive measurement, in which oriented states [see Fig. 1(a)] are prepared and probed by a detuned laser beam measuring the Faraday rotation induced by the spin-polarized sample
Summary
Atomic-vapor-based optically pumped magnetometers (OPMs) [1,2] have become state-of-the-art magnetic field sensors with numerous applications in very diverse areas, ranging from fundamental physics in searching for electric dipole moment (EDM) [3,4], to geophysical and space magnetometry, medicine, such as magnetoencephalography (MEG) [5,6] and magnetocardiography [7,8,9]. [19], in which an aligned state is prepared instead of an oriented one [see, for example, Fig. 1(b)] and read through paramagnetic resonance, i.e., nondispersive measurement This kind of state allows a vector magnetometer operation using radio-frequency fields [20] or, as it was proposed more recently [21], adopting an all-optical approach which performs a dual axis magnetometer based on the Hanle effect. [22] we have shown that it is possible to employ dispersive measurements based on Voigt rotation when working with aligned states driven by radio-frequency fields, showing vector magnetometry operation (see Fig. 2). We show that the general dynamics of the second moment in the Liouville space can be reduced to Bloch equations [see Eq (2)] and can be solved by employing the Floquet expansion This solution predicts sensitivity to all three vector components of the magnetic field as reported in the experimental work in [22].
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