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arXiv:2403.00950 · Journal of Physics B Atomic Molecular and Optical Physics

Indirect measurement of atomic magneto-optical rotation via Hilbert transform

Jack D. Briscoe, Danielle Pizzey, Steven A. Wrathmall, Ifan G. Hughes

Published Jul 2, 2024• 3 citations

Abstract

Abstract The Kramers–Kronig relations are a pivotal foundation of linear optics and atomic physics, embedding a physical connection between the real and imaginary components of any causal response function. A mathematically equivalent, but simpler, approach instead utilises the Hilbert transform. In a previous study, the Hilbert transform was applied to absorption spectra in order to infer the sole refractive index of an atomic medium in the absence of an external magnetic field. The presence of a magnetic field causes the medium to become birefringent and dichroic, and therefore it is instead characterised by two refractive indices. In this study, we apply the same Hilbert transform technique to independently measure both refractive indices of a birefringent atomic medium, leading to an indirect measurement of atomic magneto-optical rotation. Key to this measurement is the insight that inputting specific light polarisations into an atomic medium induces absorption associated with only one of the refractive indices. We show this is true in two configurations, commonly referred to in literature as the Faraday and Voigt geometries, which differ by the magnetic field orientation with respect to the light wavevector. For both cases, we measure the two refractive indices independently for a Rb thermal vapour in a 0.6 T magnetic field, finding excellent agreement with theory. This study further emphasises the application of the Hilbert transform to the field of quantum and atomic optics in the linear regime.

DOI: 10.1088/1361-6455/ad5e24

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Abstract This paper provides details of a spectroscopic investigation of a thermal 87Rb atomic vapour. The experiment was conducted with an external magnetic field of 1.5 T in the Voigt geometry. Very good quantitative agreement between experimental data and theory is found for all four Stokes parameters—with RMS errors of ∼1.5% in all cases. From the fits to our experimental data a value for the magnetic field strength is extracted, along with the angle between the magnetic field and the polarisation of the light. The effects of the cell window birefringence on the optical rotation signals are characterised. This allows us to carry out precise measurements at a high field strength and arbitrary geometries, allowing further development of possible areas of application for atomic magnetometers.

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Large Faraday rotations can be generated by circular birefringence of atomic samples in an axial magnetic field in the vicinity of atomic resonance lines. More generally, magneto-optical effects in atomic samples include circular dichroism in addition to birefringence, resulting in a modification of the ellipticity as well as the polarization alignment. Usually such effects are investigated for homogeneous linear polarizations, but the mechanisms apply also to polarization structures such as vector vortices. We investigate the effect of optical activity of a rubidium vapor in the hyperfine Paschen–Back regime along the D2 line, for the example of azimuthally polarized input light. We show that for low atomic densities, circular birefringence dominates over dichroism, and azimuthal polarization is rotated toward radial polarization. The rotation angle increases with increasing optical densities. At high vapor temperatures, dichroism becomes more and more relevant, leading to intricate variations of both alignment and ellipticity. Our results shine new light on the interplay between different magneto-optic effects at strong magnetic fields. Their highly sensitive response to detuning may find applications in spectroscopy and quantum sensing.