Indirect measurement of atomic magneto-optical rotation via Hilbert transform
arxiv(2024)
摘要
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.
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