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arXiv:2509.01561 · Physical Review A

Probing the isolated vector magnetic field of structured laser beams by atoms

R. P. Schmidt, S. Martín-Domene, A. A. Peshkov, C. Hernández-García, A. Surzhykov

Published Nov 18, 2025• 0 citations
arXivHTMLPDF

Abstract

Electric and magnetic fields are inherently coupled in an electromagnetic wave. However, structured light beams enable their spatial separation. In particular, azimuthally polarized laser beams exhibit a localized magnetic field on-axis without the electric counterpart. A recent study by Martín-Domene [S. Martín-Domene , ] has shown that combining these beams enables the generation of locally isolated magnetic fields with a controllable direction and phase. In the present paper, we propose a method to probe and characterize such magnetic fields by studying their interaction with a single trapped atom. In order to theoretically investigate magnetic sublevel populations and their dependence on the relative orientation and phase—i.e., the —of the isolated magnetic field, we use a time-dependent density-matrix method based on the Liouville–von Neumann equation. As illustrative cases, we consider the 2 s 2 2 p 2 P 0 3 − 2 s 2 2 p 2 P 1 3 , 1 s 2 2 s 2 S 0 1 − 1 s 2 2 s 2 p P 2 3 , and 2 s 2 2 p P 1 / 2 2 − 2 s 2 2 p P 3 / 2 2 transitions in Ca 14 + 40 , Be 10 , and Ar 13 + 38 , respectively. Our results indicate that monitoring atomic populations serves as an effective tool for probing isolated vector magnetic fields, which opens avenues for studying laser-induced processes in atomic systems where electric-field suppression is critical.

DOI
10.1103/b3zw-mwrn

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Electric and magnetic fields are inherently coupled in an electromagnetic wave. However, structured light beams enable their spatial separation. In particular, azimuthally polarized laser beams exhibit a localized magnetic field on-axis without the electric counterpart. A recent study by Martín-Domene [S. Martín-Domene , ] has shown that combining these beams enables the generation of locally isolated magnetic fields with a controllable direction and phase. In the present paper, we propose a method to probe and characterize such magnetic fields by studying their interaction with a single trapped atom. In order to theoretically investigate magnetic sublevel populations and their dependence on the relative orientation and phase—i.e., the —of the isolated magnetic field, we use a time-dependent density-matrix method based on the Liouville–von Neumann equation. As illustrative cases, we consider the 2 s 2 2 p 2 P 0 3 − 2 s 2 2 p 2 P 1 3 , 1 s 2 2 s 2 S 0 1 − 1 s 2 2 s 2 p P 2 3 , and 2 s 2 2 p P 1 / 2 2 − 2 s 2 2 p P 3 / 2 2 transitions in Ca 14 + 40 , Be 10 , and Ar 13 + 38 , respectively. Our results indicate that monitoring atomic populations serves as an effective tool for probing isolated vector magnetic fields, which opens avenues for studying laser-induced processes in atomic systems where electric-field suppression is critical.
Recent studies have highlighted the frequent applications of structured light modes in optically pumped atomic magnetometers. In this work, we theoretically explore how a Poincaré beam probes an optically polarized atomic medium. Specifically, we consider atoms polarized by a plane wave with linear polarization, immersed in a constant external magnetic field. We analyze how the polarization of the pump and probe light fields, along with the external magnetic field, impact the absorption profile. To this end, we employ a density-matrix approach based on the Liouville–von Neumann equation. Our results reveal that the absorption profile exhibits an asymmetric pattern that depends on the magnetic-field strength and the mutual orientation of the pump and probe light propagation directions relative to the quantization axis. For illustration, we assume the incoming radiation drives an electric dipole transition, 5 s 2 S 1 / 2 ( F = 1 ) → 5 p 2 P 3 / 2 ( F = 0 ), in rubidium atoms subjected to a magnetic field. These findings may aid in designing future experiments on optically pumped atomic magnetometers utilizing structured light modes.
Vector magnetometry using electromagnetically induced transparency with lin⊥linlin\perp linlin⊥lin polarization
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Features of complex vector light become important in any interference effects, including scattering, diffraction, and nonlinear processes. Here, we are investigating the role of polarization-structured light in atomic state interferometers. Unlike optical or atomic path interferometers, these facilitate local interference between atomic transition amplitudes and hence the orthogonal optical polarization components driving these transitions. We develop a fully analytical description for the interaction of generalized structured light with an atomic four state system, that is, multiply connected via optical as well as magnetic transitions. Our model allows us to identify spatially dependent dark states, associated with spatially structured absorption coefficients, which are defined by the geometry of the polarization state and the magnetic field direction. We illustrate this for a range of optical beams including polarization vortices, optical skyrmions, and polarization lattices. This results in a new interpretation and an enhanced understanding of atomic state interferometry, and a versatile mechanism to modify and control optical absorption as a function of polarization and magnetic field alignment.
In recent years great progress was made in the spatial control of light with dynamic phase and amplitude modulators such as spatial light modulators and digital micromirror devices. In this work we describe the theory and practice of light shaping with such devices, detailing the spatial control of amplitude, phase and polarisation of coherent laser beams. We use our expertise in generating and measuring light fields with spatially dependent polarisation structures to characterise the correlations between spatial modes and polarisation in such light fields. We do this by adapting concurrence, a quantum measure of entanglement, to these classical correlations. One of the most promising application of coherent laser light is in the control of atomic media via atom-light interactions. In this work we describe the construction of simple external cavity diode lasers designed for the generation of resonant light for atomic physics applications. We exploit these lasers and spatial light modulators to create and measure three-dimensional atomic population structures in a warm rubidium vapour. We also implement a magneto-optic and a dynamic dark spontaneous-force optical trap for rubidium. These traps produce dense (~ 10^11 cm^-3) and cold (~100 uK) clouds of rubidium atoms. We develop the theory of spatially dependent electromagnetically induced transparency in such traps using rate equations. We find that the absorption of linearly polarised light depends on the relative direction of a magnetic field and the light polarisation. We use the cold atom clouds to measure the direction of magnetic fields by using this dependence and laser beams with structured polarisation.