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arXiv:2503.18927 · Physical Review A

Interaction of a Poincaré beam with optically polarized atoms in the presence of a constant magnetic field

S. Ramakrishna, S. Fritzsche

Published Jun 11, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/5r63-5hl1

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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.
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.
Absorption profiles of vector light upon interaction with atomic vapor carries distinct signatures of an external magnetic field vector. However, this signature becomes ambiguous for antiparallel magnetic field vectors of equal magnitude, which makes their absorption profiles visually indistinguishable. To resolve this ambiguity, we present a theoretical analysis of the interaction of vector light with optically polarized atoms immersed in reference and test magnetic fields. Furthermore, we demonstrate the complete characterization of the arbitrarily oriented test magnetic field via a Fourier analysis of the absorption profile. This analysis reveals a one-to-one correspondence between the magnetic field properties and the profile's contrast and rotational angle. Our findings open an avenue to design an optical vector atomic magnetometer based on structured light fields.
High-precision Mz/Mx atomic magnetometers have “dead zones”, where the magnetic-field information will be lost because the light–atom interaction vanishes at specific field angles. To suppress dead zones, we propose a scheme with polarization-gradient optical pumping field by using counter-propagating lin⊥lin beams. We found through experiments that the lin⊥lin scheme eliminates dead zones in the transverse plane of the probe beam propagation (minimum ∼40% normalized signal) but leaves two noncanonical magic-angle-like directions (≈30 ∘ and 150 ∘ ) in the longitudinal plane, which is distinct from the standard tensor magic angle (≈54 ∘ and 126 ∘ ). These observations are quantitatively explained using a multipole-based model formulated in terms of an effective, spatially averaged density matrix, which is the first time that the spatial average density matrix has been used for energy state analysis in atomic magnetometers. Under the probing of a linearly polarized light, the measured signal is determined by the field-angle-dependent projection of the atomic longitudinal alignment moment ( m 2,0 ) onto the B 0 -defined quantization axis. Compared with other dead-zone elimination schemes, our scheme avoids polarization modulation and multi-cell architectures, showing potential for improving the spatial response range of compact atomic magnetometry.
Abstract The degree of Zeeman splitting of ground-state sublevels in the presence of a magnetic field can be measured using atomic sensors. The coherence of the spins in the ensemble affects the efficiency of an atomic magnetometer. The sensitivity of these sensors depends on the line width of the magnetic resonance curve, which is related to the coherence lifetime of the atomic spins. Atomic polarization influences the optical properties of the medium, making it anisotropic. The relatively long lifetime of ground-state polarization is a useful tool for measuring the energy-level splitting. The modification associated with the atomic coherence in the presence of an external magnetic field leads to interesting absorption effects in the atomic environment. The splitting of magnetic sublevels and the transition between them under the application of a magnetic field are quantum mechanical images of the interaction between a field and an atomic spin that must be analyzed using a density matrix. In the present work, magneto-optical effects with circularly polarized light such as the dynamic properties and evolution of sublevels of the rubidium-87 D1 line and the absorption properties of the atomic polarized environment are studied theoretically using the reduced density matrix approach.
In this paper, we present the experiment and the theory scheme of light-atom interaction in atomic magnetometers by using a hybrid Poincaré beam (HPB) to solve an annoying problem, named “dead zone.” This kind of magnetometer can be sensitive to arbitrary directions of external magnetic fields. The HPB has a complex polarization distribution, consisting of a vector radially polarized beam and a scalar circularly polarized beam in our experiment. These two kinds of beams have different directions of dead zones of external magnetic fields; thereby, the atomic magnetometer with an HPB can avoid the non-signal area when the direction of the external magnetic field is in the plane perpendicular to the light polarization plane. Furthermore, the optical magnetic resonance (OMR) signal using an HPB still has no dead zones even when the direction of the external magnetic field is in the plane parallel to the polarization plane in our scheme. Our work has the potential to simplify and optimize dead-zone-free atomic magnetometers.
In this paper, we present an analysis of the amplitude variations of the opto-magnetic resonance absorption signals obtained in a single-beam magnetometer driven by radially or azimuthally polarized light (RPL/APL). It is shown that optically polarized atoms driven by cylindrical vector beams obtained only the alignment of atomic multipole moments but not the orientation, which is in good agreement with our simulation and experimental results. In comparison with the plane polarized pump light fields, cylindrical vector beams with much more complete electric vector polarization distribution in the transverse plane, make it unlikely to create the "emptying state " (no-atom populated) among the ground-state Zeeman sublevels for any possible orientation of the applied static magnetic field. These characteristics of the RPL/APL lead to generally smaller atomic population difference and lower response intensity of the transmitted signal. The tensor decomposition of atomic polarized states and the evolution of atomic multipole moments with the sweeping radio frequency (RF) field offer the way to show the magnetic orientation sensitivity of the radially or azimuthally polarized probe light, which possess similar profiles as that of the linearly polarized light, only with a constant phase lag of about π/2 and obvious amplitude differences.