Atomic state interferometry for complex vector light

TL;DR

The paper addresses how complex vector light interacts with an atomic state interferometer by developing an analytical framework that maps polarization-structured fields onto a four-state phaseonium. It converts the closed optical-magnetic loop into a ladder of partially dressed states $|\psi_c\rangle$, $|\psi_g\rangle$, and $|\psi_d\rangle$ with energies $E_c,E_g,E_d$ and hopping rates $\mathcal{J}_{ec},\mathcal{J}_{cg},\mathcal{J}_{gd}$, introducing polarization parameters $\chi$ and $\psi'$ that govern the couplings through $J$ and $\bar{J}$. The central result for absorption is $P_{d\rightarrow e} \simeq \frac{1}{36 \Gamma^6} |\mathcal{J}_{ec} \mathcal{J}_{cg} \mathcal{J}_{gd}|^2$, highlighting how spatial polarization structure and magnetic-field orientation shape the excitation pathways via a spatially dependent dark-state mechanism. The framework is demonstrated across polarization vortices, hybrid vector beams, optical skyrmions, and Hermite-Gaussian lattices, revealing rich, beam-dependent absorption patterns that encode information about polarization topology and magnetic alignment, with potential applications in vector-beam metrology and magnetometry.

Abstract

Features of complex vector light become important in any interference effects, including scattering, diffraction, and non-linear 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 inter action 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.

Figures (10)

• Figure 1: Schematic level scheme of the atomic state interferometer. Inset: Geometry of light propagation (along $\hat{z}$) and the magnetic field direction, defined by the azimuthal angle $\phi_B$ and the inclination angle $\theta_B$. a) Atomic state interferometer with optical and magnetic transitions. b) Intermediate partially dressed states. c) Partially dressed state systems, with optical coupling between the excited state and $\ket{\psi_c}$, with magnetic coupling driving transitions to the gray state $\ket{\psi_g}$ and from there to the dark state $\ket{\psi_d}$.
• Figure 2: Definition of the optical polarization in terms of the Poincaré sphere and the associated polarization colour map. The spherical coordinates $\chi$ and $\psi$ uniquely define the polarization ellipse.
• Figure 3: Energies of the partially dressed ground states $|\psi_c\rangle$, $|\psi_g\rangle$, and $|\psi_d\rangle$ as a function of the optical polarization and magnetic field orientations. The polarization states show the energies for a magnetic field that tilted with respect to the propagation direction by an angle $\theta_B$ between 0 and $\pi/2$.
• Figure 4: Absorption rate, proportional to the probability for an atom to transition between the dark and excited state as a function of the optical polarization and magnetic field inclination. The first row shows $P_{d\to e}$, which is a product of the probabilities $P_{g\to c}$ (second row), $P_{d\to g}$ (third row), and $P_{c\to e}$ (independent of polarization and magnetic field angle, not shown. All transition rates are peak normalised for $P_{d\to e}$. Here we assume $\Omega_L\ll\Gamma$.
• Figure 5: Absorption patterns for light with a variety of polarization profiles with varying ellipticity ranging from homogeneous right polarization in row a) to radial polarization in row d) for various magnetic field inclinations $\theta_B$ (for $\phi_B =0$ so that the magnetic field rotates in the $x$-$z$ plane). Each row shows from left to right the polarizations on the Poincaré sphere with the arrow indicating $\varphi=0$, the corresponding beam profile, followed by the absorption patterns for $\theta_B\approx 0$, $\theta_B=\pi/8$, $\theta_B=\pi/4$, $\theta_B=3\pi/8$ and $\theta_B=\pi/2$ respectively. White indicates maximum absorption.