Atomic state interferometry for complex vector light

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.