All-optical Stern-Gerlach effect in a parity-time anti-symmetric nonlinear refractive medium

The famous Stern-Gerlach experiment, which established spin as an inevitable degree of freedom, is one of the cornerstones in the development of quantum physics. Over the last few decades, the existence of spinors has been widely observed in various photonic systems, and it provides a fertile ground for exploring various quantum optical phenomena. In optics, Stern-Gerlach (SG)-like splitting led laser beam-engineering forms as a pragmatic route for creating photonic quantum states. Here, we present a third-order nonlinear optics-based analytical model and an experimental route for observing all-optical SG effects in radially symmetric gauge potentials. The SG-like splitting manifests through the generation of a topologically trivial dark-hollow Gaussian (DHG) beam by the negative refractive nonlinearity of the medium. The analytical formalism elucidates the DHG beam generation by virtue of a gauge-dependent synthetic electric field in a parity-time (<i>P</i><i>T</i>) anti-symmetric nonlinear dynamical system. The simulations, interferograms, as well as intensity profile measurements of a DHG beam, provides a distinct signature of orbital angular momentum conservation in the process.