Nonlinear quantum transduction of weak topological impurities

Detecting weak field perturbations at an optical-vortex node is a fundamental challenge across wave physics, as the local signal contrast typically scales quadratically with the impurity amplitude when no reference field is used. Here, we propose a complementary, spatially resolved diagnostic that exploits the strongly nonlinear response of an electromagnetically induced transparency (EIT) medium to transduce weak topological impurities into probe transmission. Using a vortex beam with a weak coherent admixture as a concrete realization, we show theoretically that EIT coherence converts the weak field that lifts the nominal vortex node into a highly sensitive, macroscopic transmission contrast. A resonant weak-probe model with representative cold- Rb 87 parameters predicts a per-exposure detection floor for the impurity amplitude at the level of a few × 10 − 3 , relative to a separately characterized, preaveraged pure-vortex reference. We quantify the intrinsic and experimental limits of this response, analyzing its dependence on coupling strength, ground-state decoherence, optical depth, two-photon detuning, and Maxwell-Boltzmann thermal motion. While not a complete, basis-independent measurement of modal purity, this method provides a calibrated, local all-optical diagnostic for weak coherent field admixtures at a known vortex node.