Kapitza-Dirac Effect of Higgs Waves from Light-induced Vortices in superconductors

We investigate how structured light such as Laguerre-Gauss beam can quantum print spatial and topological structures onto superconductors, unveiling Kapitza-Dirac interference of Higgs waves. By solving the time-dependent Ginzburg–Landau equation with a second-order time derivative, we show that structured illumination generates vortex lattices and simultaneously excites propagating Higgs-mode oscillations of the order-parameter amplitude. The resulting Higgs waves coherently scatter from the light-induced vortex array, producing interference patterns that encode their spatial phase coherence, analogous to electron diffraction in the original Kapitza–Dirac effect. This dynamics enables the coexistence and coupling of amplitude and phase excitations in driven superconductors. Our findings establish a unified framework for manipulating nonequilibrium superconducting states with structured light and propose Higgs-wave interference as a powerful probe of vortex dynamics, opening new routes toward imaging and controlling collective quantum excitations far from equilibrium via quantum printing approach.