Kapitza-Dirac blockade: A universal tool for the deterministic preparation of non-Gaussian oscillator states

Harmonic oscillators count among the most fundamental quantum systems with important applications in molecular physics, nanoparticle trapping, and quantum information processing. Their equidistant energy level spacing is often a desired feature, but at the same time a challenge if the goal is to deterministically populate specific eigenstates. Here, we show how interference in the transition amplitudes in a bichromatic laser field can suppress the sequential climbing of harmonic oscillator states (Kapitza-Dirac blockade) and achieve selective excitation of energy eigenstates, Schr\"{o}dinger cats and other non-Gaussian states. This technique can transform the harmonic oscillator into a coherent two-level system or be used to build a large-momentum-transfer beam splitter for matter-waves. To illustrate the universality of the concept, we discuss feasible experiments that cover many orders of magnitude in mass, from single electrons over large molecules to dielectric nanoparticles.