Fast and robust cat state preparation utilizing higher order nonlinearities in Rydberg ensembles

In optical and solid-state architectures, low-order nonlinearities are commonly exploited for quantum state preparation due to their practical accessibility and controllability, while higher-order contributions are typically much weaker and treated as unwanted perturbations. Here, we alternatively show that detuned Rydberg ensembles provide a natural platform where higher-order Kerr nonlinearities can become comparable in strength to lower-orders near multiphoton resonances. We demonstrate that these nonlinearities can be harnessed as a resource for the rapid preparation of non-Gaussian states, with the coexistence of multiple Kerr orders substantially accelerating the evolution of an initial coherent state into Schr\"odinger cat states. Furthermore, by combining the nonlinear dynamics with a controllable linear drive, we can gain the full control over the evolution trajectory, thereby achieving cat-state generation directly from vacuum on timescales beyond the genuine Kerr evolution. Our results establish a paradigm in which naturally occurring higher-order nonlinearities are transformed from unwanted imperfections into a valuable resource for quantum state engineering.