Nonlocal nonlinear optical X waves and their active control in a Rydberg atomic gas

X waves are a special type of wave packet that can maintain their transverse profile of X shape during propagation, and they are of much interest for the study of fundamental physics and practical applications. Here we present a scheme to generate nonlinear X waves and realize their active control by using a cold gas of Rydberg atoms via electromagnetically induced transparency (EIT). We show that, due to the EIT effect contributed by a control laser field and the strong, nonlocal Kerr nonlinearity contributed by Rydberg-Rydberg interaction between atoms, the system supports high-dimensional, nonlocal, and nonlinear optical X waves, which have low propagation loss, ultraslow propagation velocity, and ultralow generation power. We also show that the stability domain of such X waves can be greatly enlarged by increasing the nonlocality degree of the Kerr nonlinearity, and their motion trajectory can be manipulated by using an external magnetic field. Our study opens a route for generating and controlling nonlocal ultraslow nonlinear optical X waves, which may have promising applications in optical information processing and transmission.