Photoionization microscopy of Rydberg hydrogen atom in a non-uniform electrical field

In this paper, we investigate the photoionization microscopy of the Rydberg hydrogen atom in a gradient electric field for the first time. The observed oscillatory patterns in the photoionization microscopy are explained within the framework of the semiclassical theory, which can be considered as a manifestation of interference between various electron trajectories arriving at a given point on the detector plane. In contrast with the photoionization microscopy in the uniform electric field, the trajectories of the ionized electron in the gradient electric field will become chaotic. An infinite set of different electron trajectories can arrive at a given point on the detector plane, which makes the interference pattern of the electron probability density distribution extremely complicated. Our calculation results suggest that the oscillatory pattern in the electron probability density distribution depends sensitively on the electric field gradient, the scaled energy and the position of the detector plane. Through our research, we predict that the interference pattern in the electron probability density distribution can be observed in an actual photoionization microscopy experiment once the external electric field strength and the position of the electron detector plane are reasonable. This study provides some references for the future experimental research on the photoionization microscopy of the Rydberg atom in the non-uniform external fields.