Rydberg atoms in D dimensions: entanglement, entropy and complexity

Abstract

Rydberg atoms and excitons are composed so that they have a hydrogenic energy level structure governed by the Rydberg formula. They are relevant per se and for their numerous applications, e.g. facilitating the creation of novel quantum devices in quantum technologies which are inherently robust, miniature, and scalable (basically because they exist in solid-state platforms) and the realization of synthetic dimensions in numerous quantum-mechanical systems, giving rise to quantum matter which can behave as if it were in dimensions other than three. However the quantification of their internal disorder is scarcely known. Here we show and review the knowledge of dispersion, entanglement, physical entropies (Rényi, Shannon) and complexity-like measures of D-dimensional Rydberg systems with D⩾2 in both position and momentum spaces. These uncertainty quantifiers are expressed in terms of D, the potential strength and the hyperquantum numbers of the Rydberg states. This has been possible because of the fine asymptotics of algebraic functionals the Laguerre and Gegenbauer polynomials which, together with the hyperspherical harmonics, control the Rydberg wavefunctions.