Anderson localization of a Rydberg electron

Abstract

Highly excited Rydberg atoms inherit their level structure, symmetries, and scaling behavior from the hydrogen atom. We will demonstrate that these fundamental properties enable a thermodynamic limit of a single Rydberg atom subjected to interactions with nearby ground state atoms. The limit is reached by simultaneously increasing the number of ground state atoms and the level of excitation of the Rydberg atom, for which the Coulomb potential supplies infinitely many and highly degenerate excited states. Our study reveals a surprising connection to an archetypal concept of condensed matter physics, Anderson localization, facilitated by a direct mapping between the Rydberg atom's electronic spectrum and the spectrum of a tight-binding Hamiltonian. The hopping amplitudes of this tight-binding system are determined by the arrangement of ground state atoms and can range from nearest-neighbor to power-law-tailed to effectively infinite-range, giving rise to different localization scenarios. For arrangements yielding nearest-neighbor hopping amplitudes we identify clear signatures of the Anderson localization of the Rydberg electron.

Dynamics of atoms within atoms

“…Two central conclusions are, that mean-field theory remains applicable to the Rydberg electron in a BEC, and that the detailed shape of the interaction potential at short distances, which is not too well known, is not crucial. Together, these findings provide a critical milestone that enables BEC as an instrument for in situ real time probing of dynamical processes in ultracold atomic physics and chemistry, ranging from polaron formation dynamics [3][4][5] over angular momentum changing collisions [15,22], the dynamical formation of ultra-long range molecules [22,24,55], or localized states [56] and ionisation [57][58][59][60] to phonon mediated Yukawa interactions [61]. In all of these, the initially excited Rydberg atom can be in an s-state, on which we focus here, while cold scattering processes might then causes state changes or acceleration of this atom.…”