A matter of size: exploring atom-ion interactions on mesoscopic and macroscopic length scales

Abstract

The desire to further our understanding of complex physical phenomena and exploit quantum mechanics for useful applications has driven the development of controlled quantum systems which are well-isolated from their environment. Two of the earliest and most notable platforms are (i) trapped ultracold gases of neutral atoms and (ii) trapped ions. Due to the numerous achievements of these two platforms, interest emerged in combining both within a single setup for probing atom-ion interactions. Unlike interactions between neutral species, atom-ion interactions extend over mesoscopic length scales of hundreds of nanometres. Not only do atom-ion systems permit studies of charge-neutral chemistry - responsible among other things for the formation of water in the interstellar medium - they further provide a distinctive setup for quantum information processing and the simulation of many-body systems. Today, many quantum information and simulation platforms make considerable use of the internal structure of single atoms. In particular, highly-excited atomic states have proved extremely useful for engineering entanglement between pairs of atoms over macroscopic distances. Within the context of atom-ion systems, the use of these so-called Rydberg atoms was initially proposed as a path to circumventing challenges in observing ultracold atom-ion collisions. More recently however, ion-Rydberg systems have proved themselves as attractive setups for observing fundamental chemical processes in situ due to their inherently slow vibrational dynamics on the order of microseconds. The path to understanding and exploiting many-body phenomena often rests on intuition developed in systems with fewer numbers of particles – a notable example being the Rydberg blockade mechanism, which emerged out of the understanding of interactions between pairs of Rydberg atoms. To that end, this thesis is devoted to the study of few-body ultracold systems of atoms and ions from a theoretical perspective. We consider not only mesoscopic-scale atom-ion interactions present in the electronic ground- state, but also explore interactions between ions and Rydberg atoms, where interactions inflate to the macroscopic-scale. We present our results cumulatively in five successive scientific contributions, which can be roughly grouped into three different themes. Our first theme examines how atom-ion interactions compete with other forces to influence a system’s static properties. Here, we explore a trapped system of two ground-state bosonic atoms interacting with an ion. We characterise the energy and spatial structure of the lowest few eigenstates in different regimes of interatomic interaction and relative trapping strength of the two species. Our second theme is quantum control. Here, we first consider the use of an externally-swept ion-like potential for deterministically driving trapped atoms between different vibrational states. In a subsequent work in collaboration with experiment, we examine the collisional dynamics of an interacting ion-Rydberg pair. We develop a semi-classical coupled-channel model to describe these collisions and explore the tunability of beyond Born-Oppenheimer physics exhibited by the colliding pair. Our final theme concerns the formation and stability of weakly-bound triatomic Rydberg molecular ions. In one work, we reveal that a bound ion-Rydberg dimer can capture additional neutral ground-state atoms through attractive scattering with the Rydberg electron. Ion-induced mixing of different Rydberg states leads to distinctive patterns of maxima in the electronic density of the Rydberg electron, which support both linear and non-linear triatomic configurations. In our final work, we examine a system of two cations interacting with a Rydberg atom. The large repulsion between the cation pair means that such systems are generally unstable. However, we find that the ion-Rydberg interaction can stabilise the system against Coulomb explosion above a critical value of the principal quantum number. In other words, introducing additional energy to the system in the form of a Rydberg excitation can paradoxically make it more stable.