On the structure, dynamics, and chemistry of ultra-long-range Rydberg molecules

Abstract

In this cumulative thesis, we investigate ultra-long-range Rydberg molecules (ULRM), consisting of one highly excited Rydberg atom and one or several ground-state atoms, and occuring in ultracold atomic quantum gases. The molecular binding mechanism is based on the attractive Coulomb interaction between the Rydberg electron and the positively charged core of the Rydberg atom, as well as on the attractive low-energy electron-atom scattering off the neutral atoms. This electron-atom interaction can be modeled by a generalized Fermi pseudo potential including s- and p-wave contact interactions. In the Born-Oppenheimer approximation, this spawns oscillatory adiabatic potential energy surfaces that support vibrational bound states whose huge bond lengths are on the order of thousands of Bohr radii. We obtain these potentials via diagonalization of the electronic Hamiltonian within a finite basis set of electronic orbitals or via Green's function methods. The corresponding vibrational eigenstates are retrieved from solutions of the time-independent few-body Schrödinger equation using finite difference methods and discrete variable representations.

Our research spans different aspects of ULRM. One focus is the impact of spin interactions onto the diatomic molecular structure in the presence of an external magnetic field. The description of the molecular system includes the electronic spins of the atomic valence electrons as well as the nuclear spins and their interactions. In the case of dominant s-wave scattering, the spin structure allows for control over the molecular binding energy via the mixing of the singlet and triplet scattering channels. In the case of dominant p-wave scattering, the underlying fine structure of the ionic electron-atom system engenders a unique alignment mechanism of the molecular axis with respect to the field axis. The experimental observation of this alignment is utilized to perform a high-precision measurement of the ionic fine-structure splitting. In the absence of external fields, the presence of spin-spin and spin-orbit interactions is experimentally confirmed by unique doublet and triplet substructures of the vibrational levels.

A second focus is the formulation of specific applications of ULRM in broader physical frameworks. We propose a certain class of ULRM bound by singlet p-wave interaction as the ideal initial state for the photoassociation of a heavy Rydberg system. Heavy Rydberg systems are bound pairs of oppositely charged ions that resemble a Rydberg atom, but in which the electron is replaced by a heavy anion. Beyond that, we identify conical intersections in the potential energy surfaces of diatomic ULRM spanned in the adiabatic parameter of the internuclear distance and the synthetic dimension of the electron energy. The conical intersections have observable consequences for the rates of angular-momentum-changing transitions of colliding ground-state atoms with Rydberg atoms that can be obtained from a beyond Born-Oppenheimer treatment of the coupled potentials. Furthermore, we undertake a first investigation of the nuclear quantum dynamics of ULRM exposed to external electric fields, paving the way for the study of molecular decay processes and ultracold chemistry. The wave-packet propagation is obtained from the multiconfigurational time-dependent Hartree method that solves the time-dependent Schrödinger equation ab initio.

The third and final focus is on the formation of triatomic ULRM consisting of one Rydberg atom in an electronically mixed state of high angular momenta and two ground-state atoms. Here, the Rydberg electron takes the role of a mediator, inducing nontrivial inter-atomic three-body interactions. Stable trimer equilibrium configurations can be deduced from dimer states via a simple building principle. Different classes of trimers show largely varying geometric arrangement as well as confinement and, correspondingly, in some cases, the vibrational bending and stretching modes adiabatically decouple.