Ultracold Rydberg dimers: a toolbox for quantum dynamics, vibronics, and precision spectroscopy

Abstract

This cumulative thesis investigates the dynamical and spectral properties of Ultralong-range Rydberg molecules (ULRM), a peculiar form of quantum matter bound through the low-energy scattering between a Rydberg electron and nearby ground-state perturbers. Particularly, our focus lies on trilobite and butterfly molecules, featuring a Rydberg electron with high orbital angular momentum l that undergoes S-wave and P-wave scattering with the perturber, respectively. Their internal structure is usually studied within the confines of the Born-Oppenheimer approximation, wherein the constituent electronic and nuclear configurations can be treated as separate. While the adiabatic stationary states of these molecules have been examined with much scrutiny, their dynamic and nonadiabatic features were left relatively unexplored. Consequently, this thesis aims to further our understanding of ULRM, by exploring the role of nonadiabatic effects and dynamical effects, while also investigating the underlying spin-dependent electron-atom scattering channels. The results of these investigations are published as a series of articles, whose contents can be broadly classified into three different yet overlapping themes.

The first theme catalogues our study of various nonadiabatic phenomena occurring in the spectra of the ULRM, as a result of the breakdown of the Born-Oppenheimer approximation. We use both Landau-Zener based semi-classical calculations, and exact two-channel vibronic spectral calculations to locate and study the nonadiabatic stabilization and decay of molecular states. In 23Na dimers, we investigate the effects of avoided crossings between the trilobite and energetically nearby l =2 quantum defect state, and discover above-threshold resonance states, without an adiabatic equivalence. We also observe nonadiabatic localization effects in the radial probability density of vibronic states. In 87Rb dimers, we were able to recognize and understand the observation of high-lying trilobite states, stabilized against decay to the $P$-wave butterfly state via avoided crossings, through nonadiabatic surface hopping. In both cases, we find that the nonadiabatic coupling strengths and their spectral influence is highly dependent on the principal quantum number n, of the Rydberg electron.

The second theme explores the internal quantum dynamics of the ULRM, describing the motion of nuclear wavepackets in the adiabatic PECs. For appropriate n-values, we find that pure trilobite potentials feature an oscillatory structure that can act as a molecular diffraction grating, by backscattering incedent wavepackets with appropriate initial conditions. We study the phenomena using Fourier analysis, and propose a pump-probe scheme that utilizes vibrational states in low-$\ell$ potentials, to experimentally resolve the diffraction effect. As an extension, we also study the effects of including the P-wave butterfly states into our model, and find that nonadiabatic interactions can stabilize the propagating diffraction pattern against shape resonance-induced decay pathways. Our work also explores other exciting dynamical effects, like multi-well interference patterns, exhibited by the time-evolving molecule.

Our final theme of research is centered around the precision spectroscopy of bound ULRM states, combining state-of-the-art numerical and experimental methodology. A high-precision spectroscopic study of the binding energies of these molecules reveal the spin structure, and scattering phase shifts of the electron-atom scattering problem in extremely low energies, typically inaccessible to free electrons. We exploit the predominant S-wave nature and the deep potential energy structure of the trilobite molecule to directly access the electron-atom scattering channel and extract the corresponding scattering lengths with great sensitivity. Moreover, we are also able to observe and characterize for the first time, bound singlet P-wave states of the ULRM, a critical intermediary step in the creation of ultracold anions and two-component neutral plasmas.