We present a comprehensive study of the diverse properties of heteronuclear Rydberg molecules, placing a special emphasis on those composed of the light alkali-metal atoms, Li, Na, and K. Electron-atom scattering phase shifts, which determine the strength of the molecular bond, are calculated at very low energy and then used in a spin-dependent theoretical model to calculate accurate Rydberg molecule potential-energy curves. The wide parameter range accessible by combining the various properties of different alkali-metal atoms often leads to hybridized electronic states accessible via one or two photon excitation schemes. This analysis of heteronuclear molecules leads to a prediction that the relative densities and spatial distributions of atoms in an ultracold mixture can be probed at controllable length scales via spectroscopic detection of these molecules.
We present a comprehensive study of the diverse properties of heteronuclear Rydberg molecules, placing a special emphasis on those composed of the light alkali-metal atoms, Li, Na, and K. Electron-atom scattering phase shifts, which determine the strength of the molecular bond, are calculated at very low energy and then used in a spin-dependent theoretical model to calculate accurate Rydberg molecule potential-energy curves. The wide parameter range accessible by combining the various properties of different alkali-metal atoms often leads to hybridized electronic states accessible via one or two photon excitation schemes. This analysis of heteronuclear molecules leads to a prediction that the relative densities and spatial distributions of atoms in an ultracold mixture can be probed at controllable length scales via spectroscopic detection of these molecules.
The work presented in this dissertation represents a comprehensive study on long-range interactions between alkali Rydberg atoms. As a consequence of their size, Rydberg atoms possess very large dipole moments, making them highly sensitive to external fields and to other Rydberg atoms. The strong dipole-dipole interaction between two Rydberg atoms results in a mixing of their angular momentum characters, which is the cornerstone of the work presented here. We describe the ℓ-mixing between various local molecular asymptotes through a residual Coulomb potential, assuming no electron cloud overlap. We then directly diagonalize an interaction Hamiltonian consisting of these Rydberg-Rydberg interactions and spin-orbit (fine structure) coupling in the Hund's case (c). In this manner, we calculate potential energy curves for various molecular symmetries and find that some of these curves exhibit deep potential wells, capable of supporting very extended bound molecular states ( macrodimers). We analyze the specific structure of the ℓ-mixing for these potential wells and derive convenient n-scaling relations for both their equilibrium separations Re and well depths De. We also explore various properties of the macrodimers, including their response to small electric fields and stability with respect to predissociation. We note throughout the dissertation that the detection of such extended dimers could help progress studies in a variety of areas such as exotic, ultracold chemistry and quantum information and computing. To facilitate detection, we propose a scheme to form and study the macrodimers via photoassociation (PA). We present calculated PA lineshapes from two different electronic ground states based on a harmonic trapping model. We find that both PA signals vary significantly with the laser detunings, indicating that different ℓ-characters could be probed at different equilibrium lengths. Finally, we extend the two-body formalism to the case of three interacting Rydberg atoms and present preliminary results for triply excited 58p rubidium atoms along a common axis. We provide a few examples of surface plots corresponding to different local asymptotes, each with a unique three-dimensional "landscape" and discuss the relevance of the physical features. The highlight of our analysis is the appearance of a potential well, which indicates the formation of a linear trimer. ^
Ultralong-range Rydberg molecules, composed of an excited Rydberg atom and a ground-state atom, are characterized by large bond lengths, dipole moments, sensitivity to external fields, and an unusual binding mechanism based on low-energy elastic electron scattering. Although Rydberg molecules formed between alkali atoms have received the most attention, the additional complexity found in atoms with more than a single valence electron poses new theoretical challenges as well as new possibilities for control and design of the molecular structure. In this paper, we extend the theory of Rydberg molecules to include the additional spin coupling of the Rydberg states of a multivalent atom. We employ this theory to describe the properties of Rydberg molecules composed of mercury atoms. We calculate the potential energy curves of both heteronuclear (Hg∗Rb) and homonuclear (Hg∗Hg) molecules. In the former case, we propose the realization of long-range spin entanglement and remote spin flip. In the latter, we show how long-lived metastable molecular states of Hg∗Hg exist as resonances above the dissociation threshold.
Ultracold diatomic molecules find application in quantum studies ranging from controlled chemistry and precision measurement physics to quantum many-body simulation and potentially quantum computing. Accurate knowledge of molecular properties is required to guide and explain ongoing experiments. Here, in an extensive and comparative study, we theoretically investigate the electronic properties of the ground-state diatomic molecules composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 78 heteronuclear and homonuclear diatomic combinations, including 21 alkali-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic states, 36 alkali-metal--alkaline-earth-metal molecules in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state, and 21 alkaline-earth-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state. We calculate potential energy curves, permanent electric dipole moments, and polarizabilities using the hierarchy of coupled-cluster methods up to CCSDTQ with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We collect and analyze corresponding spectroscopic constants. We estimate computational uncertainties and compare the present values with previous experimental and theoretical data to establish a different theoretical benchmark. The presented results should be useful for further application of the studied molecules in modern ultracold physics and chemistry experiments.
Abstract Ultralong-range Rydberg molecules (ULRMs) comprise a Rydberg atom in whose electron cloud are embedded one (or more) ground-state atoms that are weakly-bound through their scattering of the Rydberg electron. The existence of such novel molecular species was first predicted theoretically in 2000 but they were not observed in the laboratory until 2009. Since that time, interest in their chemical properties, physical characteristics, and applications has increased dramatically. We discuss here recent advances in the study of ULRMs. These have yielded a wealth of information regarding low-energy electron scattering in an energy regime difficult to access using alternate techniques, and have provided a valuable probe of non-local spatial correlations in quantum gases elucidating the effects of quantum statistics. Studies in dense environments, where the Rydberg electron cloud can enclose hundreds, or even thousands, of ground-state atoms, have revealed many-body effects such as the creation of Rydberg polarons. The production of overlapping clouds of different cold atoms has enabled the creation of heteronuclear ULRMs. Indeed, the wide variety of atomic and molecular species that can now be cooled promises, through the careful choice of atomic (or molecular) species, to enable the production of ULRMs with properties tailored to meet a variety of different needs and applications.
Abstract Ultralong-range Rydberg molecules (ULRMs) have attracted significant interest due to their unique formation mechanisms and distinctive properties. We theoretically investigate the formation and characteristics of heteronuclear ULRMs, focusing on Rb-Cs systems. We calculate the vibrational energy levels of nS heteronuclear ULRMs and extend our analysis to polyatomic systems, tracing the evolution of binding energies as the molecular configuration changes. Our theoretical results are presented in terms of potential energy curves and the associated vibrational spectra, providing insight into the formation dynamics of these systems. These results also provide a framework for experimental efforts in probing heteronuclear ULRMs, which serve as a sensitive platform for investigating the fundamental properties of Rydberg atoms and their interactions with ground-state atoms, while providing a benchmark for \textit{ab initio} calculations.
In this article we address the general approach for calculating dynamical dipole polarizabilities of small quantum systems, based on a sum-over-states formula involving in principle the entire energy spectrum of the system. We complement this method by a few-parameter model involving a limited number of effective transitions, allowing for a compact and accurate representation of both the isotropic and anisotropic components of the polarizability. We apply the method to the series of ten heteronuclear molecules composed of two of (Li,Na,K,Rb,Cs) alkali-metal atoms. We rely on both up-to-date spectroscopically-determined potential energy curves for the lowest electronic states, and on our systematic studies of these systems performed during the last decade for higher excited states and for permanent and transition dipole moments. Such a compilation is timely for the continuously growing researches on ultracold polar molecules. Indeed the knowledge of the dynamic dipole polarizabilities is crucial to model the optical response of molecules when trapped in optical lattices, and to determine optimal lattice frequencies ensuring optimal transfer to the absolute ground state of initially weakly-bound molecules. When they exist, we determine the so-called ‘magic frequencies’ where the ac-Stark shift and thus the viewed trap depth, is the same for both weakly-bound and ground-state molecules.