The most attractive and the most repulsive potential-energy curves for interaction between two Rydberg atoms in a broad superposition of internal angular momentum states are studied. The extreme Stark states have the largest dipole moments and provide the dominant contribution to the interaction which is then expressed as a long-range expansion involving the permanent multipole moments Q j of each polar atom. Analytical expressions are obtained for all Q j associated with principal quantum number n of H( n ) and permit the long-range expansion for the H( n )–H( n ') first-order interaction to be explicitly expressed analytically in terms of n , n ' and internuclear distance R . Possible quasi-molecular formation is investigated. Direct calculations show that the H( n = 2)–H( n ' = 2) interaction is capable of supporting 47 bound vibrational levels. As n increases, the long-range interaction becomes increasingly attractive so that molecular formation at large internuclear distances is expected to be scarcely possible for these extreme Stark levels.
The most attractive and the most repulsive potential-energy curves for interaction between two Rydberg atoms in a broad superposition of internal angular momentum states are studied. The extreme Stark states have the largest dipole moments and provide the dominant contribution to the interaction which is then expressed as a long-range expansion involving the permanent multipole moments Q j of each polar atom. Analytical expressions are obtained for all Q j associated with principal quantum number n of H( n ) and permit the long-range expansion for the H( n )–H( n ') first-order interaction to be explicitly expressed analytically in terms of n , n ' and internuclear distance R . Possible quasi-molecular formation is investigated. Direct calculations show that the H( n = 2)–H( n ' = 2) interaction is capable of supporting 47 bound vibrational levels. As n increases, the long-range interaction becomes increasingly attractive so that molecular formation at large internuclear distances is expected to be scarcely possible for these extreme Stark levels.
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. ^
Abstract We present an overview over theoretical models to describe adiabatic potential-energy curves, experimental excitation spectra, and electronic and nuclear dynamics in interacting Rydberg-atom pairs at large internuclear separations. The potential-energy curves and molecular wavefunctions are determined from the multipole expansion of the static Coulomb interaction which is evaluated numerically in a product basis of atomic orbitals. The convergence of this approach both in the truncation of the multipole expansion as well as in the size of the product basis is discussed, and the comparison of simulated excitation spectra is established as a useful criterium to test the convergence of the calculation. We finally discuss the dynamics of electronic and nuclear motions of pairs of Rydberg atoms, focusing on the stability of ultralong range Rydberg molecules with respect to autoionization.
Summary form only given. The discovery of ultracold and dilute ensembles of atoms and molecules in magneto-optical traps (MOT) and in atomic Bose-Einstein condensates (BECs) has ushered in a new era of precision atomic and molecular spectroscopy. Since the atoms in such cold environments predominantly interact via long-range forces, the creation of BECs and dilute atomic samples has made the study of very long-range molecular states possible. In this work (Greene et al, Phys. Rev. Lett. vol. 85, p. 2458, 2000), we discuss a particular interatomic arrangement that should be favored in modern-day MOT and BEC setups and should result in the production of molecular Rydberg states whose vibrational wave functions are localized at internuclear distances of order n/sup 2/ Bohr radii, where n is the principal quantum number. The vibrational binding energies of these molecules for n=20-50 fall in the MHz and GHz range, for molecules excited from /sup 87/Rb ultracold atomic gas. We predict two distinct classes of molecular Rydberg states. The nonpolar class of Rydberg molecules form from the interaction between a Rb(nl/sub j/) Rydberg atom with low orbital angular momentum l/sub j//spl les/2 and a distant Rb ground state atom. Rydberg molecules of the second class form from the interaction between an excited Rb atom in high (l/sub j/>2) orbital angular momentum states with a ground state Rb atom.
Rydberg molecule, formed by one or more Rydberg atoms, exhibits remarkable properties, including an exceptionally large spatial extent, rich rovibrational level structures, permanent electric dipole moments, and a pronounced sensitivity to external fields. Based on the underlying binding mechanisms, Rydberg molecules can be divided into three categories, the ground-Rydberg molecule that is bound via a low-energy electron-atom scattering interaction between ground atom and Rydberg electron, the Rydberg-Rydberg molecule that is bound via a long-range electrostatic interaction between Rydberg atoms, and the ion-Rydberg molecule that is bound via single- or multi-polar interactions between Rydberg atom and ion. This review focuses on recent theoretical and experimental advances in diatomic Rydberg molecules, covering their formation and binding mechanisms, potential energy curves, experimental observations, and spectroscopic properties, with the aim of providing a comprehensive overview of the current state and future prospects of this rapidly developing field.
The interaction between a Rydberg electron and a neutral atom situated inside its extended orbit is described via contact interactions for each atom-electron scattering channel. In ultracold environments, these interactions lead to long-range molecules with binding energies typically ranging from 10 to $1\ifmmode\times\else\texttimes\fi{}{10}^{4}$ MHz. These energies are comparable to the relativistic and hyperfine structure of the separate atomic components. Studies of molecular formation aiming to reproduce observations with spectroscopic accuracy must therefore include the hyperfine splitting of the neutral atom and the spin-orbit splittings of both the Rydberg atom and the electron-atom interaction. Adiabatic potential energy curves and permanent electric dipole moments are presented for Rb2 and Cs2. The influence of spin degrees of freedom on the potential energy curves and multipole moments probed in recent experimental work is elucidated, and the observed dipole moments of butterfly molecules are explained by the generalized 3PJ pseudopotential derived here.
We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at a large internuclear distance. The binding mechanism is based on Stark shifts and level crossings that are induced in the Rydberg atom due to the electric field of the ion. At particular internuclear distances between the Rydberg atom and the ion, potential wells occur that can hold atom–ion molecular bound states. Apart from the binding mechanism, we describe important properties of the long-range atom–ion Rydberg molecule, such as its lifetime and decay paths, its vibrational and rotational structure, and its large dipole moment. Furthermore, we discuss methods of how to produce and detect it. The unusual properties of the long-range atom–ion Rydberg molecule give rise to interesting prospects for studies of wave packet dynamics in engineered potential energy landscapes.