High Rydberg states about a dipolar molecular core can exhibit special features due to the exceptionally long range of the electrical anisotropy of the core. Unlike all other, more localized, couplings of the Rydberg electron to the ion, here the interaction is not shielded by the centrifugal barrier. The influence of the core even on states of the electron with higher angular momentum l and the significant matrix elements between states that differ considerably in the principal quantum number n make this problem worthy of separate considerations. Using specialized computational techniques (both analytical and numerical) for the exact evaluation of the relevant matrix elements, the role of both inter- and intra-Rydberg series coupling is discussed. The importance of the latter (i.e., the coupling of the Rydberg electron to the rotation of the core) is emphasized. Special attention is given to the role of an external dc electrical field that is different in the present problem in that it does not significantly dilute the strength of the electron-core interaction. A positively charged core can have a dipole moment (defined with respect to its center of mass) larger than that of neutral polar molecules, particularly if the charge is localized. Hence the interseries and intraseries dynamics discussed in this paper can give rise to experimentally measurable special effects. \textcopyright{} 1996 The American Physical Society.
High Rydberg states about a dipolar molecular core can exhibit special features due to the exceptionally long range of the electrical anisotropy of the core. Unlike all other, more localized, couplings of the Rydberg electron to the ion, here the interaction is not shielded by the centrifugal barrier. The influence of the core even on states of the electron with higher angular momentum l and the significant matrix elements between states that differ considerably in the principal quantum number n make this problem worthy of separate considerations. Using specialized computational techniques (both analytical and numerical) for the exact evaluation of the relevant matrix elements, the role of both inter- and intra-Rydberg series coupling is discussed. The importance of the latter (i.e., the coupling of the Rydberg electron to the rotation of the core) is emphasized. Special attention is given to the role of an external dc electrical field that is different in the present problem in that it does not significantly dilute the strength of the electron-core interaction. A positively charged core can have a dipole moment (defined with respect to its center of mass) larger than that of neutral polar molecules, particularly if the charge is localized. Hence the interseries and intraseries dynamics discussed in this paper can give rise to experimentally measurable special effects. \textcopyright{} 1996 The American Physical Society.
Rydberg states of atoms or molecules for which the inner turning point of the Rydberg electron on the radial plus centrifugal potential lies outside the bulk of the ion core electron density are known as core-non-penetrating states. Interpretation of Rydberg spectroscopic data for polar molecules makes use of effective potentials that include ionic bonding and polarizability in order to represent electric properties of the ion core. We examine the accuracy and convergence properties of single-center polarization potentials and show that the center of charge representation, for which the core dipole moment is zero so that first-order l-mixing can be neglected, is excluded by the convergence sphere for use with l-states that can be treated by an expansion about the center or mass, the center of dipole or a newly-defined center of polarizability. The potential expansion converges only outside a sphere enclosing the charge distribution, and the sphere is much larger when the center of charge is used. For higher l-states of the rotating molecule (turning points defined in center of mass), the sphere required for convergence is much smaller for an origin within the charge distribution, so that lower l states are modeled correctly.
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. ^
Ultra-cold long-range Rydberg-ground molecule consisting of a Rydberg atom and one or more ground-state atoms is formed by low-energy scattering between the Rydberg electron and ground-state atoms located inside the Rydberg electron’s wave function. The low-energy scattering interaction, initially investigated by Fermi and Omont, has been predicted to lead to molecular binding in a novel type of Rydberg molecules, including the trilobite and butterfly molecules. Their unconventional binding mechanism, which is unlike covalent, or ionic, or van der Waals bonds, results in loosely bound molecules with bond lengths on the order of thousands of Bohr radius. This kind of molecule with large size and huge permanent electric dipole moment is a good candidate for realizing the certain strongly correlated many-body gases and for quantum information processing, as well as for dipolar quantum gases and spin systems with long-range interactions. Consequently, these molecules have received considerable attention in recent years. In this paper, we review the recent theoretical and experimental investigations of ultra-cold long-range Rydberg-ground molecules, including the scattering interaction between the Rydberg electron and ground-state atom and the resulting adiabatic potential curves, experimental observations of photo-associated Rydberg-ground molecules spectra, as well as the measurements of permanent electric dipole moment. Ultra-cold long-range Rydberg-ground molecules are prepared by photoassociation in a high-density cold atom sample. Therefore, the Rydberg electron can bind several ground-state atoms to form a polyatomic Rydberg-ground molecule. The permanent molecular electric-dipole moments are revealed by spectral line broadening in the electric fields. The latest research pointed out that the permanent electric dipole moments of the Cs nDJ -type Rydberg-ground molecules are negative, which is different from the previous reports (the electric dipole moments are positive). The negative sign reflects a deficiency of Rydberg-electron density near the ground-state perturber, which is caused by electronic configuration mixing.
We present calculations of long-range interactions in Rydberg atoms, with a focus on the dipole-dipole interactions of strontium Rydberg states. The growing use of Rydberg states in the field of cold atoms necessitates a more detailed understanding of the effects of dipole-dipole interactions, which are currently being investigated in a number of research groups worldwide. Calculations of long-range interactions in Rydberg states of caesium, cal- cium, rubidium, strontium and ytterbium are presented. By taking the one active electron approximation we develop consistent models of these long- range interactions, and construct a survey of the Rydberg state dipole-dipole interactions and quadrupole-quadrupole interactions. We compare the inter- actions between series and between atoms, highlighting the importance of certain series for applications suggested in previous works. In order to include two-electron effects in the description of dipole-dipole interactions in divalent atoms, we use multichannel quantum defect theory (MQDT) to develop models of the Rydberg series of strontium. We use an empirical reactance matrix formalism, where the reactance matrix is fitted to reproduce experimentally measured values of the bound state energy levels. Models are found for all series of strontium with L ≤ 3. We extend the MQDT formalism to the description of the natural radiative lifetimes of strontium, where the perturbers are found to have a large quenching effect on these lifetimes. By incorporating the MQDT description of the Rydberg states of strontium into the calculation of dipole-dipole interactions, we find a spin-forbidden two-atom resonance in the 3D2 states of strontium. We consider a one- dimensional lattice of strontium atoms, and find that the internal dynamics of the Rydberg atoms demonstrates spin transport for large lattice spacings and a separation of the spin and total angular momentum dynamics for small lattice spacings. Spin-angular momentum separation (analogous to spin-charge separation in condensed matter) in strontium Rydberg atoms may have uses in the investigation of one-dimensional Fermi gases and their description using Luttinger liquid theory.
The study of subtle interactions in atomic and molecular systems has stirred scientific curiosity since the dawn of quantum mechanics. Even today, research into perturbative long-range interactions continues to push into new territory, driven largely by the experimental capabilities of Rydberg state spectroscopy to detect effects of extremely weak interactions. While static long-range multipole interactions have been studied for years, the presence of dynamic terms that involve both position and momentum operators has been demonstrated only surprisingly recently. In this paper we document the existence of an effective vector interaction term in the long-range potential experienced by a moving charged particle in the presence of an anisotropic ionic core. In contrast to ordinary static quadrupole or dipole interaction terms, the existence of this vector interaction hinges on the motion of the distant charge as it roams beyond the confines of the core.
We investigate the impact of an electric field on the structure of ultra-long-range polar diatomic rubidium Rydberg molecules. Both the s-wave and p-wave interactions of the Rydberg electron and the neutral ground-state atom are taken into account. In the presence of the electric field the angular degree of freedom between the electric field and the internuclear axis acquires vibrational character and we encounter two-dimensional oscillatory adiabatic potential energy surfaces with an antiparallel equilibrium configuration. The electric field allows shifting of the corresponding potential wells in such a manner that the importance of the p-wave interaction can be controlled and the individual wells are energetically lowered at different rates. As a consequence the equilibrium configuration and corresponding energetically lowest well move to larger internuclear distances for increasing field strength. For strong fields the admixture of nonpolar molecular Rydberg states leads to the possibility of exciting the large angular momentum polar states via two-photon processes from the ground state of the atom. The resulting properties of the electric dipole moment and the vibrational spectra are analyzed with varying field strength.