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arXiv:1909.02141 · Journal of Physics B Atomic Molecular and Optical Physics

Triatomic butterfly molecules

Matthew T. Eiles, Christian Fey, Frederic Hummel, Peter Schmelcher

Published Feb 7, 2020• 4 citations
arXivHTMLPDF

Abstract

Abstract We detail the rich electronic and vibrational structure of triatomic ‘butterfly’ molecules, ultra-long-range Rydberg molecules bound by resonant p -wave scattering. We divide these molecules into two sub-classes depending on their parity under reflection of the electronic wave function through the molecular plane. The trimers with odd reflection parity have smoothly varying, non-oscillatory potential energy surfaces except near the collinear configuration. Here, the vibrational wave function is confined tightly in the symmetric-stretch and bending modes, but only loosely in the asymmetric stretch mode. The trimers with even reflection parity exhibit far richer potential surfaces with abundant minima, but only a few of these are deep enough to localize the vibrational states. These minima are correlated with the electronic wave functions of the butterfly dimer, contributing to a building principle for trimers.

DOI
10.1088/1361-6455/ab73af

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Abstract We detail the rich electronic and vibrational structure of triatomic ‘butterfly’ molecules, ultra-long-range Rydberg molecules bound by resonant p -wave scattering. We divide these molecules into two sub-classes depending on their parity under reflection of the electronic wave function through the molecular plane. The trimers with odd reflection parity have smoothly varying, non-oscillatory potential energy surfaces except near the collinear configuration. Here, the vibrational wave function is confined tightly in the symmetric-stretch and bending modes, but only loosely in the asymmetric stretch mode. The trimers with even reflection parity exhibit far richer potential surfaces with abundant minima, but only a few of these are deep enough to localize the vibrational states. These minima are correlated with the electronic wave functions of the butterfly dimer, contributing to a building principle for trimers.
We investigate triatomic molecules that consist of two ground-state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of angstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential-energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and develop a simple building principle that predicts the triatomic equilibrium configurations. As a representative example we focus on 87Rb^{87}\mathrm{Rb}87Rb trimers correlated to the n=30n=30n=30 Rydberg state. Using an exact diagonalization scheme we determine and characterize localized vibrational states in these potential minima with energy spacings on the order of 100 $\mathrm{MHz}\ifmmode\times\else\texttimes\fi{}h$.
Abstract We investigate the electronic structure of a triatomic Rydberg molecule formed by a Rydberg atom and two neutral ground-state atoms. Taking into account the s -wave and p -wave interactions, we perform electronic structure calculations and analyze the adiabatic electronic potentials evolving from the Rb ( n = 35 , l ≥ 3 ) Rydberg degenerate manifold. We hereby focus on three different classes of geometries of the Rydberg molecules, including symmetric, asymmetric and planar configurations. The metamorphosis of these potential energy surfaces in the presence of an external electric field is explored.
We investigate polyatomic ultralong-range Rydberg molecules consisting of three ground-state atoms bound to a Rydberg atom via sss- and ppp-wave interactions. By employing the finite basis set representation of the unperturbed Rydberg electron Green's function we reduce the computational effort to solve the electronic problem substantially. This method is subsequently applied to determine the potential energy surfaces of triatomic systems in electronic sss- and ppp-Rydberg states. Their molecular geometry and resulting vibrational structure are analyzed within an adiabatic approach that separates the vibrational bending and stretching dynamics. This procedure yields information on the radial and angular arrangement of the nuclei and indicates in particular that kinetic couplings between bending and stretching modes induce a linear structure in triatomic l=0l=0l=0 ultralong-range Rydberg molecules.
Abstract This PhD tutorial discusses ultra-long-range Rydberg molecules, the exotic bound states of a Rydberg atom and one or more ground state atoms immersed in the Rydberg electron’s wave function. This novel chemical bond is distinct from an ionic or covalent bond, and is accomplished by a very different mechanism: the Rydberg electron, elastically scattering off of the ground state atoms, exerts a weak attractive force sufficient to form the molecule in long-range oscillatory potential wells. In the last decade this topic has burgeoned into a vibrant and mature subfield of atomic and molecular physics following the rapidly developing capability of experiment to observe and manipulate these molecules. This tutorial focuses on three areas where this experimental progress has demanded more sophisticated theoretical descriptions: the structure of polyatomic molecules, the influence of electronic and nuclear spin, and the behavior of these molecules in external fields. The main results are a collection of potential energy curves and electronic wave functions which together describe the physics of Rydberg molecules. Additionally, to facilitate future progress in this field, this tutorial provides a general overview of the current state of experiment and theory.
We show that the recently observed class of long-range ion-Rydberg molecules can be divided into two families of states, which are characterized by their unique electronic structures resulting from the ion-induced admixture of quantum defect-split Rydberg nPnPnP states with different low-field-seeking high-lll states. We predict that in both cases, these diatomic molecular states can bind additional ground-state atoms lying within the orbit of the Rydberg electron, thereby forming charged ultralong-range Rydberg molecules (ULRMs) with binding energies similar to that of conventional nonpolar ULRMs. To demonstrate this, we consider a Rydberg atom interacting with a single ground-state atom and an ion. The additional atom breaks the system's cylindrical symmetry, which leads to mixing between states that would otherwise be decoupled. The electronic structure is obtained using exact diagonalization over a finite basis and the vibrational structure is determined using the multiconfiguration time-dependent Hartree method. Due to the lobelike structure of the electronic density, bound trimers with both linear and nonlinear geometrical configurations of the three nuclei are possible. The predicted trimer binding energies and excitation series are distinct enough from those of the ion-Rydberg dimer to be observed using current experimental techniques.
We predict the existence of a ubiquitous class of long-range molecular Rydberg states, whose Born-Oppenheimer potential curves are oscillatory in nature. These oscillations reflect the nodal structure of the atomic Rydberg state wave functions. The temperature and density of atoms in a Bose-Einstein condensate are particularly favorable for the laser excitation of ultra-long-range vibrational bound states localized at internuclear distances in the range 10(3)- 10(5) a.u. A surprising trilobitelike class of polar homonuclear diatomics should exhibit electric dipole moments in the kilodebye range.