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Physics

Trilobite Molecules Measured

Marric Stephens

Published Jun 4, 2025• 0 citations
Publisher

Abstract

Rydberg atom is one with a highly excited electron, and this electron can interact with a second atom in its ground state to form a weakly bound Rydberg molecule.One example of such a bound state is a "trilobite Rydberg molecule," so-called because the electron's probability distribution resembles the long-extinct sea creature.Markus Exner at the Technical University of Kaiserslautern, Germany, and colleagues have now obtained high-resolution measurements of the vibrational spectra of trilobite Rydberg molecules formed from pairs of rubidium atoms [1].The results offer a rigorous test of theoretical models.

DOI
10.1103/physics.18.s72

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Rydberg atom is one with a highly excited electron, and this electron can interact with a second atom in its ground state to form a weakly bound Rydberg molecule.One example of such a bound state is a "trilobite Rydberg molecule," so-called because the electron's probability distribution resembles the long-extinct sea creature.Markus Exner at the Technical University of Kaiserslautern, Germany, and colleagues have now obtained high-resolution measurements of the vibrational spectra of trilobite Rydberg molecules formed from pairs of rubidium atoms [1].The results offer a rigorous test of theoretical models.
The "trilobite"-type of molecule, predicted in 2000 and observed experimentally in 2015, arises when a Rydberg electron exerts a weak attractive force on a neutral ground state atom. Such molecules have bond lengths exceeding 100 nm. The ultralong-range chemical bond between the two atoms is a nonperturbative linear combination of the many degenerate electronic states associated with high principal quantum numbers, and the resulting electron probability distribution closely resembles a fossil trilobite from antiquity. We show how to coherently engineer this same long-range orbital through a sequence of electric and magnetic field pulses even when the ground-state atom is not present and propose several methods to observe the resulting orbital. The existence of such a ghost chemical bond in which an electron reaches out from one atom to a nonexistent second atom is a consequence of the high level degeneracy.
Molecular Physics Atoms are generally compact objects. However, if one of the electrons orbiting the nucleus is given an extra boost of energy so that it's barely still attached, you get a much larger Rydberg atom. Booth et al. created an even more exotic species: a giant molecule consisting of a regular cesium atom bound within a Rydberg atom of the same element. The molecules are named “trilobites” because their electronic density visually resembles fossils of these extinct marine creatures. Science , this issue p. [99][1] [1]: /lookup/volpage/348/99?iss=6230
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 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.
In this work the existence of a novel type of molecule is shown whose binding is based solely on electron-atom scattering. These molecules are composed of a Rydberg atom and a ground state atom - here Rb(ns) and Rb(5s) - where the binding arises from scattering of the Rydberg electron from the ground state atom. The ground state atom is bound to the Rydberg wavefunction, which has radii on the order of 100nm, and thus these molecules are of long-range. Although the theoretical description of this interaction goes back to the famous work of Fermi in the year 1934 which was expanded in the following decades by Omont and Greene, the experimental proof of their existence was still missing. Up to now, experimental evidence for the ultralong-range Rydberg molecules was found only in spectral line broadenings. The present experiments have demonstrated the direct photoassociation of these ultralong-range Rydberg molecules for Rb(ns)-Rb(5s) triplet states from a cold and dense sample of rubidium 87 atoms for a range of principal quantum numbers, n, between 34 and 40. The high-resolution photoassociation spectra allowed for the observation of several vibrational states separated by only a few Megahertz. Based on the model by Greene the vibrational ground states v=0 are assigned and the dependence of their binding energy on the principal quantum number, n, is used to extract the triplet s-wave scattering length for electron-Rb(5s) collisions from the data. The remarkably good agreement between experiment and theory for the vibrational ground state v=0 over a range of principal quantum numbers attests to the accuracy of Fermi's original pseudopotential approach in describing interactions in excited multi-atom systems. Aside from this good agreement for the state v=0, the measurements also show that contributions from p-wave scattering cannot be neglected, as a number of excited vibrational states is observed in the experiment that are not predicted from the theory assuming only s-wave scattering. Calculations of Li, Pohl and coworkers have shown that a full solution of the electron-atom scattering is necessary for the assignment of all vibrational states. This work finds the molecular bound states to be very sensitive to both s-wave as well as p-wave electron-atom scattering and the Rydberg molecules turn out to be an accurate experimental platform to study electron-atom collisions in a previously inaccessible ultralow-energy regime. In general, the ultralong-range Rydberg molecules investigated here for rubidium are expected for all species with negative scattering length for electron-atom interaction, e. g. the other alkali atoms. Rydberg atom and ground state atom do not even have to be of the same chemical element, the only requirement is a negative scattering length of the ground state atom for electron scattering. Moreover, the binding force of the Rydberg electron is not restricted to a single ground state atom and molecules with more than one ground state atom can be created. The fact that these exotic molecules have huge bond lengths but nevertheless a vibrational spectrum with several states make a new type of ultracold Rydberg chemistry feasible. In the future, larger polymers or even heteronuclear molecules can be realized, where the number of atoms, the constituent atomic elements and the addressed Rydberg state allow to precisely select the properties of the long-range molecule.
We perform three-photon photoassociation to obtain high resolution spectra of ^{87}Rb trilobite dimers for the principal quantum numbers n=22, 24, 25, 26, and 27. The large binding energy of the molecules in combination with a relative spectroscopic resolution of 10^{-4} provides a rigorous benchmark for existing theoretical models. A recently developed Green's function framework, which circumvents the convergence issues that afflicted previous studies, is employed to theoretically reproduce the vibrational spectrum of the molecule with high accuracy. The relatively large molecular binding energy is primarily determined by the low-energy S-wave electron-atom scattering length, thereby allowing us to extract the ^{3}S_{1} scattering phase shift with unprecedented accuracy, at low-energy regimes inaccessible to free electrons.