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arXiv:2102.03195 · Physical Review Letters

Synthetic Dimension-Induced Conical Intersections in Rydberg Molecules

Frederic Hummel, Matthew T. Eiles, Peter Schmelcher

Published Jul 9, 2021• 24 citations
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Abstract

We observe a series of conical intersections in the potential energy curves governing both the collision between a Rydberg atom and a ground-state atom and the structure of Rydberg molecules. By employing the electronic energy of the Rydberg atom as a synthetic dimension we circumvent the von Neumann-Wigner theorem. These conical intersections can occur when the Rydberg atom's quantum defect is similar in size to the electron-ground-state atom scattering phase shift divided by π, a condition satisfied in several commonly studied atomic species. The conical intersections have an observable consequence in the rate of ultracold l-changing collisions of the type Rb(nf)+Rb(5s)→Rb(nl>3)+Rb(5s). In the vicinity of a conical intersection, this rate is strongly suppressed, and the Rydberg atom becomes nearly transparent to the ground-state atom.

DOI
10.1103/physrevlett.127.023003

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We observe a series of conical intersections in the potential energy curves governing both the collision between a Rydberg atom and a ground-state atom and the structure of Rydberg molecules. By employing the electronic energy of the Rydberg atom as a synthetic dimension we circumvent the von Neumann-Wigner theorem. These conical intersections can occur when the Rydberg atom's quantum defect is similar in size to the electron-ground-state atom scattering phase shift divided by π, a condition satisfied in several commonly studied atomic species. The conical intersections have an observable consequence in the rate of ultracold l-changing collisions of the type Rb(nf)+Rb(5s)→Rb(nl>3)+Rb(5s). In the vicinity of a conical intersection, this rate is strongly suppressed, and the Rydberg atom becomes nearly transparent to the ground-state atom.
We find that energy surfaces of more than two atoms or molecules interacting via transition dipole-dipole potentials generically possess conical intersections (CIs). Typically only few atoms participate strongly in such an intersection. For the fundamental case, a circular trimer, we show how the CI affects adiabatic excitation transport via electronic decoherence or geometric phase interference. These phenomena may be experimentally accessible if the trimer is realized by light alkali atoms in a ring trap, whose interactions are induced by off-resonant dressing with Rydberg states. Such a setup promises a direct probe of the full many-body density dynamics near a CI.
Conical intersections are common in molecular physics and photochemistry, and are often invoked to explain observed reaction products. A conical intersection can occur when an excited electronic potential energy surface intersects with the ground electronic potential energy surface in the coordinate space of the nuclear positions. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface. Although conical intersections have been observed experimentally, the geometric phase has not been observed in a molecular system. Here we use a trapped atomic ion system to perform a quantum simulation of a conical intersection. The internal state of a trapped atomic ion serves as the electronic state and the motion of the atomic nuclei are encoded into the normal modes of motion of the ions. The simulated electronic potential is constructed by applying state-dependent forces to the ion with a near-resonant laser. We experimentally observe the geometric phase on the ground-state surface using adiabatic state preparation followed by motional state measurement. Our experiment shows the advantage of combining spin and motion degrees of freedom in a quantum simulator.
Conical intersections between electronic potential energy surfaces are paradigmatic for the study of nonadiabatic processes in the excited states of large molecules. However, since the corresponding dynamics occurs on a femtosecond timescale, their investigation remains challenging and requires ultrafast spectroscopy techniques. We demonstrate that trapped Rydberg ions are a platform to engineer conical intersections and to simulate their ensuing dynamics on larger length scales and timescales of the order of nanometers and microseconds, respectively; all this in a highly controllable system. Here, the shape of the potential energy surfaces and the position of the conical intersection can be tuned thanks to the interplay between the high polarizability and the strong dipolar exchange interactions of Rydberg ions. We study how the presence of a conical intersection affects both the nuclear and electronic dynamics demonstrating, in particular, how it results in the inhibition of the nuclear motion. These effects can be monitored in real time via a direct spectroscopic measurement of the electronic populations in a state-of-the-art experimental setup.
We consider nonadiabatic coupling in the “trilobite”-like long-range Rydberg molecules created by perturbing degenerate high- ℓ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular nonadiabatic coupling. We find that the gap between the trilobite potential curve and neighboring “butterfly” or “dragonfly” potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the s -wave radial wave function. This is an unanticipated outcome of Kato's theorem. Published by the American Physical Society 2024
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.
Ultralong-range Rydberg molecules, formed by the interaction between a highly excited Rydberg atom and a ground-state atom, provide a unique platform for exploring quantum phenomena spanning nanometer-to-micrometer distances as well as exotic few-body interactions. The formation mechanisms and resultant physical properties differ markedly between s-wave and p-wave scattering channels. Here we report the experimental observation of node-dependent p-wave molecular signals in Rb(nS)-Rb(5S) Rydberg molecular spectra, where variations in the principal quantum number n directly reveal the shift of molecular binding energies induced by the moving nodal structure of the Rydberg electron wavefunction. This node-dependence is attributed to a cooperative effect between the local gradient of the nS-electron wavefunction and the energydependent p-wave scattering length. In addition, resolving two p-wave bound states associated with adjacent nodes highlights the remarkable sub-nanometer spatial resolution achieved in our experiment. Our findings reveal a more profound quantum control mechanism, wherein the principal quantum number acts as a switch for nodal-selective molecular bound states, and the reported method provides a sensitive spectroscopic probe of electron-atom scattering.