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arXiv:1909.01097 · Physical Review X

Rydberg Composites

A. Hunter, Matthew T. Eiles, Alexander Eisfeld, Jan Michael Rost

Published Aug 26, 2020• 16 citations
arXivHTMLPDF

Abstract

We introduce the Rydberg composite, a new class of Rydberg matter where a single Rydberg atom is interfaced with a dense environment of neutral ground state atoms.The properties of the composite depend on both the Rydberg excitation, which provides the gross energetic and spatial scales, and the distribution of ground state atoms within the volume of the Rydberg wave function, which sculpt the electronic states.The latter range from the "trilobites," for small numbers of scatterers, to delocalized and chaotic eigenstates, for disordered scatterer arrays, culminating in the dense scatterer limit in symmetry-dominated wave functions which promise good control in future experiments.We discuss one-, two-, and threedimensional arrangements of scatterers using different theoretical methods, enabling us to obtain scaling behavior for the regular spectrum and measures of chaos and delocalization in the disordered regime.We also show that analogous quantum dot composites can elucidate in particular the dense scatterer limit.Thus, we obtain a systematic description of the composite states.The two-dimensional monolayer composite possesses the richest spectrum with an intricate band structure in the limit of homogeneous scatterers, experimentally accessible with pancake-shaped condensates.

DOI
10.1103/physrevx.10.031046

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We introduce the Rydberg composite, a new class of Rydberg matter where a single Rydberg atom is interfaced with a dense environment of neutral ground state atoms.The properties of the composite depend on both the Rydberg excitation, which provides the gross energetic and spatial scales, and the distribution of ground state atoms within the volume of the Rydberg wave function, which sculpt the electronic states.The latter range from the "trilobites," for small numbers of scatterers, to delocalized and chaotic eigenstates, for disordered scatterer arrays, culminating in the dense scatterer limit in symmetry-dominated wave functions which promise good control in future experiments.We discuss one-, two-, and threedimensional arrangements of scatterers using different theoretical methods, enabling us to obtain scaling behavior for the regular spectrum and measures of chaos and delocalization in the disordered regime.We also show that analogous quantum dot composites can elucidate in particular the dense scatterer limit.Thus, we obtain a systematic description of the composite states.The two-dimensional monolayer composite possesses the richest spectrum with an intricate band structure in the limit of homogeneous scatterers, experimentally accessible with pancake-shaped condensates.
The properties and behavior of a Ring Rydberg Composite are explicated. This system consists of a ring of ground state atoms centered on a Rydberg atom, whose electron elastically scatters off the ground state atoms. We transform the electronic Hamiltonian into a discrete tight-binding representation in which the on-site energies and long-range hopping between sites are controlled and mediated by the Rydberg electron. From this new representation, which to a large extent enables an analytic treatment, we derive scaling laws and analytic expressions for the wave functions and eigenspectrum. The interface between ring and Rydberg geometries leads to a range of rich properties which can be tuned as a function of ring size, number of scatterers, and principal quantum number.
The properties of a Rydberg atom immersed in an ultracold environment were investigated. Two scenarios were considered, one of which involves the neighbouring ground-state atoms arranged in a spatially structured configuration, while the other involves them distributed randomly in space. To calculate the influence of the multiple ground-state atoms on the Rydberg atom, Fermi-pseudopotential was used, which simplified greatly the numerical effort. In many cases, the few-body interaction can be written down analytically which reveals the symmetry properties of the system. In the structured case, we report the first prediction of the formation of ``Rydberg Borromean trimers''. The few-body interactions and the dynamics of the linear A-B-A trimer, where A is the ground-state atom and B is the Rydberg atom, were investigated in the framework of normal mode analysis. This exotic ultralong-range triatomic bound state exists despite that the Rydberg-ground-state interaction is repulsive. Their lifetimes were estimated using both quantum scattering calculations and semi-classical approximations which are found to be typically sub-microseconds. In the disordered case, the Rydberg-excitation spectra of a frozen-gas were simulated, where the nuclear degrees of freedom can be ignored. The systematic change of the spectral shape with respect to the density of the gas and the excitation of the Rydberg atom were found and studied. Some parts of the spectral shape can be described by simple scaling laws with exponents given by the basic properties of the atomic species such as the polarizability and the zero-energy electron-atom scattering length.
Abstract The properties and behavior of a Ring Rydberg Composite are explicated. This system consists of a ring of ground state atoms centered on a Rydberg atom, whose electron elastically scatters off the ground state atoms. We transform the electronic Hamiltonian into a discrete tight-binding representation in which the on-site energies and long-range hopping between sites are controlled and mediated by the Rydberg electron. From this new representation, which to a large extent enables an analytic treatment, we derive scaling laws and analytic expressions for the wave functions and eigenspectrum. The interface between ring and Rydberg geometries leads to a range of rich properties which can be tuned as a function of ring size, number of scatterers, and principal quantum number.
We examine topological phases and symmetry-protected electronic edge states in the context of a Rydberg composite: a Rydberg atom interfaced with a structured arrangement of ground-state atoms. We show that the spectrum of the electronic Hamiltonian of such a composite possesses a mapping to that of a tight-binding Hamiltonian, which can exhibit nontrivial topology depending on the arrangement of the ground-state atoms and the principal quantum number of the Rydberg state. The Rydberg electron moves in a combined potential including the long-ranged Coulomb interaction with the Rydberg core and short-ranged interactions with each neutral atom; the effective hopping amplitudes between sites are determined by this combination. We first confirm the existence of topologically-protected edge states in a Rydberg composite by mapping it to the paradigmatic Su-Schrieffer-Heeger dimer model. Following that, we show that more complicated systems with trimer unit cells can be studied in a Rydberg composite. Published by the American Physical Society 2024
Highly excited Rydberg atoms inherit their level structure, symmetries, and scaling behavior from the hydrogen atom. We demonstrate that these fundamental properties enable a thermodynamic limit of a single Rydberg atom subjected to interactions with nearby ground-state atoms. The limit is reached by simultaneously increasing the number of ground-state atoms and the level of excitation of the Rydberg atom, for which the Coulomb potential supplies infinitely many and highly degenerate excited states. Our study reveals a surprising connection to an archetypal concept of condensed matter physics, Anderson localization, facilitated by a direct mapping between the Rydberg atom's electronic spectrum and the spectrum of a tight-binding Hamiltonian. The hopping amplitudes of this tight-binding system are determined by the arrangement of ground-state atoms and can range from oscillatory and long-ranged to nearest-neighbor. In the latter we identify clear signatures of the Anderson localization of the Rydberg electron.
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.