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.
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.
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
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.
Rydberg molecule, formed by one or more Rydberg atoms, exhibits remarkable properties, including an exceptionally large spatial extent, rich rovibrational level structures, permanent electric dipole moments, and a pronounced sensitivity to external fields. Based on the underlying binding mechanisms, Rydberg molecules can be divided into three categories, the ground-Rydberg molecule that is bound via a low-energy electron-atom scattering interaction between ground atom and Rydberg electron, the Rydberg-Rydberg molecule that is bound via a long-range electrostatic interaction between Rydberg atoms, and the ion-Rydberg molecule that is bound via single- or multi-polar interactions between Rydberg atom and ion. This review focuses on recent theoretical and experimental advances in diatomic Rydberg molecules, covering their formation and binding mechanisms, potential energy curves, experimental observations, and spectroscopic properties, with the aim of providing a comprehensive overview of the current state and future prospects of this rapidly developing field.
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 topical review addresses how Rydberg atoms can serve as building blocks for emerging quantum technologies. Whereas the fabrication of large numbers of artificial quantum systems with the uniformity required for the most attractive applications is difficult if not impossible, atoms provide stable quantum systems which, for the same species and isotope, are all identical. Whilst atomic ground states provide scalable quantum objects, their applications are limited by the range over which their properties can be varied. In contrast, Rydberg atoms offer strong and controllable atomic interactions that can be tuned by selecting states with different principal quantum number or orbital angular momentum. In addition Rydberg atoms are comparatively long-lived, and the large number of available energy levels and their separations allow coupling to electromagnetic fields spanning over 6 orders of magnitude in frequency. These features make Rydberg atoms highly desirable for developing new quantum technologies. After giving a brief introduction to how the properties of Rydberg atoms can be tuned, we give several examples of current areas where the unique advantages of Rydberg atom systems are being exploited to enable new applications in quantum computing, electromagnetic field sensing, and quantum optics.