arXiv:1409.5625 · Physical Review A

Spectral backbone of excitation transport in ultracold Rydberg gases

Torsten Scholak, Thomas Wellens, Andreas Buchleitner

Published Dec 9, 2014• 29 citations

Abstract

The spectral structure underlying excitonic energy transfer in ultracold Rydberg gases is studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are of short range, and is ultimately determined by the spectral and eigenvector structure. In the energy levels' spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the relative weight of localized states is reduced. At the same time, the spectral statistics, in particular, the density of states and the nearest-neighbor level-spacing statistics, exhibits a transition from approximately a 1-stable L\'evy to a Gaussian orthogonal ensemble. Deviations from random matrix statistics are shown to stem from correlations between interatomic interaction strengths that lead to an asymmetry of the spectral density and profoundly affect localization properties. We discuss approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.

DOI: 10.1103/physreva.90.063415

Related papers

Extended Coherently Delocalized States in a Frozen Rydberg Gas

Ghassan Abumwis, Matthew T. Eiles, Alexander Eisfeld

The long-range dipole-dipole interaction can create delocalized states due to the exchange of excitation between Rydberg atoms. We show that even in a random gas many of the single-exciton eigenstates are surprisingly delocalized, composed of roughly one quarter of the participating atoms. We identify two different types of eigenstates: one which stems from strongly-interacting clusters, resulting in localized states, and one which extends over large delocalized networks of atoms. These two types of states can be excited and distinguished by appropriately tuned microwave pulses, and their relative contributions can be modified by the Rydberg blockade and the choice of microwave parameters.

arXiv:1909.12705Physical Review LettersMay 12, 202013 citations

Formation of Aggregates and Energy Transport in Ultracold Rydberg Interacting Gases

H. Schempp

This thesis investigates different aspects of strongly interacting ultracold Rydberg gases coupled by light, including the excitation of correlated structures called Rydberg aggregates and dipolar energy transport. For this purpose an experimental apparatus has been constructed. We study coherent population trapping (CPT) and electromagnetically induced transparency (EIT) involving Rydberg states. To study the formation of Rydberg aggregates we use full counting statistics (FCS) which makes it possible to infer the size of Rydberg aggregates. Dephasing during the excitation is found to have a dramatic effect on the formation process, leading to sequential growth around an initial grain. Rydberg state EIT is used to realize a new direct optical imaging scheme for Rydberg atoms which combines highly sensitive detection with high spatial and temporal resolution. Applying this technique we observe dipole-mediated energy transport processes between Rydberg atoms. We study classical transport in the presence of strong measurement induced decoherence. The strong interactions are seen to mediate long-range hopping significantly beyond nearest neighbors. We present first indications for coherent transport in this system. These experiments shed light on the role of correlations in the excitation and evolution of strongly interacting quantum systems and e.g. could possibly be used to model energy transport in biological systems. \n

Jan 1, 20140 citations

Statistical properties of interacting Rydberg gases

D. Breyel

The present thesis treats the interacting ultracold Rydberg gas with special emphasison the statistical footprint of the phase transition between unordered and crystalline phase, which can be understood as a consequence of the dipole blockade effect. After mapping the system onto an effective spin-1/2-model, exact diagonalization of the effective Hamiltonian is used to obtain the many-body ground state. Repeated application of this procedure on random realizations reveals the underlying probability distribution of the number of Rydberg atoms, allowing to calculate its statistical moments. In the regimes of weak and strong interaction these observables have power law character. The critical interaction strength is estimated by extrapolating these power laws up to their intersection point. The same procedure is applied to interacting excitons in bilayer heterostructures uncovering a phase transition here as well. Furthermore, new methods are introduced to handle the effects of finite detection efficiency and parameter fluctuations to establish a better connection between experimental and theoretical results. Finally, new models are introduced to include dynamics or additional Rydberg states. The last model is of purely statistical nature and its results may be used as a tool for detecting a potential clustering of Rydberg atoms.

Jan 1, 20140 citations

Effects of strong interactions in ultracold Rydberg gases

Jovica Stanojevic

In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^

Jan 1, 20071 citation

Modeling Rydberg gases using random sequential adsorption on random graphs

Daan Rutten, Jaron Sanders

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects and quantum mechanical effects. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a random sequential adsorption (RSA) process on a random geometric graph (RGG), and a RSA process on a decomposed random intersection graph (DRIG). The last model refers to choosing a particular subgraph of a mixture of two other random graphs. Contrary to the first two models, it lends itself for a rigorous mathematical analysis, and it is built specifically to have particular structural properties of a RGG. We establish for it a fluid limit describing the time evolution of the number of Rydberg atoms and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi random graph (ERRG). Finally, we also develop a heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long timescales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short timescales the statistics are affected most by quantum mechanical effects.

arXiv:2010.13728Physical Review AMar 3, 20210 citations

Ultracold Rydberg Atoms in Structured and Disordered Environments

Ivan Chen-Hsiu Liu

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.

Jun 30, 20080 citations