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arXiv:1604.04658

Multi-Manifold Stark Splittings Lift the Rydberg Blockade

Yurii V. Dumin, Jan Michael Rost

Published Apr 15, 2016• 0 citations
arXivHTMLPDF

Abstract

The spatial evolution of the Rydberg blockade is studied taking into account Stark-split energy levels across several manifolds. We find that the unexpected restoration of a blockaded Rydberg excitation at small interatomic distances, e.g., experimentally observed by P.Schauss, et al. [Nature 491, 87 (2012)], can be explained by the perturbed energy levels from neighboring manifolds that enter the energy window of excitation defined by the bandwidth of the exciting laser. The same mechanism can also explain why the pair correlation function of Rydberg atoms remains nonzero in the entire region of Rydberg blockade.

DOI
10.48550/arxiv.1604.04658

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The spatial evolution of the Rydberg blockade is studied taking into account Stark-split energy levels across several manifolds. We find that the unexpected restoration of a blockaded Rydberg excitation at small interatomic distances, e.g., experimentally observed by P.Schauss, et al. [Nature 491, 87 (2012)], can be explained by the perturbed energy levels from neighboring manifolds that enter the energy window of excitation defined by the bandwidth of the exciting laser. The same mechanism can also explain why the pair correlation function of Rydberg atoms remains nonzero in the entire region of Rydberg blockade.
Abstract The process of the Rydberg blockade, which is currently regarded as one of the most promising approaches to quantum computation, can become significantly less effective due to interatomic interactions that shift the excitation frequency of initially blocked particles to the region of resonance with external laser radiation. In this article, we develop an analytical theory of this effect based on a self-consistent model of two Rydberg atoms acting on each other with their dipole electric fields and experiencing a Stark splitting of energy levels under the action of these fields. It follows from our calculations that the typical interatomic distances at which the unblocking effect due to ‘‘parasitic’’ resonances begins to occur are in rough agreement with earlier qualitative estimates; however, the number of such resonances can be much larger than in recent numerical simulations of some particular systems. Therefore, the possibility of breaking the Rydberg blockade at small interatomic distances should be carefully taken into account in any future applications to quantum computing.
Abstract Splitting the energy levels of a hydrogen-like atom by the electric field nonuniform at the atomic scale is studied. This situation is important for the multi-level treatment of the phenomenon of Rydberg blockade (Dumin Y V 2014 J. Phys. B: At. Mol. Opt. Phys. 47 175502 ). An explicit formula for the energy levels is derived. A typical value of the energy shift by the electric field gradient turns out to be proportional to the fourth power of the principal quantum number (i.e. the square of atomic size), as would be expected from a qualitative consideration. Finally, the fine spatial structure of the Rydberg blockade is analyzed when the electric-field-gradient term plays the dominant role, and the results are compared with the experimental data.
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.
Results of numerical Monte Carlo simulations for the Stark-tuned $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster resonance and dipole blockade between two to five cold rubidium Rydberg atoms in various spatial configurations are presented. The effects of the atoms' spatial uncertainties on the resonance amplitude and spectra are investigated. The feasibility of observing coherent Rabi-like population oscillations at a $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster resonance between two cold Rydberg atoms is analyzed. Spectra and the fidelity of the Rydberg dipole blockade are calculated for various experimental conditions, including nonzero detuning from the $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster resonance and finite laser linewidth. The results are discussed in the context of quantum-information processing with Rydberg atoms.
Crystalline structures of highly excited Rydberg atoms can be a model for dilute metallic solids with tunable parameters, and provide access to the regime of strongly coupled systems. In practice, crystal creation is made difficult by the 'Rydberg blockade', where one atom in the Rydberg state shifts the energy levels of its neighbours out of resonance with the excitation laser. In our experiment, we can spatially detect Rydberg atoms by a combination of field-ionization, and subsequent acceleration of the remaining ions onto a multi-channel plate. In this way, we were able to determine the blockade radius from measuring second-order correlations. We have also made small ordered Rydberg structures by optically imprinting local excitations in a disordered atomic gas using a spatial light modulator. With this diffractive optical element it is possible to control the intensity of light in the far ¿eld and create almost any desired intensity pattern. We found that a Rydberg system with a dissipative mechanism can be mapped onto a set of rate equations that describe a wireless computer network. In these networks neighbouring transmitters have a similar blockade effect on each other. For the Rydberg system, we used mathematical tools developed for wireless networks, and applied this to optically imprinted square lattices.
One of the most striking features of the strong interactions between Rydberg atoms is the Rydberg blockade effect, which allows only a single excitation to the Rydberg state within the volume of the blockade sphere. Here we present a method that spatially visualizes this phenomenon in an inhomogeneous gas of ultracold rubidium atoms. In our experiment we scan the position of one of the excitation lasers across the cold cloud and determine the number of Rydberg excitations detected as a function of position. Comparing this distribution to the one obtained for the number of ions created by a two-photon ionization process via the intermediate 5P5P5P level, we demonstrate that the blockade effect modifies the width of the Rydberg excitation profile. Furthermore, we study the dynamics of the Rydberg excitation and find that the time scale for the excitation depends on the atomic density at the beam position.