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arXiv:1312.7865 · Journal of Physics B Atomic Molecular and Optical Physics

Fine structure of the Rydberg blockade zone

Yurii V Dumin

Published Aug 21, 2014• 5 citations
arXivHTMLPDF

Abstract

A spatial structure of the zone blocked by the dipolar electric field of a Rydberg atom is calculated taking into account a possibility of excitation to the states with neighboring values of the principal quantum number. As a result, it was found that the blocked zone represents a number of co-centric spherical shells rather than a solid ball, and the respective pair correlation function should have additional maxima at small interparticle distances.

DOI
10.1088/0953-4075/47/17/175502

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Stark effect in the nonuniform field and its influence on the fine structure of Rydberg blockade

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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.

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High resolution laser Stark excitation of np (60<n<85) Rydberg states of ultracold cesium atoms shows an efficient blockade of the excitation attributed to long-range dipole-dipole interaction. The dipole blockade effect is observed as a quenching of the Rydberg excitation depending on the value of the dipole moment induced by the external electric field. Effects of ions which could match the dipole blockade effect are discussed in detail but are ruled out for our experimental conditions. Analytic and Monte Carlo simulations of the excitation of an ensemble of interacting Rydberg atoms agree with the experiments and indicate a major role of the nearest neighboring Rydberg atom.

arXiv:physics/0703102•Physical Review Letters•Aug 16, 2007•147 citations
A spatial structure of the zone blocked by the dipolar electric field of a Rydberg atom is calculated taking into account a possibility of excitation to the states with neighboring values of the principal quantum number. As a result, it was found that the blocked zone represents a number of co-centric spherical shells rather than a solid ball, and the respective pair correlation function should have additional maxima at small interparticle distances.
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.
Systems of cold, interacting Rydberg atoms are of interest because they exhibit a wide range of collective quantum phenomena. This thesis describes experimental and theoretical work related to these systems with an emphasis on two phenomena: Rydberg excitation blockades and quantum-state-changing collisions. I begin by presenting a detailed calculation of the interaction energies of two Rydberg atoms for a variety of orientations, quantum states, and applied electric fields. The calculated energies are used to interpret the experimental results that follow. I then describe measurements showing that the widths of the distributions of Rydberg excitation number are related to the effectiveness of a Rydberg excitation blockade. These distributions are investigated as a function of principal quantum number, n, and applied electric field. In the presence of a Forster resonant field, sub-Poissonian distributions are measured. I next present a spectroscopic measurement of the energy level shift of a system of atoms which collectively shares two Rydberg excitations. The qualitative nature of the shift depends sensitively on the type of interactions between the atoms (van der Waals or dipole-dipole) and may be changed by changing the quantum state or applied electric field. This measurement provides the first spectroscopic proof that Rydberg excitation blockades are operative. Finally, I describe measurements of the probability for quantum state-changing and Penning-ionizing collisions to provide evidence for intrinsic, electric field-free-interaction resonances and complex many-body interactions in systems of cold 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.
Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.
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.
High resolution laser Stark excitation of np (60<n<85) Rydberg states of ultracold cesium atoms shows an efficient blockade of the excitation attributed to long-range dipole-dipole interaction. The dipole blockade effect is observed as a quenching of the Rydberg excitation depending on the value of the dipole moment induced by the external electric field. Effects of ions which could match the dipole blockade effect are discussed in detail but are ruled out for our experimental conditions. Analytic and Monte Carlo simulations of the excitation of an ensemble of interacting Rydberg atoms agree with the experiments and indicate a major role of the nearest neighboring Rydberg atom.