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The European Physical Journal Special Topics

Anisotropy and state mixing in the interactions between Rydberg states

Benoît Vermersch

Published Dec 1, 2016• 1 citation
Publisher

Abstract

We present a guide to calculate the interactions between Rydberg states, and put into evidence the importance of the anisotropic and state-mixing character of these interactions for p and d states. We then summarize recent theoretical results obtained in this context related to the formation of anisotropic Rydberg excitation patterns and the influence of state-mixing on the familiar Rydberg blockade phenomenon.

DOI
10.1140/epjst/e2015-50337-x

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We present a guide to calculate the interactions between Rydberg states, and put into evidence the importance of the anisotropic and state-mixing character of these interactions for p and d states. We then summarize recent theoretical results obtained in this context related to the formation of anisotropic Rydberg excitation patterns and the influence of state-mixing on the familiar Rydberg blockade phenomenon.
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We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers nnn, $\ensuremath{\ell}$, jjj, and mj{m}_{j}mj​, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.
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.
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