Consequences of Zeeman degeneracy for the van der Waals blockade between Rydberg atoms

Thad G. Walker and M. Saffman
Phys. Rev. A 77, 032723 – Published 26 March 2008
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Abstract

We analyze the effects of Zeeman degeneracies on the long-range interactions between like Rydberg atoms, with particular emphasis on applications to quantum-information processing using the van der Waals blockade. We present a general analysis of how degeneracies affect the primary error sources in blockade experiments, emphasizing that blockade errors are sensitive primarily to the weakest possible atom-atom interactions between the degenerate states, not the mean interaction strength. We present explicit calculations of the van der Waals potentials in the limit where the fine-structure interaction is large compared to the atom-atom interactions. The results are presented for all potential angular momentum channels involving s, p, and d states. For most channels there are one or more combinations of Zeeman levels that have extremely small dipole-dipole interactions and are therefore poor candidates for effective blockade experiments. Channels with promising properties are identified and discussed. We also present numerical calculations of Rb and Cs dipole matrix elements and relevant energy levels using quantum defect theory, allowing for convenient quantitative estimates of the van der Waals interactions to be made for principal quantum numbers up to 100. Finally, we combine the blockade and van der Waals results to quantitatively analyze the angular distribution of the blockade shift and its consequence for angular momentum channels and geometries of particular interest for blockade experiments with Rb.

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  • Received 19 December 2007

DOI:https://doi.org/10.1103/PhysRevA.77.032723

©2008 American Physical Society

Authors & Affiliations

Thad G. Walker and M. Saffman

  • Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

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Issue

Vol. 77, Iss. 3 — March 2008

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