Atomic Waveguides for Atom Chips

Report No. ARL-TR-5014
Authors: William M. Golding
Date/Pages: October 2009; 38 pages
Abstract: This report studies the quantum behavior of a spin one-half magnetic atom guided by a two-dimensional quadrupole magnetic field of infinite extent. The technique used is based on the Frobenius series technique and gives a complete understanding of the guide mode structure for small radial coordinates. Asymptotic solutions are used to establish boundary conditions for large radii. Various guide modes that have not been included in earlier studies are made clear by this technique. Although, in principle, the series solutions are complete, convergence is slow and the present study, therefore, uses these solutions only to establish consistent initial conditions for a differential equation solver. In this way, radial modes and eigenvalues are calculated. The results can be extended to higher spin atoms and more complicated guiding fields. These extensions along with detailed analysis of experimental limitations will be the subject of future work.
Distribution: Approved for public release
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Last Update / Reviewed: October 1, 2009