Topological constraints on magnetostatic traps

Abstract

We theoretically investigate properties of magnetostatic traps for cold atoms that are subject to externally applied uniform fields. We show that Ioffe Pritchard traps and other stationary points of $B$ are confined to a two-dimensional curved manifold defined by $\det (\partial B_i/\partial x_j)=0$. We describe how stationary points can be moved over the manifold by applying external uniform fields. The manifold also plays an important role in the behavior of points of zero field. Field zeroes occur in two distinct types, in separate regions of space divided by the manifold. Pairs of zeroes of opposite type can be created or annihilated on the manifold. Finally, we give examples of the manifold for cases of practical interest.

7 pages, 5 figures

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• Guiding Neutral Atoms
• An AC electric trap for ground-state molecules
• Continuous loading of an electrostatic trap for polar molecules
• Permanent magnetic lattices for ultracold atoms and quantum degenerate gases
• A permanent magnetic film atom chip for Bose-Einstein condensation
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