Topological constraints on magnetostatic traps

TL;DR

This paper provides a theoretical analysis of magnetostatic traps for cold atoms, revealing that stationary points and zero-field points are constrained to a specific two-dimensional manifold influenced by external fields.

Contribution

It introduces the concept of a two-dimensional manifold constraining stationary points and zero-field points in magnetostatic traps, and explains how external fields can manipulate these points.

Findings

Stationary points are confined to a curved manifold defined by a determinant condition.

Zero-field points occur in two types and are separated by the manifold.

Pairs of zeroes can be created or annihilated on the manifold.

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.