Series Solutions for Atom Guides

WILLIAM M. GOLDING

Atom waveguides are used to manipulate cold atoms in atom interferometers. The creation of atom interferometers using cold atoms in miniature magnetic waveguides is one of many goals of current atom chip research. To achieve a complete understanding of atom propagation in a complicated device such as a guided atom interferometer, a detailed understanding of the ground state and other nearby states is needed. The Frobenius series solutions for the bounded transverse modes of an atomic waveguide are presented here and arbitrary precision arithmetic is used to evaluate the series solutions without roundoff errors. The waveguide potential considered is an infinitely long quadrupole magnetic potential as used in various atom chip waveguides. The simplest case of a guided spin-12 particle is presented here. However, the basic series techniques can be extended to both higher order multipole potentials and higher spin particles, including atoms with hyperfine splitting. The low-field and the high-field seeking states together form the spectrum of the waveguide Hamiltonian. In the limit where the transverse dimension of the guide tends to infinity, the spectrum of the guide changes from a discrete set of low- and high-field seeking states to a continuum of high-field seeking states embedded with a discrete set of low-field seeking states. Although the low-field seeking states are not truly bound, the system is an approximate example of bound states in a continuum first discussed by von Neumann and Wigner. Depending on boundary conditions, the solutions form either a discrete set or a continuum of orthogonal waveguide modes. These are useful for further analysis of ideal waveguide behavior as well as the detailed perturbation studies necessary for analysis of atomic waveguide interferometers.

Herman Batelaan, Roland Abfalterer, Stefan Wehinger +1 more

Joshua P. Beardmore, A. J. Palmer, K. C. Kuiper +1 more

In this paper we present a multiple element magnetic device to guide atoms using a spatially inhomogeneous magnetic field formed by a series of permanent hexapole magnets. The operation of the device is demonstrated using an enhanced beam of neon atoms in the 3P2 metastable state. These atoms are guided around a bend of 30 degrees from their original path. A flux of 4.35 x 10(9) +/- 2 x 10(7) atoms s(-1) was measured after the device yielding a transmission efficiency of approximately 9% of the input flux. Simulations of the center of mass motion of the atoms through the magnetic guide have been performed giving reasonable agreement with the experimental results.

Otto Robert Frisch

Katrin Dulitz, T. P. Softley

An original design of magnetic guide is presented, suitable for use with Zeeman-decelerated supersonic beams of ground-state hydrogen atoms and other light paramagnetic species. Three-dimensional particle trajectory simulations show that, by combining a series of permanent-magnet Halbach arrays with pulsed high-current wire electromagnets, this guide can be used to efficiently transmit the slow, decelerated atoms and discard the faster, undecelerated atoms and other species in the gas beam. The curved guide would be suitable for guiding hydrogen atoms into an ion trap to investigate low temperature ion-molecule collisions. It is also shown that the device could be used for the guiding or velocity selection from an undecelerated supersonic or effusive beam.

Szabolcs Iván