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arXiv:physics/0009096 · Physical Review Letters

Two-Wire Waveguide and Interferometer for Cold Atoms

Edward A. Hinds, Chris J. Vale, M. G. Boshier

Published Feb 19, 2001• 141 citations
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Abstract

A versatile miniature de Broglie waveguide is formed by two parallel current-carrying wires in the presence of a uniform bias field. We derive a variety of analytical expressions to describe the guide and present a quantum theory to show that it offers a remarkable range of possibilities for atom manipulation on the submicron scale. These include controlled and coherent splitting of the wave function as well as cooling, trapping, and guiding. In particular, we discuss a novel microscopic atom interferometer with the potential to be exceedingly sensitive.

DOI
10.1103/physrevlett.86.1462

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A versatile miniature de Broglie waveguide is formed by two parallel current-carrying wires in the presence of a uniform bias field. We derive a variety of analytical expressions to describe the guide and present a quantum theory to show that it offers a remarkable range of possibilities for atom manipulation on the submicron scale. These include controlled and coherent splitting of the wave function as well as cooling, trapping, and guiding. In particular, we discuss a novel microscopic atom interferometer with the potential to be exceedingly sensitive.
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Summary form only given. Just as optical waveguides play a central role in many aspects of modern optics, from communications to integrated optics, atom waveguides are likely to be an enabling technology for future atom-optics-based science. In particular, well-characterized atom waveguides may make possible inertial and rotation measurements of exquisite sensitivity via large-enclosed-area atom interferometers. The first guides for atoms were based on optical forces, where hollow glass fibers guide light, and the light in turn guides atoms. In this paper we have guided neutral atoms using photolithographically patterned current-carrying wires in two different configurations.
Clouds of cold atoms, collected and refrigerated by laser light, can be cooled to nanoKelvin temperatures. This has created the new field of atom optics where cold atoms are manipulated, much as photons are controlled in traditional optics using mirrors, lenses, and gratings. It is also becoming possible to confine and manipulate atoms in extremely small traps and waveguides, which give access to de Broglie wave physical optics. Atoms flowing in such structures could provide a new technology based on the flow and quantum interactions of neutral atoms. Atom 'chips' could lead to integrated atom interferometers and even possibly to a quantum information processor.
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.
A cloud of laser-cooled 85Rb atoms is coupled through a magnetic funnel into a miniature waveguide formed by four current-carrying wires embedded in a silica fiber. The atom cloud has a approximately 100 &mgr;m radius within the fiber and propagates over cm distances. We study the coupling, propagation, and transverse distribution of atoms in the fiber, and find good agreement with theory. This prototype demonstrates the feasibility of miniature guides as a tool in the new field of integrated atom optics, leading to single-mode propagation of de Broglie waves and the possible preparation of 1D atom clouds.