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arXiv:cond-mat/0512102 · Physical Review A

Limits on weak magnetic confinement of neutral atoms

Charles A. Sackett

Published Jan 26, 2006• 12 citations
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Abstract

It is shown that when a magnetic field is used to support neutral atoms against the gravitational force $mg$, the total curvature of the field magnitude $B$ must be larger than ${m}^{2}{g}^{2}∕(2{\ensuremath{\mu}}^{2}B)$, where $\ensuremath{\mu}$ is the magnetic moment of the atoms. This limits the minimum confinement strength obtainable for a trapped atomic gas. It is also conjectured that the curvature must be larger than twice this value for a magnetic potential that varies in only one or two dimensions, such as an atomic waveguide.

DOI
10.1103/physreva.73.013626

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It is shown that when a magnetic field is used to support neutral atoms against the gravitational force mgmgmg, the total curvature of the field magnitude BBB must be larger than m2g2∕(2\ensuremathμ2B){m}^{2}{g}^{2}∕(2{\ensuremath{\mu}}^{2}B)m2g2∕(2\ensuremathμ2B), where \ensuremathμ\ensuremath{\mu}\ensuremathμ is the magnetic moment of the atoms. This limits the minimum confinement strength obtainable for a trapped atomic gas. It is also conjectured that the curvature must be larger than twice this value for a magnetic potential that varies in only one or two dimensions, such as an atomic waveguide.
Magnetic trapping of laser-cooled neutral atoms has been demonstrated at NBS and is progressing in other laboratories. Confinement of any object requires exchanging kinetic for potential energy, and for neutral atoms, this necessarily derives from shifts of internal energy levels. This is implemented through the force experienced by the atomic magnetic moment in a carefully designed, highly inhomogeneous field. Since magnetic fields of convenient strength can shift atomic energy levels by only a few gigahertz (temperature ≌ 0.1 K), neutral atom traps are very shallow and must be loaded with very cold atoms. We present some motivations for using magnetic traps and then discuss the constraints and optimal configurations of various arrangements. For example, no trap can be isotropic. Next we discuss both the classical and quantum mechanical motions of trapped atoms. These motions are important for at least two reasons: First, several schemes under study for further cooling depend on knowing the position and velocity of the atoms, as well as the vector field at each point along the orbit. Second, magnetic traps depend on the atomic moment remaining aligned with the field as the atom orbits in the trap, and this precludes rapid motion through a low-field region.
We have been studying the use of inhomogeneous magnetic fields for the trapping of neutral atoms via the interaction with their magnetic moments. Apart from gravitational forces (which may turn out to be of great importance in atom traps), only electromagnetic forces are of real interest for trapping neutral atoms, and these forces must necessarily arise from the interaction of multipole moments and inhomogeneous fields. In this paper we restrict ourselves to static traps and magnetic dipoles, even though optical, quasi‐static, and Stark effect traps have been discussed. We present some discussion of the field configurations that might be used, of the motion of ‘‘warm’’ trapped atoms (about 1 K), and of the states of ‘‘cold’’ trapped atoms (about 0.1 μK). The basic scale of the interaction is set by the ratio of the Bohr magneton to the Boltzmann constant, about 1.5 Tesla/Kelvin.
The magnetic methods most successful so far for tight, stable confinement of cold neutral atoms in the dark explore three-dimensional-nonuniform magnetic configurations. A different method, using revolving planar-nonuniform fields, is developed in the present work. The paper gives an idea of the method, describes its basic features, and shows its superiority, such as (i) a greater product of curvatures of the trap well in the three spatial directions by a factor of two orders of magnitude given the same magnitude of field gradient, (ii) tight, stable, and more isotropic confinement in both the trap center and an easy-to-change orbit, (iii) vast possibilities to change the form of the trap well, and (iv) the possibility to separately detect the effective spin and translational motion temperatures of the cloud via observations of its density distribution.
The trapping of charged elementary particles and ions by various electromagnetic field configurations is a well established art. Last month (page 17) we told of a lone electron that was confined for almost a year in the vacuum of a Penning trap, yielding a superbly delicate observation of lowenergy relativistic hysteresis. But the trapping of electrically neutral particles—atoms in particular—is quite another matter. In the absence of the simple Lorentz force acting on a charged particle, one has to reach for a much weaker, second-order handle—the atom's magnetic or induced electric dipole moment. A variety of ingenious magnetic and laser traps have been proposed for atoms, but they all suffer a severe limitation: The weak dipole interaction with the trapping field yields only very shallow trapping potential wells, generally incapable of holding an atom moving much faster than a man can run—about 10 meters/second.