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.
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.