The energy spectrum for a system of atoms in a periodic potential can
exhibit a gap in the band structure. We describe a system in which a l
aser is used to produce a mechanical potential for the atoms, and a st
anding-wave light field is used to shift the atomic levels using the A
utler-Townes effect, which produces a periodic potential. The band str
ucture for atoms guided by a hollow optical fiber waveguide is calcula
ted in three dimensions with quantized external motion. The size of th
e band gap is controlled by the light guided by the fiber. This variab
le band structure may allow the construction of devices that can cool
atoms. The major limitation on this device would be the spontaneous em
ission losses.