  We study the quantum properties of Rydberg atoms in a magnetic
Ioffe-Pritchard trap which is superimposed by a homogeneous electric field.
Trapped Rydberg atoms can be created in long-lived electronic states exhibiting
a permanent electric dipole moment of several hundred Debye. The resulting
dipole-dipole interaction in conjunction with the radial confinement is
demonstrated to give rise to an effectively one-dimensional ultracold Rydberg
gas with a macroscopic interparticle distance. We derive analytical expressions
for the electric dipole moment and the critical linear density of Rydberg
atoms.
