  We discuss the properties of ultracold Rydberg atoms in a Ioffe-Pritchard
magnetic field configuration. The derived two-body Hamiltonian unveils how the
large size of Rydberg atoms affects their coupling to the inhomogeneous
magnetic field. The properties of the compound electronic and center of mass
quantum states are thoroughly analyzed. We find very tight confinement of the
center of mass motion in two dimensions to be achievable while barely changing
the electronic structure compared to the field free case. This paves the way
for generating a one-dimensional ultracold quantum Rydberg gas.
