  We propose to apply atom-chip techniques to the trapping of a single atom in
a circular Rydberg state. The small size of microfabricated structures will
allow for trap geometries with microwave cut-off frequencies high enough to
inhibit the spontaneous emission of the Rydberg atom, paving the way to
complete control of both external and internal degrees of freedom over very
long times. Trapping is achieved using carefully designed electric fields,
created by a simple pattern of electrodes. We show that it is possible to
excite, and then trap, one and only one Rydberg atom from a cloud of ground
state atoms confined on a magnetic atom chip, itself integrated with the
Rydberg trap. Distinct internal states of the atom are simultaneously trapped,
providing us with a two-level system extremely attractive for atom-surface and
atom-atom interaction studies. We describe a method for reducing by three
orders of magnitude dephasing due to Stark shifts, induced by the trapping
field, of the internal transition frequency. This allows for, in combination
with spin-echo techniques, maintenance of an internal coherence over times in
the second range. This method operates via a controlled light shift rendering
the two internal states' Stark shifts almost identical. We thoroughly identify
and account for sources of imperfection in order to verify at each step the
realism of our proposal.
