  We report a theoretical study of a double-well Ramsey interferometer using
internal state labelling. We consider the use of a thermal ensemble of cold
atoms rather than a Bose-Einstein condensate to minimize the effects of atomic
interactions. To maintain a satisfactory level of coherence in this case, a
high degree of symmetry is required between the two arms of the interferometer.
Assuming that the splitting and recombination processes are adiabatic, we
theoretically derive the phase-shift and the contrast of such an interferometer
in the presence of gravity or an acceleration field. We also consider using a
"shortcut to adiabaticity" protocol to speed up the splitting process and
discuss how such a procedure affects the phase shift and contrast. We find that
the two procedures lead to phase-shifts of the same form.
