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

Contrast and phase-shift of a trapped atom interferometer using a thermal ensemble with internal state labelling