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

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.