Rabi Interferometry and Sensitive Measurement of the Casimir-Polder Force with Ultra-Cold Gases

We show that Rabi oscillations of a degenerate fermionic or bosonic gas trapped in a double-well potential can be exploited for the interferometric measurement of external forces at micrometer length scales. The Rabi interferometer is less sensitive, but easier to implement, than the Mach-Zehnder since it does not require dynamical beam-splitting/recombination processes. As an application we propose a measurement of the Casimir-Polder force acting between the atoms and a dielectric surface. We find that even if the interferometer is fed with a coherent state of relatively small number of atoms, and in the presence of realistic experimental noise, the force can be measured with a sensitivity sufficient to discriminate between thermal and zero-temperature regimes of the Casimir-Polder potential. Higher sensitivities can be reached with spin squeezed states.