Theory of a Kaptiza-Dirac Interferometer with Cold Trapped Atoms

Abstract

We theoretically analyse a multi-modes atomic interferometer consisting of a sequence of Kapitza-Dirac pulses (KD) applied to cold atoms trapped in a harmonic trap. The pulses spatially split the atomic wave-functions while the harmonic trap coherently recombines all modes by acting as a coherent spatial mirror. The phase shifts accumulated among different KD pulses are estimated by measuring the number of atoms in each output mode or by fitting the density profile. The sensitivity is rigorously calculated by the Fisher information and the Cramér-Rao lower bound. We predict, with typical experimental parameters, a temperature independent sensitivity which, in the case of the measurement of the gravitational constant g can significantly exceed the sensitivity of current atomic interferometers.