Interacting sources for high-precision atom interferometry - a theoretical study

We theoretically study the possibilities to use binary quantum mixtures as sources for high-precision atom interferometers with interferometry times ranging over several seconds. Such schemes are of timely interest in the context of inertial navigation or fundamental physics laws tests. The mixture expansion dynamics are solved by integrating a set of two coupled Gross-Pitaevskii equations. In order to satisfy the severe requirements of a precise differential interferometer, a common delta-kick cooling stage is applied to the two ensembles simultaneously to induce ultra-slow expansion ($\sim$ 50 pk regime). Other systematic effects are analysed and mitigation strategies identified. To illustrate this study, we consider the case of three mixtures of $^{87}$Rb/$^{85}$Rb, $^{87}$Rb/$^{39}$K and $^{87}$Rb/$^{41}$K widely used in atom interferometry measurements. The advantages and drawbacks of every pair are highlighted and discussed.