Theory of a one-dimensional double-X atom interferometer

The dynamics of an atom waveguide X-junction beam splitter becomes truly 1D in a regime of low temperatures and densities and large positive scattering lengths where the transverse mode becomes frozen and the many-body Schrodinger dynamics becomes exactly soluble via a generalized Fermi-Bose mapping theorem. We analyze the interferometric response of a double-X interferometer of this type due to potential differences between the interferometer arms.