Interferometry of atoms in concentric ring traps

Recently, an interference experiment of a rotating and a stationary Bose-Einstein condensate was conducted in NIST, as a part of efforts to create the atomic analogue of a SQUID. Inspired by this experiment, we model the interference of two atoms after release from a ``double-ring'' trap. The trap consist of two concentric rings with tight radial and azimuthal confinement, which makes the system before release effectively one-dimensional. One of the rings has a rotating barrier potential, which we model as a $\delta$-function potential. Initially, the particles are in a coherent superposition of being present in either ring. After the trap is released or turned off, the atoms produce a spiral interference pattern. The number of arms of the spiral is determined by the rotation rate of the barrier potential. We investigate numerically and analytically the effect of atom-atom interactions between the atoms and the strength of the barrier on the interference pattern.