%0 Journal Article
%J Physical Review A
%D 2015
%T Self-heterodyne detection of the \it in-situ phase of an atomic-SQUID
%A Ranchu Mathew
%A Avinash Kumar
%A Stephen Eckel
%A Fred Jendrzejewski
%A Gretchen K. Campbell
%A Mark Edwards
%A Eite Tiesinga
%X We present theoretical and experimental analysis of an interferometric measurement of the {\it in-situ} phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the {\it in-situ} phase can be accurately determined. Mean-field estimates and numerical simulations show that the inter-atomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the {\it in-situ} phase drop.
%B Physical Review A
%V 92
%P 033602
%8 2015/09/03
%G eng
%U http://arxiv.org/abs/1506.09149v2
%N 3
%! Phys. Rev. A
%R 10.1103/PhysRevA.92.033602