Title: Readout of the atomtronic quantum interference device,
Abstract: A Bose-Einstein condensate confined in ring shaped lattices interrupted by a
weak link and pierced by an effective magnetic flux defines the atomic
counterpart of the superconducting quantum interference device: the atomtronic
quantum interference device (AQUID). In this paper, we report on the detection
of current states in the system through a self-heterodyne protocol. Following
the original proposal of the NIST and Paris groups, the ring-condensate
many-body wave function interferes with a reference condensate expanding from
the center of the ring. We focus on the rf-AQUID which realizes effective qubit
dynamics. Both the Bose-Hubbard and Gross-Pitaevskii dynamics are studied. For
the Bose-Hubbard dynamics, we demonstrate that the self-heterodyne protocol can
be applied, but higher-order correlations in the evolution of the interfering
condensates are measured to readout of the current states of the system. We
study how states with macroscopic quantum coherence can be told apart analyzing
the noise in the time of flight of the ring condensate.