Complex circuits of cold atoms can be exploited to devise new protocols for
the diagnostics of cold-atoms systems. Specifically, we study the quench
dynamics of a condensate confined in a ring-shaped potential coupled with a
rectilinear guide of finite size. We find that the dynamics of the atoms inside
the guide is distinctive of the states with different winding numbers in the
ring condensate. We also observe that the depletion of the density, localized
around the tunneling region of the ring condensate, can decay in a pair of
excitations experiencing a Sagnac effect. In our approach, the current states
of the condensate in the ring can be read out by inspection of the rectilinear
guide only, leaving the ring condensate minimally affected by the measurement.
We believe that our results set the basis for definition of new quantum
rotation sensors. At the same time, our scheme can be employed to explore
fundamental questions involving dynamics of bosonic condensates.Comment: Figures are enlarged. Section IV is added. Journal reference adde
