  Inspired from Sutherland's work [Phys. Rev. Lett. {\bf 74}, 816 (1995)] on
detecting bound spin waves, we propose that bound electron states can be
detected from the dependence of interacting electron systems to the
Aharonov-Bohm flux in the `extended zone' scheme, where the electron pairing
halves the original period $N_a$ flux quanta in a system of linear size $N_a$.
Along with the Bethe-ansatz analysis, a numerical implementation for keeping
track of the adiabatic flow of energy levels is applied to the
attractive/repulsive Hubbard models and the $t-J$ ladder.
