  Multi-terminal Aharonov-Bohm (AB) rings are ideal building blocks for quantum
networks (QNs) thanks to their ability to map input states into controlled
coherent superpositions of output states. We report on experiments performed on
three-terminal GaAs/Al_(x)Ga_(1-x)As AB devices and compare our results with a
scattering-matrix model including Lorentz forces and decoherence. Our devices
were studied as a function of external magnetic field (B) and gate voltage at
temperatures down to 350 mK. The total output current from two terminals while
applying a small bias to the third lead was found to be symmetric with respect
to B with AB oscillations showing abrupt phase jumps between 0 and pi at
different values of gate voltage and at low magnetic fields, reminiscent of the
phase-rigidity constraint due to Onsager-Casimir relations. Individual outputs
show quasi-linear dependence of the oscillation phase on the external electric
field. We emphasize that a simple scattering-matrix approach can not model the
observed behavior and propose an improved description that can fully describe
the observed phenomena. Furthermore, we shall show that our model can be
successfully exploited to determine the range of experimental parameters that
guarantee a minimum oscillation visibility, given the geometry and coherence
length of a QN.
