Controlled electron transport in coupled Aharonov-Bohm rings

We propose a simple model of two coupled mesoscopic rings threaded by magnetic flux which mimics a device for electron transmission in a controlled fashion. Within a tight binding formalism we work out exactly the conditions when a completely ballistic transmission can be triggered at any desired position of the Fermi level within a continuous range of energy. The switching action can be easily controlled by appropriately tuning the values of the flux through the two rings. The general transmission across the ring system displays interesting features characterized by the appearance and collapse of Fano resonances, and the suppression of the Aharonov-Bohm oscillations in several cases. We report and analyze exact analytical results for a few such cases.