Aharonov-Bohm interferometry with a tunnel-coupled wire

Recent experiments (Yamamoto et al 2012 Nature Nanotechnology 7 247) used the transport of electrons through an Aharonov-Bohm (AB) interferometer and two coupled channels (at both ends of the interferometer) to demonstrate a manipulable flying qubit. Results included in-phase and anti-phase (AB) oscillations of the two outgoing currents as a function of the magnetic flux, for strong and weak inter-channel coupling, respectively. Here we present new experimental results for a three terminal interferometer, with a tunnel coupling between the two outgoing wires. We show that in some limits, this system is an even simpler realization of the 'two-slit' experiment. We also present a simple tight-binding theoretical model which imitates the experimental setup. For weak inter-channel coupling, the AB oscillations in the current which is reflected from the device are very small, and therefore the oscillations in the two outgoing currents must cancel each other, yielding the anti-phase behavior, independent of the length of the coupling regime. Technically, the tight binding equations within the two coupled wires have four solutions for each electronic energy. In the 'anti-phase' region all of these solutions are wave-like, oscillating with the distance along the wires. As the coupling between the wires increases, two of these solutions become evanescent, and their amplitudes decay as the electron moves in the wires. In this regime, the amplitudes of the two remaining 'running' waves are proportional to each other, with a ratio which is practically flux-independent. As a result, the two outgoing currents are proportional to each other, yielding the 'in phase' behavior. For larger coupling all the solutions are evanescent, and the outgoing currents become very small.