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Aharonov-Bohm interferometry with a tunnel-coupled wire

Recent experiments [M. Yamamoto et al., Nature Nanotechnology 7, 247 (2012)] used the transport of electrons through an Aharonov-Bohm interferometer and two coupled channels (at both ends of the interferometer) to demonstrate a manipulable flying qubit. Results included in-phase and anti-phase Aharonov-Bohm (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. For strong inter-channel coupling, whose range depends on the asymmetry between the channels, and for a relatively long coupling distance, all except two of the waves in the coupled channels become evanescent. For the remaining running waves one has a very weak dependence of the ratio between the currents in the two channels on the magnetic flux, implying that these currents are in phase with each other.