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Abstract
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.
Highlights
In a recent paper, [1] some of us demonstrated a scalable flying qubit architecture in a four-terminal setup
The early experiments on two-terminal ‘closed’ AB interferometers [2] exhibited a phase rigidity: The minima and maxima of the AB oscillations in the outgoing current stayed at the same values of the magnetic flux through the interferometer ring, irrespective of the details of a quantum dot which was placed on one arm of the interferometer
We have demonstrated a novel two-slit experiment, using an AB ring connected to a tunnel-coupled wire in a three-terminal setup
Summary
In a recent paper, [1] some of us demonstrated a scalable flying qubit architecture in a four-terminal setup. In the present paper we discuss an alternative way to cross between the ‘two-slit’ and the ‘two-terminal’ limits, i.e. between the case in which the oscillation phase reflects the scattering phase through one branch of the interferometer and the case of full phase rigidity. This is achieved by having two outgoing wires, namely by our novel threeterminal setup, consisting of an AB ring and a coupled-wire.
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