Measurement of the transmission phase of an electron in a quantum two-path interferometer

Abstract

A quantum two-path interferometer allows for direct measurement of the transmission phase shift of an electron, providing useful information on coherent scattering problems. In mesoscopic systems, however, the two-path interference is easily smeared by contributions from other paths, and this makes it difficult to observe the true transmission phase shift. To eliminate this problem, multi-terminal Aharonov-Bohm (AB) interferometers have been used to derive the phase shift by assuming that the relative phase shift of the electrons between the two paths is simply obtained when a smooth shift of the AB oscillations is observed. Nevertheless the phase shifts using such a criterion have sometimes been inconsistent with theory. On the other hand, we have used an AB ring contacted to tunnel-coupled wires and acquired the phase shift consistent with theory when the two output currents through the coupled wires oscillate with well-defined anti-phase. Here, we investigate thoroughly these two criteria used to ensure a reliable phase measurement, the anti-phase relation of the two output currents and the smooth phase shift in the AB oscillation. We confirm that the well-defined anti-phase relation ensures a correct phase measurement with a quantum two-path interference. In contrast we find that even in a situation where the anti-phase relation is less well-defined, the smooth phase shift in the AB oscillation can still occur but does not give the correct transmission phase due to contributions from multiple paths. This indicates that the phase relation of the two output currents in our interferometer gives a good criterion for the measurement of the true transmission phase while the smooth phase shift in the AB oscillation itself does not.The transmission phase of an electron plays a crucial role in various quantum interference phenomena. Full characterization of the coherent transport therefore requires a reliable phase measurement, but this is still challenging. One may envisage a quantum two-path interferometer because the interference is measured as a function of the phase difference between the two paths. For instance the phase shift across a quantum dot (QD), in which one can control the quantum state of single electrons, can be measured using a QD embedded in one of the two arms of the interferometer. The theory predicts a Breit-Wigner type phase shift across a Coulomb peak (CP) 1 and a π/2 phase shift across a Kondo-singlet state 2 and both were experimentally investigated. The Breit-Wigner type phase shift was confirmed by a pioneering experiment for a QD embedded in a multiterminal Aharonov-Bohm (AB) interferometer 3 . The phase shift was derived from a smooth shift of AB oscillation phase. However, unanticipated results have sometimes been observed, such as a universal phase lapse between CPs for a large QD 3,4 and a large phase shift exceeding π across two Coulomb peaks of a spin degenerated level for a Kondo correlated QD 5,6 . Although a) Electronic mail: shintaro.takada@neel.cnrs.fr several mechanisms have b...

Time-dependent wave packet simulations of transport through Aharanov–Bohm rings with an embedded quantum dot

“…However, the main focus was in the opening of the systems and in partial coherent transport using one-dimensional models for the leads without taking into account other distorting effects like possible scattering in the junctions of the interferometric arms. Experimental advances in this direction have been made recently trying to find more clear criteria about when the phase measurements can be trusted and when the contributions from multiple path can be neglected [33]. A different approach was taken by Fischer et al [34].…”

Mesoscopic phase behavior in a quantum dot around crossover between single-level and multilevel transport regimes

“…The measured phase shift can be unintentionally modified from the true phase shift by contributions from multi-path interferences [18,19]. Recently we have demonstrated a way how to measure the true transmission phase of an electron [20]. We have shown that the criterion used in our experiments using our original two-path interferometer ensures the proper measurement [20] while those used in other previous experiments are a bit less reliable [1,3].…”

“…Recently we have demonstrated a way how to measure the true transmission phase of an electron [20]. We have shown that the criterion used in our experiments using our original two-path interferometer ensures the proper measurement [20] while those used in other previous experiments are a bit less reliable [1,3]. Therefore a careful experimental investigation of is required to have comprehensive understanding of the phase behavior across a QD.Here we investigate the transmission phase across a QD around the crossover between single-level and multi-arXiv:1709.08876v1 [cond-mat.mes-hall]…”

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