Measurement of the Transmission Phase of an Electron in a Quantum Two-Path Interferometer

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 \textit{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 \textit{true} transmission phase while the smooth phase shift in the AB oscillation itself does not.Comment: 5 pages, 4 figure

Magneto-capacitance probing of the many-particle states in InAs dots

We use frequency-dependent capacitance-voltage spectroscopy to measure the tunneling probability into self-assembled InAs quantum dots. Using an in-plane magnetic field of variable strength and orientation, we are able to obtain information on the quasi-particle wave functions in momentum space for 1 to 6 electrons per dot. For the lowest two energy states, we find a good agreement with Gaussian functions for a harmonic potential. The high energy orbitals exhibit signatures of anisotropic confinement and correlation effects.Comment: 3 pages, 3 figure

Noise thermometry in narrow 2D electron gas heat baths connected to a quasi-1D interferometer

Thermal voltage noise measurements are performed in order to determine the electron temperature in nanopatterned channels of a GaAs/AlGaAs heterostructure at bath temperatures of 4.2 and 1.4 K. Two narrow two-dimensional (2D) heating channels, close to the transition to the one-dimensional (1D) regime, are connected by a quasi-1D quantum interferometer. Under dc current heating of the electrons in one heating channel, we perform cross-correlated noise measurements locally in the directly heated channel and nonlocally in the other channel, which is indirectly heated by hot electron diffusion across the quasi-1D connection. We observe the same functional dependence of the thermal noise on the heating current. The temperature dependence of the electron energy-loss rate is reduced compared to wider 2D systems. In the quantum interferometer, we show the decoherence due to the diffusion of hot electrons from the heating channel into the quasi-1D system, which causes a thermal gradient.Comment: 6 pages, 5 figure

Non-universal transmission phase behaviour of a large quantum dot

The electron wave function experiences a phase modification at coherent transmission through a quantum dot. This transmission phase undergoes a characteristic shift of $\pi$ when scanning through a Coulomb-blockade resonance. Between successive resonances either a transmission phase lapse of $\pi$ or a phase plateau is theoretically expected to occur depending on the parity of the corresponding quantum dot states. Despite considerable experimental effort, this transmission phase behaviour has remained elusive for a large quantum dot. Here we report on transmission phase measurements across such a large quantum dot hosting hundreds of electrons. Using an original electron two-path interferometer to scan the transmission phase along fourteen successive resonances, we observe both phase lapses and plateaus. Additionally, we demonstrate that quantum dot deformation alters the sequence of transmission phase lapses and plateaus via parity modifications of the involved quantum dot states. Our findings set a milestone towards a comprehensive understanding of the transmission phase of quantum dots.Comment: Main paper: 18 pages, 5 figures, Supplementary materials: 8 pages, 4 figure