Recent measurements of the phase evolution in quantum dots (QD) have attracted much attention.  In these experiments, it had been shown that as electrons transverse the QD, phase climbs by π through each conductance peak [1].  In many-electron dots (containing more than about 15 electrons), a universal behavior of phase lapses was observed.  The phase lapses occur in the Coulomb blockade conductance valleys, between the peaks [2].  A large number of theoretical works were devoted to explain the experimental findings, with the more recent ones agreeing better with the experimental observations [3,4].  The experiments have been performed with a QD embedded in one arm of an Aharonov-Bohm interferometer around zero magnetic field.  In this work, we have realized a QD embedded in one arm of an electronic Mach-Zehnder Interferometer [5], which operates under high magnetic field and in the Quantum Hall Effect regime.

Working in filling factor 2, with the outer edge channel traversing the QD, we found the transport through the QD to be nearly fully coherent.  In the strong coupling regime of the QD, the transmission phase climbs by π across a conductance peak in a nearly linear fashion.  Since in this regime level broadening is of the order of single particle level spacing, single electron transport involves many partly overlapping levels and the nearly linear phase evolution is reasonable.  However, phase lapses take place every two or three conductance peaks.  Even though the periodicity of the phase lapses per number of conductance peaks is not constant, the periodicity in the plunger gate voltage seems to be relatively fixed.  Phase lapses can occur anywhere, be it on the conductance peak or in a valley.  This stands in contrast to the previous measurements conducted at zero magnetic field, where phase lapses were observed only at the conductance valleys.

In the weak coupling regime of the QD, the transmission phase climbs across each conductance peak in a typical Breit-Wigner like coherent resonant tunneling, however, the phase lapses are similar to the above.  Note that the experiments described here are yet preliminary; hence, we will present the latest data and highlight possible scenarios for the physical origin of the observations.

1. "Phase measurement in a quantum dot via a double-slit interference experiment", Schuster R, Buks E, Heiblum M, Mahalu D, Umansky V, Shtrikman H, Nature, Vol. 385, p.417-20 (1997).

2. "Crossover from 'mesoscopic' to 'universal' phase for electron transmission in quantum dots", Avinun-Kalish M, Heiblum M, Zarchin O, Mahalu D, Umansky V, Nature, Vol. 436, p. 529-33 (2007).

3. "Towards an explanation of the mesoscopic double-slit experiment: A new model for charging of a quantum dot", Silvestrov PG and Imry Y, Physical Review Letters, Vol. 85, p. 2565-68 (2000).

4. "Universal phase lapses in a noninteracting model", Oreg Y, New Journal of Physics, Vol. 9, Ar.122 (2007)

5. "An electronic Mach-Zehnder interferometer", Yang Ji, Yunchul Chung, Sprinzak, D., Heiblum, M. Mahalu, D. Shtrikman, H., Nature, Vol.422, p.415-18 (2003).