Monitored quantum transport: full counting statistics of a quantum Hall interferometer

Abstract

We generalize the Levitov-Lesovik formula for the probability distribution function of the electron charge transferred through a phase coherent conductor, to include projective measurements that monitor the chiral propagation in quantum Hall edge modes. When applied to an electronic Mach-Zehnder interferometer, the monitoring reduces the visibility of the Aharonov-Bohm conductance oscillations while preserving the binomial form of the counting statistics, thereby removing a fundamental shortcoming of the dephasing-probe model of decoherence.

Figures (2)

• Figure 1: Schematic illustration of charge transfer via $N=6$ chiral modes, in which unitary propagation (scattering operators $\hat{S}_i$) alternates with $p=4$ projective measurements of the occupation number of specific modes. In this example the measurement outcomes are "empty" for the third measurement (of mode number $n=5$), and "filled" for the other three measurements.
• Figure 2: Schematic illustration of the Mach-Zehnder interferometer in a quantum Hall insulator. Two chiral edge modes ($n=1,2$) are coupled at a pair of beam splitters (scattering matrices $S_1$ and $S_2$). Charge is injected into the edge modes at the Fermi level by a voltage source $V$. A projective measurement (with probability $\varepsilon$) of the occupation of the $n=1$ edge mode provides "which-path" information that reduces the visibility in the outgoing current $I(t)$ of the Aharonov-Bohm oscillations as a function of the enclosed magnetic flux $\Phi$. For the time-averaged current the dephasing-probe model gives the same result as the projective measurement, for the current fluctuations only the projective measurement gives results consistent with binomial statistics.