Nonequilibrium Dephasing in an Electronic Mach-Zehnder Interferometer

We study nonequilibrium dephasing in an electronic Mach-Zehnder interferometer. We demonstrate that the shot noise at the beam splitter of the interferometer generates an ensemble of nonequilibrium electron density configurations and that electron interactions induce configuration-specific phase shifts of an interfering electron. The resulting dephasing exhibits two characteristic features, a lobe pattern in the visibility and phase jumps of $\pi$, in good agreement with experimental data.

Figure 1

(a) Schematic EMZI setup. It has two beam splitters $j=a,b$ with transmission probabilities $T_j$ and $R_j$, two arms $l=u,d$, two sources $i=1,2$, and two drains $i=3,4$. Only source 1 is biased. (b)–(e) Schematic nonequilibrium ensemble of electron density configurations in the two arms resulting from the shot noise at the splitter (a) when the two arms have two nonequilibrium electrons. The configurations can be described by two packets (dashed lines) propagating towards the drains as marked by solid arrows. The probability $P_m$ of each ensemble element $m$ is marked.

Figure 2

Nonequilibrium dephasing factor $D(\delta )$ (solid curves) and phase shift ${\eta }_D(\delta )$ of $\mathcal{T}$ (dashed curves). In (a) we plot Eqs. (7, 8) while (b) and (c) show the numerical results; see text. In (b), $N$ varies from 0 to 2 as $\delta$ increases up to $1.8\pi$.

Figure 3

Visibility $F$ (solid curves) and phase shift ${\eta }_F$ (dashed curves) of $dI/dV$, as a function of $\delta$.