Exactly solved model for an electronic Mach-Zehnder interferometer

We study nonequilibrium properties of an electronic Mach-Zehnder interferometer built from integer quantum Hall edge states at filling fraction $\nu =1$. For a model in which electrons interact only when they are inside the interferometer, we calculate exactly the visibility and phase of Aharonov-Bohm fringes at finite source-drain bias. When interactions are strong, we show that a lobe structure develops in visibility as a function of bias, while the phase of fringes is independent of bias, except near zeros of visibility. Both features match the results of recent experiments [Neder et al., Phys. Rev. Lett. 96, 016804 (2006)].

Figure 1

Visibility as a function of bias voltage for MZI with $d_1=d_2$ and $t_a^2=t_b^2=1/2$ at interaction strengths: $\tilde{\gamma }=1$ (dot-dashed line), $\tilde{\gamma }=2$ (dashed line), and $\tilde{\gamma }=3$ (full line), where $\tilde{\gamma }=2\pi \gamma$. Inset: schematic view of model studied.

Figure 2

Dependence of interference fringe phase on bias voltage for MZI with unequal arm lengths, $d_2/d_1=1.2$, at interaction strengths: $\tilde{\gamma }=0$ (dot-dashed line), $\tilde{\gamma }=3$ (dashed line), and $\tilde{\gamma }=10$ (full line). Inset: the kernel $Q\left(x\right)$ of Eq. (11) at $\tilde{\gamma }=10$ (full line) and that of Ref. 11 (dashed line).