Anyonic analogue of optical Mach-Zehnder interferometer

TL;DR

The paper introduces an anyonic analogue of an optical Mach-Zehnder interferometer built from co-propagating edge channels with two tunneling constrictions, eliminating a drain inside the device to keep the trapped topological charge time-independent. By mapping to a free-fermion problem in specific limits, it derives exact expressions for electric current and noise, revealing a simple current form $I = A + B\cos\varphi$ and phase jumps $\Delta\varphi = -\frac{4\pi}{2k+1}$ tied to anyonic statistics, with $e^*=e/(2k+1)$ for Jain states. The analysis extends to thermal transport, showing analogous interference effects and a Wiedemann–Franz-type relation with an anomalous Lorenz factor, and it provides perturbative results beyond the exactly solvable limits. The work offers a transparent, testable framework for probing Abelian anyon statistics and suggests avenues toward non-Abelian statistics, while highlighting reduced sensitivity to bulk-edge coupling and clear experimental accessibility.

Abstract

Anyonic interferometry is a direct probe of fractional statistics. We propose an interferometry geometry that parallels an optical Mach-Zehnder interferometer and offers several advantages over existing interferometry schemes. In contrast to the currently studied electronic Mach-Zehnder interferometer, our setup has no drain inside the device so that the trapped topological charge is time-independent. In contrast to electronic Fabry-Pérot interferometry, anyons cannot go around the device more than once. Thus, the interference signal has a straightforward interpretation in terms of anyonic statistical phases. The proposed geometry suppresses the undesirable effects of bulk-edge coupling. Moreover, the setup allows for simple exact solutions for the electric current and noise for an arbitrary quasiparticle tunneling strength in a broad range of conditions. The structure of the solutions is similar to that for non-interacting electrons but reflects fractional charge and statistics. We present results for electric current and noise in Jain states and address thermal interferometry at zero voltage bias.

Figures (8)

• Figure 1: Previously studied anyon interferometer designs. a) A Fabry-Pérot interferometer. Charge travels along the edges from sources S and G to drains D1 and D2. Dotted lines show tunneling between the opposite edges with the amplitudes $\Gamma_{1,2}$. (b) A Mach-Zehnder interferometer. The same Ohmic contact D1 serves as the source and drain for the inner edge.
• Figure 2: Optical Mach-Zehnder interferometer. The beam is emitted from source S. Once split, the beam has its paths go along the same direction and then meet at a later point. The anyonic device we present here is able to realize this key principle.
• Figure 3: An anyonic analogue of an optical Mach-Zehnder interferometer. Arrows on thick black lines show the direction of charge propagation. Two constrictions allow quasiparticle tunneling between the two channels with the amplitudes $\Gamma_{1,2}$.
• Figure 4: We consider $\varphi=0$, $V_2=0$, and the filling factor of the topological liquid probed by the device is $k/(2k+1)$. Panel (a) shows the dependence of $F^{\rm int}_k$ on the normalized bias $\lambda$ at a fixed difference $\chi=0.5$ of the normalized propagation times between the constrictions along the two channels. Panel (b) shows the dependence of $F^{\rm int}_2$, which corresponds to a fixed filling factor $\nu=2/5$, on the bias $\lambda$ at various differences $\chi$ of the travel times along the two paths. In the limit $\chi\rightarrow 0$, a simple result (\ref{['Eq36']}) is recovered. Beyond that limit, the interference contribution to the current oscillates as the voltage bias increases.
• Figure 5: For a topological liquid with a filling factor of $\nu=k/(2k+1)$, the function $F^{\text{int}}_k$ describes the behavior of the thermal current via Eq. (\ref{['Eq85']}). We consider $\varphi=0$ here. Panel (a) shows the dependence of $F^{\rm int}_k$ on the temperature ratio $n\equiv \Theta_1/\Theta_2$ at a fixed difference $\chi=0.5$ of the normalized propagation times between the constrictions along the two channels. Panel (b) shows the dependence of $F^{\rm int}_2$, which corresponds to a fixed filling factor $\nu=2/5$, on the temperature ratio $n$ at various differences $\chi$ of the travel times along the two paths. In the limit $\chi\rightarrow 0$, a simple result (\ref{['Eq89']}) is recovered.