Extracting the Anyonic Exchange Phase from Hanbury Brown-Twiss Correlations

Abstract

In recent years, interferometry experiments in fractional quantum Hall devices have reported signatures of a fractional braiding phase for quasiparticles. It was noted, however, that the braiding phase alone does not uniquely determine the exchange phase because of a $π$-ambiguity. Here we analyze a Hanbury Brown-Twiss interferometer in a cross geometry that provides direct access to the fractional exchange phase. Using a non-equilibrium Keldysh calculation in an experimentally relevant regime, we show that the exchange phase can be obtained as the phase shift between Aharonov-Bohm oscillations in a single-particle interference current and those in the current cross-correlation arising from two-particle interference.

Figures (5)

• Figure 1: Schematic of the cross-geometry interferometer. Four chiral edges are connected pairwise to their neighbors by QPCs, enabling both single-particle and two-particle interference. On each edge the two QPCs are separated by a distance $a$, and the tunneling amplitudes are denoted by $\gamma_{nm}$. The enclosed magnetic flux produces the Aharonov--Bohm phase $\phi_{AB}$.
• Figure 2: Interfering processes contributing to two-particle interference in the current cross-correlation (a) and to single-particle interference in the current (b). Both acquire an Aharonov--Bohm phase from the enclosed flux. In (a), the two outgoing states differ by exchanging the two quasiparticles, yielding an additional statistical phase $\theta$ and therefore shifting the AB oscillations relative to (b).
• Figure 3: Normalized Aharonov--Bohm oscillations of the interference current and of the AB-dependent current cross-correlation in their respective voltage configurations. The relative phase shift equals the exchange phase $\theta=\pi\nu$, shown here for $\nu=1/3$.
• Figure 4: Additional phase shift $\delta$ of the single-particle interference current as a function of bias $V$ for several temperatures $T$. For $\nu=1/3$ and fixed dimensionless $e^*a\Delta V/(\hbar v)=0.06$, we extract $\delta$ from $I_{3,AB}\propto\cos(\phi_{AB}+\delta)$ in the regime of Eq. \ref{['eq:I_AB']}.
• Figure 5: In general, the AB-dependent part of the current cross-correlation can be written as $S_{AB}\propto\cos(\phi_{AB}+\pi\nu+\delta_S)$. The numerical results show that for the voltage configuration used in the main text the additional phase shift $\delta_S$ vanishes even at finite temperature and for finite separation of the tunneling points. Parameters: $\tilde{V}=10$ and $\Delta\tilde{V}=2.5$.