Fabry-Pérot interferometry with stochastic anyonic sources

Abstract

We investigate the interference of Laughlin quasiparticles (QPs) in the fractional quantum Hall regime that are stochastically injected into a Fabry-Pérot interferometer. We find that the effective Aharonov-Bohm (AB) phase accumulated along the interferometer loop acquires an additional contribution of $\sin(2πλ)/2$ per QP present on it, where $πλ$ is the QP exchange phase. This contribution originates from time-domain braiding processes associated with injected QPs passing the interferometer quantum point contacts. In the limit of symmetric QP injection, the tunneling current noise exhibits AB oscillations as a function of the total injected current, providing access to the exchange phase $πλ$. In the regime of large total injection, we identify a universal Fano factor that displays power-law scaling and a characteristic phase shift reflecting real-space QP braiding along the interferometer edges. These results are relevant for accessing anyonic exchange statistics in mesoscopic interferometers.

Figures (3)

• Figure 1: Schematic of an anyonic Fabry--Pérot interferometer (FPI). The blue region denotes the fractional quantum Hall fluid. Dilute beams of Laughlin quasiparticles (QPs) are injected via the source contacts, QPCU and QPCD, from sources $S_1$ and $S_4$, with average currents $\langle I_{{\rm u},0}\rangle$ and $\langle I_{{\rm d},0}\rangle$, respectively. The QPs then backscatter and interfere via QPCL and QPCR, forming an interference loop of total perimeter $L_+ = L_{\rm u} + L_{\rm d}$, where $L_{\rm u,d}$ are the lengths of the loop arms. $\Phi_{\rm eff}$ represents the total effective Aharonov-Bohm phase accumulated upon traversing the loop once. In the nonequilibrium steady state, the outgoing currents $\langle I_{\rm u} \rangle$ and $\langle I_{\rm d} \rangle$ are detected at $D_2$ and $D_3$, respectively.
• Figure 2: Interference contributions $\langle I_{\rm int}\rangle$, $\langle S_{\rm int}\rangle$, and $\langle K_{\rm int}\rangle$ to the average tunneling current, its noise, and the outgoing current cross-correlator, shown as functions of $N = I_+ L_+ /(v e^\ast)$ for Laughlin filling fractions $e\lambda = e^\ast = e/m$. Here, $I_B = |\zeta_{\rm L}|\,|\zeta_{\rm R}|\,\tau_c^{2\lambda} I_+^{2\lambda-1}$, $I_- = 0.4 I_+$ and the bare AB phase $\Phi = \pi/2$. In the large-$N$ limit, interference effects are washed out due to the power-law decay of equilibrium correlation functions and random phase fluctuations along the edges $\mathrm{u}$ and $\mathrm{d}$. The quantity $I_-$ captures a phase imbalance between the edges $\mathrm{u}$ and $\mathrm{d}$, such that increasing it from zero results in stronger dephasing compared to $I_-=0$, see Fig. \ref{['fig:Sint_AB_oscillations']}.
• Figure 3: Aharonov--Bohm (AB) oscillations of the interference contribution to the tunneling current noise, $\langle S_{\rm int}\rangle$, shown as a function of $N = I_+ L_+ /(v e^\ast)$ for $e\lambda = e^\ast = e/m$. The parameters are $I_B = |\zeta_{\rm L}|\,|\zeta_{\rm R}|\,\tau_c^{2\lambda} I_+^{2\lambda-1}$, $\Phi = \pi/2$, and $I_- = 0$. The oscillation frequency is $\sin(2\pi\lambda)/2$.