Hanbury Brown–Twiss Interference of Anyons

Abstract

We present a study of an Hanbury Brown and Twiss (HBT) interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate HBT cross-correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmutation from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought as intermediate between bosons and fermions.Two-particle interference is a major pillar of quantum mechanics, very much like the phenomenon of single particle interference. Such interference has been observed with photons in the historical Hanbury Brown and Twiss (HBT) experiment [1,2], and much later with electrons [3]. Quantum Hall systems can exhibit emergent particles (dubbed anyons) with fractional statistics [4,5]. Despite intensive study, direct signatures of anyonic statistics remain elusive. Here we study an HBT interferometer with anyons, which can directly probe entanglement and fractional statistics of initially uncorrelated particles. Specifically, we calculate HBT crosscorrelations of Abelian Laughlin anyons. The correlations exhibit partial bunching similar to bosons, indicating a substantial statistical transmutation from the underlying electronic degrees of freedom [6]. Furthermore, we find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought as intermediate between bosons and fermions.Edge channels of a fractional quantum Hall system offer a natural framework to study transport properties of anyons. Earlier attempts to consider entanglement of such quasiparticles (QPs) either addressed time-resolved correlation functions [7] (which may be very hard to measure) or relied on a single source geometry setup [8][9][10] (which may introduce superfluous interaction-induced correlations). Here we study zero frequency currentcurrent correlations in a truly HBT interferometer setup, whose physics is governed by QPs dynamics. Because of their fractional charge and fractional statistics, scattering of these QPs results in non trivial correlations. Below, we consider the case ν = 1/3 for concreteness, but, our analysis can be generalized to other Laughlin fractions.Consider first a heuristic estimate of these correlations, outlined in Fig. 1. Two particles are emitted respectively from two sources S 1 and S 2 and scattered towards two detectors D 1 and D 2 by a beam splitter, e.g. a quantum point contact (QPC) for electrons and QPs, or a half silvered mirror for photons. We evaluate the probability P (m, 2 − m), m = 0, 1, 2, that m particles are collected at the drain D 1 while (2 − m) are collected at the drain D 2 . Consider, e.g., the diagrams contributing to P (1, 1) [cf. Fig. 1(a)]. Each diagram represents an amp...

Hanbury Brown and Twiss correlations in quantum Hall systems

“…This work substantiates and details some of the results reported in Ref. [1], and extends the analysis of electronic (and anyonic) HBT interferometry to new setups and further filling fractions. Our analysis applies to a two-dimensional electron gas in both an integer (ν = 1) filling fraction, and a fractional (Laughlin) ν = 1/(2n+1) filling fraction.…”

“…We, note, though that barring additional manipulations δt block ∼ /W (1) , and the inequality Eq. (E27) is not satisfied.…”

“…The size of a block is proportional to /W (1) (W (1) is the singleparticle rate). We could now require that W (1) δt block ,…”

“…Thus, we are able to represent the 12 th -order perturbative contribution to the current correlation function as a sum of all possible triple products corresponding to the three quasiparticle loops: 3,6), (1,6), (3,9), (1 where we denote the products of quasiparticle loops symbolically as follows:…”

Influence of device geometry on tunneling in theν=52quantum Hall liquid

“…3, with metal. Other methods that could show unique signatures of Abelian and nonAbelian states include thermopower measurements 28,37 and Mach-Zehnder interferometry 18,52,[58][59][60][61][62][63][64] . The nonequilibrium fluctuation-dissipation theorem 65,66 would provide an independent test of the existence of upstream modes.…”