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Article Dans Une Revue Science Année : 2020

Fractional statistics in anyon collisions

M. Kumar
  • Fonction : Auteur
A. Marguerite
Jean-Marc Berroir
E. Bocquillon
Bernard Placais
A. Cavanna
U. Gennser
G. Fève
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Résumé

Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor n = 1/m (where m is an odd integer) have been predicted to obey Abelian fractional statistics, with a phase f associated with the exchange of two particles equal to p/m. However, despite numerous experimental attempts, clear signatures of fractional statistics have remained elusive. We experimentally demonstrate Abelian fractional statistics at filling factor n = ⅓ by measuring the current correlations resulting from the collision between anyons at a beamsplitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract f = p/3, in agreement with predictions. I n three-dimensional space, elementary exci-tations fall into two categories depending on the phase f accumulated by the many-body wave function while exchanging two particles. This phase governs the statistics of an ensemble of particles: Bosonic particles, for which f = 0, tend to bunch together, whereas fermions (f = p) antibunch and follow Pauli's exclusion principle. In two-dimensional systems, other values of f can be realized (1, 2), defining types of elementary excitations called anyons (3) that obey fractional or anyonic statistics with intermediate levels of bunching or exclusion. The fractional quantum Hall effect (4, 5), obtained by applying a strong magnetic field perpendicular to a two-dimensional electron gas, is one of the physical systems predicted to host anyons. For a filling factor n of the first Landau level belonging to the Laughlin series (5)-that is, n = 1/m, where m is an odd integer-the exchange phase is predicted to be given by f = p/m (6, 7) interpolating between the bosonic and fermionic limits. Direct experimental evidence of fractional statistics has remained elusive. To date, most efforts have focused on the implementation of single-particle interferometers (8, 9), where the output current is expected to be directly sensitive to the exchange phase f. However, despite many experimental attempts (10-15), clear signatures are still lacking because the observed modulations of the current result not only from the variation of the exchange phase but also from Coulomb blockade and Aharonov-Bohm interference (16). In the case of non-Abelian anyons (17), where the exchange of quasiparticles is described by topological uni-tary transformations, recent heat conduction measurements showed evidence of a non-Abelian state (18, 19), although these results give only indirect evidence of the underlying quantum statistics. Here, we measured the fluctuations or noise of the electrical current generated by the collision of anyons on a beamsplitter (20), thereby demonstrating that the elementary excitations of the fractional quantum Hall effect at filling factor n = ⅓ obey fractional statistics with f = p/3. The measurement of the current noise generated by a single scatterer of fractional quasiparticles (21, 22) has already shown that they carry a fractional charge e* = e/3. Shortly after these seminal works, it was theoretically predicted (20, 23-26) that in conductors comprising several scatterers, noise measurements would exhibit two-particle interference effects where exchange statistics play a central role, and would thus be sensitive to the exchange phase f. In this context, current-current correlation measurements in collider geometries are of particular interest, as they have been extensively used to probe the quantum statistics of particles colliding on a beamsplitter. In a seminal two-particle collision experiment, Hong et al. (27) demonstrated that photons tend to bunch together in the same splitter output, as expected from their bosonic statistics. In contrast, collision experiments implemented in quantum conductors (28-30) have shown a suppression of the cross-correlations between the output current fluctuations caused by the antibunching of electrons, as expected from their fermionic statistics. This behavior can also be understood as a consequence of the Pauli exclusion principle that forbids two fer-mions from occupying the same quantum state at the splitter output. This exclusion principle can be generalized to fractional statistics (31, 32) by introducing an exclusion quasi-probability p (20) interpolating between the fermionic and bosonic limits. In a classical description of a two-particle collision (Fig. 1A) (33), p accounts for the effects of quantum statistics on the probability K of finding two quasiparticles in the same output arm of the beamsplitter: K = T(1-T)(1-p), where T is the single-particle backscattering probability (Fig. 1A). The fermionic case is p = 1, leading to perfect antibunching, K = 0. Contrary to fermions, the bunching of bosons enhances K, meaning that 1-p > 1 and p < 0. To implement collision experiments in quantum conductors, it is necessary to combine a beamsplitter for quasiparticles, a way to guide them ballistically, and two sources to emit them. The two first ingredients can be easily implemented in two-dimensional electron gases in the quantum Hall regime. Quantum point contacts (QPCs) can be used as tunable beamsplitters and, at high magnetic field, charge transport is guided along the chiral edge channels. By combining these elements, single-particle (34) and two-particle (35) electronic interferometers have been realized, and fer-mionic antibunching resulting from the collision between two indistinguishable electrons has been observed (30). Investigating the any-onic case requires replacing the conventional electron sources (such as biased ohmic contacts) by sources of fractional anyonic quasi-particles. As suggested in (20) and as sketched in Fig. 1B, this implies using three QPCs. Two input QPCs labeled QPC1 and QPC2 are biased by dc voltages V 1 and V 2 and tuned in the weak backscattering regime to generate diluted beams of fractional quasiparticles. Indeed, it is known that in the fractional quantum Hall regime, the partitioning of a dc electrical current I 0 with a small backscattering probability T ≪ 1 occurs through the random transfer of quasiparticles of fractional charge q = e* (24). As experimentally observed, the proportionality of the current noise (21, 22) with the input current I 0 , the transmission T, and the fractional charge e* shows that this random transfer follows a Poissonian law. QPC1 and QPC2 can thus be used as Poissonian sources of anyons, which then collide on a third quantum point contact labeled cQPC; cQPC is used as a beamsplitter in the collision experiment. The fractional statistics of the colliding quasiparticles can be revealed by measuring the cross-correlations between the electrical currents at the output of the beamsplitter. The sample (Fig. 1C) is a two-dimensional electron gas (GaAs/AlGaAs). The magnetic field is set to B = 13 T, corresponding to a filling factor n = ⅓ for a charge density n s = 1.09 × 10 15 m-2. At this field and at very low electronic temperature T el = 30 mK, ballistic charge transport occurs along the edges of the sample without backscattering (33). As discussed above, the two quasiparticle sources comprise two quantum point contacts with transmissions T 1 and T 2 (T 1 , T 2 ≪ 1). We apply the voltages V 1 and V 2 to ohmic contacts 1 and 2 in order to RESEARCH
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Dates et versions

hal-02989116 , version 1 (20-11-2020)

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Hugo Bartolomei, M. Kumar, R. Bisognin, A. Marguerite, Jean-Marc Berroir, et al.. Fractional statistics in anyon collisions. Science, 2020, 368 (6487), pp.173-177. ⟨10.1126/science.aaz5601⟩. ⟨hal-02989116⟩
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