Moty Heiblum

Shot-noise measurements through a quantum point contact reveal e/4-charged quasiparticles in the fractional quantum Hall state at \ensuremath{\nu}=1/2, providing evidence consistent with the non-Abelian topological order sought for topological quantum computing.

Aharonov–Bohm interference of fractional quasiparticles in the quantum Hall effect generally reveals their elementary charge (e*)^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}. Recently, our interferometry experiments with several ‘particle states’ reported flux periods of ΔΦ = (e/e*)Φ₀ (with Φ₀ the flux quantum) at moderate temperatures¹⁶. Here we report interference measurements of ‘particle–hole conjugated’ states at filling factors ν = 2/3, 3/5 and 4/7, which revealed unexpected flux periodicities of ΔΦ = ν⁻¹Φ₀. The measured shot-noise Fano factor (F) of the partitioned quasiparticles in each of the quantum point contacts of the interferometer was F = ν (ref. ¹⁷) rather than that of the elementary charge F = e*/e (refs. ^18,19). These observations indicate that the interference of bunched (clustered) elementary quasiparticles occurred for coherent pairs, triples and quadruplets, respectively. A small metallic gate (top gate), deposited in the centre of the interferometer bulk, formed an antidot (or a dot) when charged, thus introducing local quasiparticles at the perimeter of the (anti)dot. Surprisingly, such charging led to a dissociation of the ‘bunched quasiparticles’ and, thus, recovered the conventional flux periodicity set by the elementary charge of the quasiparticles. However, the shot-noise Fano factor (of each quantum point contact) consistently remained at F = ν, possibly due to the neutral modes accompanying the conjugated states. The two observations—bunching and debunching (or dissociation)—were not expected by current theories. Similar effects may arise in Jain’s ‘particle states’ (at lower temperatures) and at even denominator fractional quantum Hall states²⁰.

Aharonov-Bohm (AB) interference in fractional quantum Hall states generally reveals the fractional charge e* of their elementary quasiparticles. Indeed, flux periods of ΔΦ=(e/e*)Φ₀ were observed in interference of ‘particle-like’ fractional states. Here, we report interference measurements of ‘particle-hole conjugated’ states at filling factors ν=2/3, 3/5, and 4/7, revealing the unexpected periodicities, ΔΦ=ν^-1Φ₀. Moreover, the measured shot noise Fano factor (F) of partitioned quasiparticles in the interferometer’s quantum point contacts (QPCs) was F=ν and not the expected F=e*/e. These combined observations indicate that fractional quasiparticles tunnel in the QPCs and interfere as coherently bunched pairs, triples, and quadruplets, respectively. Charging a small metallic gate in the center of the two-path interferometer forms an antidot (or a dot) and introduces local quasiparticles, leading, unexpectedly, to a dissociation of the bunched quasiparticles, thus restoring the flux periodicity set by the elementary quasiparticle charge. The surprising observations of bunching and dissociation, unsupported by current theory, suggest similar effects in particle-like states at lower temperatures.

Fractional quantum statistics are the defining characteristic of anyonic quantum states. Here, we present the observation of Anyonic interference and exchange phases in a novel co-propagating, 'optical-like,' Mach-Zehnder Interferometer (OMZI). Based on co-propagating interface modes, this architecture avoids backscattering and is free of charging effects that often plague the Fabry-Perot interferometer. Consequently, it exhibits a pristine and robust Aharonov-Bohm (AB) interference. At the filling factors ν = 1/3, 2/5, and 3/7, the observed AB flux periodicities: 3Φ₀, 5Φ₀, and 7Φ₀, (Φ₀ = h/e the flux quantum), agree with the fundamental fractionally charged excitations that correspond to Jain states. These flux periodicities depended only on the bulk topological order and not on the variety of tested interface modes for each bulk filling. To probe the Anyonic statistics, we positioned a small charged ‘top gate’ at the interferometer's center, allowing localized quasiparticles to be induced locally without modifying the AB phase of the interferometer. Being spatially isolated from the OMZI edge states, the observed quantized phase slips in the AB pajamas are purely quantum statistical effect. The magnitude of each phase slip corresponds to adding a fractional quasiparticle under the top gate. For ν = 1/3, their signs match theoretical expectations and prior FPI experiments, yet we observe systematic and unexpected deviations in the direction at ν = 2/5 and 3/7. The control over individual quasiparticles in this novel design will be essential for measuring the coveted non-Abelian statistics in the future.

Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an ‘entanglement pointer’ and a ‘statistics-induced entanglement entropy’. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong–Ou–Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following ‘collisions’), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.