Collision of quantum particles remains an effective way of probing their mutual statistics. Colliders based on quantum point contacts in quantum Hall edge states have been successfully used to probe the statistics of the underlying quantum particles. Notwithstanding the extensive theoretical work focusing on pointlike colliders, when it comes to experiment, the colliders are rarely pointlike objects and can support a resonant level or multiple tunneling points. We present a study of a paradigmatic extended (non-point-like) fermionic collider (and an extension to bosonic colliders). As with particle interferometers, in an extended collider there is an infinite number of trajectories for any single- or multiparticle event. Self-interference of the former can lead to an apparent bunching of fermions when we compare the cross-current correlator with a classical benchmark representing two colliding beams. In view of this apparent bunching behavior of fermions, we identify an experimentally accessible current correlator, which reveals the true mutual statistics of fermions.
Collision of quantum particles remains an effective way of probing their mutual statistics. Colliders based on quantum point contacts in quantum Hall edge states have been successfully used to probe the statistics of the underlying quantum particles. Notwithstanding the extensive theoretical work focusing on pointlike colliders, when it comes to experiment, the colliders are rarely pointlike objects and can support a resonant level or multiple tunneling points. We present a study of a paradigmatic extended (non-point-like) fermionic collider (and an extension to bosonic colliders). As with particle interferometers, in an extended collider there is an infinite number of trajectories for any single- or multiparticle event. Self-interference of the former can lead to an apparent bunching of fermions when we compare the cross-current correlator with a classical benchmark representing two colliding beams. In view of this apparent bunching behavior of fermions, we identify an experimentally accessible current correlator, which reveals the true mutual statistics of fermions.
Mesoscopic colliders provide an effective platform for probing the mutual statistics of quantum particles. Recent experiments have successfully extracted the mutual statistics of fermions, and more exotic anyons using quantum point contacts (QPCs). Coupling a point-like collider, such as a quantum point contact, to a two-level impurity or qubit can induce statistical transmutation of fermions, causing them to display boson-like bunching tendencies. Here, we extend the analysis to an extended collider. We investigate the scattering of two incoming fermionic and bosonic wave packets in the presence of post-selection on the impurity state, and systematically analyze the possible benchmarks used to characterize bunching and infer the underlying mutual statistics. We show that only a specific benchmark faithfully captures the mutual statistics of the colliding particles, while alternative choices can produce spurious statistical signatures. Hence, the correct benchmark for probing the quantum statistics depends on the intricate details of the mesoscopic collider.
Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the many-particle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we show that the collective interference of three or more particles leads to much more diverse behavior than expected from the boson–fermion dichotomy known from quantum statistical mechanics. The emerging complexity of many-particle interference is tamed by a simple law for the strict suppression of events in the Bell multiport beam splitter. The law shows that counting events are governed by widely species-independent interference, such that bosons and fermions can even exhibit identical interference signatures, while their statistical character remains subordinate. Recent progress in the preparation of tailored many-particle states of bosonic and fermionic atoms promises experimental verification and applications in novel many-particle interferometers.
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; (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, 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.
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.
Abstract A collider where particles are injected onto a beam splitter from opposite sides has been used for identifying quantum statistics of identical particles. The collision leads to bunching of the particles for bosons and antibunching for fermions. In recent experiments, a collider was applied to a fractional quantum Hall regime hosting Abelian anyons. The observed negative cross-correlation of electrical currents cannot be understood with fermionic antibunching. Here we predict, based on a conformal field theory and a non-perturbative treatment of non-equilibrium anyon injection, that the collider provides a tool for observation of the braiding statistics of various Abelian and non-Abelian anyons. Its dominant process is not direct collision between injected anyons, contrary to common expectation, but braiding between injected anyons and an anyon excited at the collider. The dependence of the resulting negative cross-correlation on the injection currents distinguishes non-Abelian SU(2)k anyons, Ising anyons, and Abelian Laughlin anyons.
Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. This interference is a direct result of quantum exchange statistics, however, it is observed only in the joint probability to find the particles in two separated detectors. Here we report the first observation of such interference fringes between two independent and non-interacting electrons in an interferometer proposed by Yurke et al. and Samuelsson et al. Our experiment resembles the "Hanbury Brown and Twiss" (HBT) experiment, which was performed with classical waves. In the experiment, two independent and mutually incoherent electron beams were each partitioned into two trajectories. The combined four trajectories enclosed an Aharonov-Bohm (AB) flux (but not the two trajectories of a single electron). While individual currents were found to be independent of the AB flux, as expected, the cross-correlation between current fluctuations in two opposite points across the device exhibited strong AB oscillations. This is a direct signature of orbital entanglement between two electrons even though they never interact with each other.