On the edge of certain fractional quantum Hall states, e.g., at 2/3 and 5/2 filling, a local fractional excitation, occurring by anyon tunneling at a quantum point contact, is further fractionalized into counterpropagating charge and neutral (Abelian or non-Abelian) anyonic excitations. We propose a scheme to detect the braiding statistics of the charge and neutral anyons separately. It is the injection of a dilute beam of a target (charge or neutral) anyon to a Fabry-Perot interferometer. The monodromy of the target anyon is obtained by comparing the amplitude and phase of the interference current with a reference signal of the same setup but without the injection. Our proposal relies on braiding between anyons on the edge, and applies even in the presence of bulk-edge couplings.On the edge of certain fractional quantum Hall states, e.g., at 2/3 and 5/2 filling, a local fractional excitation, occurring by anyon tunneling at a quantum point contact, is further fractionalized into counterpropagating charge and neutral (Abelian or non-Abelian) anyonic excitations. We propose a scheme to detect the braiding statistics of the charge and neutral anyons separately. It is the injection of a dilute beam of a target (charge or neutral) anyon to a Fabry-Perot interferometer. The monodromy of the target anyon is obtained by comparing the amplitude and phase of the interference current with a reference signal of the same setup but without the injection. Our proposal relies on braiding between anyons on the edge, and applies even in the presence of bulk-edge couplings.

Physical Review LettersOct 29, 20240 citations

Open quantum systems in optical microcavities

Violetta Sharoglazova, Marius Puplauskis, Carl Ulrich Mattschas +3 more

Sep 23, 20240 citations

Long-range entanglement and role of realistic interaction in braiding of non-Abelian quasiholes in fractional quantum Hall phases

Ha Quang Trung, Qianhui Xu, Bo Yang

Parity conservation dictates that when fusing pairs of Moore-Read (MR) quasiholes, such that each pair of charge- $e/4$ anyons forms a charge- $e/2$ anyon, the parity of the numbers of 1-anyon and $\ensuremath{\psi}$-anyon must be conserved within a given system. This idea is illustrated here using the Jack polynomial formalism, which also provides a basis to numerically study the dynamics of MR anyons. We find that parity conservation gives rise to a long-range ``entanglement'' between statistics of one pair of anyons and the fusion channels of other anyons in the background. It is, therefore, important to account for all quasiholes in an experimental system in order to accurately predict the measurement outcome. We also examine the effect of two-body electron-electron interaction on the degeneracy of two anyon fusion channels. This understanding of the quasihole dynamics can help to fine-tune two-body interactions in order to stabilize the non-Abelian degeneracy, which is important for detecting non-Abelian braiding in experiments.Parity conservation dictates that when fusing pairs of Moore-Read (MR) quasiholes, such that each pair of charge-$e/4$ anyons forms a charge-$e/2$ anyon, the parity of the numbers of 1-anyon and $\ensuremath{\psi}$-anyon must be conserved within a given system. This idea is illustrated here using the Jack polynomial formalism, which also provides a basis to numerically study the dynamics of MR anyons. We find that parity conservation gives rise to a long-range ``entanglement'' between statistics of one pair of anyons and the fusion channels of other anyons in the background. It is, therefore, important to account for all quasiholes in an experimental system in order to accurately predict the measurement outcome. We also examine the effect of two-body electron-electron interaction on the degeneracy of two anyon fusion channels. This understanding of the quasihole dynamics can help to fine-tune two-body interactions in order to stabilize the non-Abelian degeneracy, which is important for detecting non-Abelian braiding in experiments.

arXiv:2503.13380Physical review. B./Physical review. BOct 8, 20252 citations

General procedure for determining braiding and statistics of anyons using entanglement interferometry

Yi Zhang, Tarun Grover, Ashvin Vishwanath

Recently, it was argued that the braiding and statistics of anyons in a two-dimensional topological phase can be extracted by studying the quantum entanglement of the degenerate ground states on the torus. This construction either required a lattice symmetry (such as $\ensuremath{\pi}/2$ rotation) or tacitly assumed that the minimum entanglement states (MESs) for two different bipartitions can be uniquely assigned quasiparticle labels. Here we describe a procedure to obtain the modular $\mathcal{S}$ matrix, which encodes the braiding statistics of anyons, which does not require making any of these assumptions. Our strategy is to coherently compare MESs of three independent entanglement bipartitions of the torus, which leads to a unique modular $\mathcal{S}$ . This procedure also puts strong constraints on the modular $\mathcal{T}$ and $\mathcal{U}$ matrices without requiring any symmetries, and in certain special cases, completely determines it. Our method applies equally to Abelian and non-Abelian topological phases.Recently, it was argued that the braiding and statistics of anyons in a two-dimensional topological phase can be extracted by studying the quantum entanglement of the degenerate ground states on the torus. This construction either required a lattice symmetry (such as $\ensuremath{\pi}/2$ rotation) or tacitly assumed that the minimum entanglement states (MESs) for two different bipartitions can be uniquely assigned quasiparticle labels. Here we describe a procedure to obtain the modular $\mathcal{S}$ matrix, which encodes the braiding statistics of anyons, which does not require making any of these assumptions. Our strategy is to coherently compare MESs of three independent entanglement bipartitions of the torus, which leads to a unique modular $\mathcal{S}$. This procedure also puts strong constraints on the modular $\mathcal{T}$ and $\mathcal{U}$ matrices without requiring any symmetries, and in certain special cases, completely determines it. Our method applies equally to Abelian and non-Abelian topological phases.

arXiv:1412.0677Physical Review BJan 26, 201525 citations

Parity conservation dictates that when fusing pairs of Moore-Read (MR) quasiholes, such that each pair of charge-

e/4

anyons forms a charge-

e/2

anyon, the parity of the numbers of 1-anyon and $\ensuremath{\psi}$-anyon must be conserved within a given system. This idea is illustrated here using the Jack polynomial formalism, which also provides a basis to numerically study the dynamics of MR anyons. We find that parity conservation gives rise to a long-range ``entanglement'' between statistics of one pair of anyons and the fusion channels of other anyons in the background. It is, therefore, important to account for all quasiholes in an experimental system in order to accurately predict the measurement outcome. We also examine the effect of two-body electron-electron interaction on the degeneracy of two anyon fusion channels. This understanding of the quasihole dynamics can help to fine-tune two-body interactions in order to stabilize the non-Abelian degeneracy, which is important for detecting non-Abelian braiding in experiments.

\mathcal{S}

matrix, which encodes the braiding statistics of anyons, which does not require making any of these assumptions. Our strategy is to coherently compare MESs of three independent entanglement bipartitions of the torus, which leads to a unique modular

\mathcal{S}

. This procedure also puts strong constraints on the modular

\mathcal{T}

and

\mathcal{U}

matrices without requiring any symmetries, and in certain special cases, completely determines it. Our method applies equally to Abelian and non-Abelian topological phases.