Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scattering, interference, and quantum chaos in the anyon-Hubbard model

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

In textbook physics, all particles are categorized as either bosons or fermions. When exchanging two bosons, the corresponding wavefunction is dressed with an exchange phase $\varphi=0$, whereas for fermions the exchange phase is $\varphi=\pi$, reflecting the well-known symmetrization postulate of quantum mechanics. While this is true in three spatial dimensions, one- and two-dimensional systems can host particles with non-trivial exchange phase $0\leq\varphi<2\pi$, so-called anyons, which exhibit exchange statistics intermediate between those of bosons and fermions. Here, we consider a Hubbard-type model for one-dimensional anyons, consisting in a discrete lattice on which anyons can tunnel and interact.\\ We first address the case of two anyons on an infinite lattice and solve the Schrödinger equation analytically, deriving bound- and scattering state solutions. We demonstrate the existence of scattering resonances related to the anyonic exchange phase. We confirm this via numerical simulations of two-wavepacket scattering dynamics, where we observe Wigner time delays and lateral shifts. These two phenomena are accurately explained by studying the behavior of the scattering phase in the analytical solution. By further introducing a potential barrier, we model two-anyon interference on a beamsplitter and show that the exchange phase allows to interpolate between bosonic bunching and fermionic antibunching behaviors.\\ We further examine many-anyon systems from the perspective of quantum chaos. Comparing the eigenvalue statistics, in particular the mean level-splitting-ratio with random matrix predictions, allows us to identify the non-interacting limit of the anyon-Hubbard model as chaotic, in sharp contrast to the bosonic case, which we attribute to the effective interaction mediated by the exchange phase. We further consider the collective delocalization of eigenstates in the site basis via their fractal dimensions as an additional indicator of quantum chaos. Lastly, we discuss signatures of many-body interference in the long-time average variance $\overline{\Delta n_j}$ of a single site's population, and the dependence of these on the exchange phase. In the chaotic regime, we find that $\overline{\Delta n_j}$ neither significantly depends on the initial state, nor on the exchange phase.

Related papers

Quantum gas microscopy of the anyon-Hubbard model

Kwan, Joyce

Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of one-dimensional (1D) anyons remains largely unexplored. Using ultracold bosonic Rb-87 atoms in an optical lattice, we realize and explore the anyon-Hubbard model, which hosts 1D anyons and features a rich phase diagram. We implement the model using techniques from Floquet engineering, realizing the statistical phase in the form of a density-dependent Peierls phase. Using our high-resolution imaging system, we explore both the dynamical and ground state behavior in the anyon-Hubbard model. In the first set of experiments, we probe 1D anyons via two-particle quantum walks, observing the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. In the next set of experiments, we adiabatically prepare and probe ground states in the anyon-Hubbard model. First, we observe continuous fermionization in the density profile with increasing statistical phase. Then, we probe the chirality of the bound states in the anyon-Hubbard model, drawing similarities to a continuum model of 1D anyons. This work constitutes the first experimental study of the anyon-Hubbard model, and lays the foundation for exploration in the strongly correlated many-body regime.

•Jan 1, 2025•0 citations

Few-body bound states in the anyon-Hubbard model

Isaac Tesfaye, Christina Mascherbauer, Joyce Kwan +6 more

Quantum statistics in low-dimensional systems predicts anyonic particles with fractional exchange statistics which are neither that of bosons nor fermions. While anyons are typically found in two dimensions as excitations of topologically-ordered states of matter, anyon-like exchange statistics has also been discussed in one dimension, for instance, in the context of the anyon-Hubbard model (AHM), the physics of which has recently been observed in experiment [Kwan et al., arXiv:2306.01737; Dhar et al., arXiv:2412.21131; and Bakkali-Hassani et al., arXiv:2602.20421]. The AHM can be formulated in terms of bosons featuring density-dependent Peierls phases, described by a statistical phase angle $θ$, which controls asymmetric transport and the formation of dynamically bound pairs at finite momentum. Here, we show theoretically that the AHM also hosts exact two-body bound states in the continuum (BICs) for arbitrary $θ\neq 0$, and genuine three- and four-body bound states. Unlike conventional bound states stabilized by attractive (or repulsive) interactions, which are energetically localized with a large effective mass, these clusters here are bound by a purely kinematic mechanism endowing them with fast chiral transport properties. We provide a simple variational approximation to the three-body bound states and explain their binding mechanism. Moreover, we show that the signatures of three-body bound states in the AHM can be directly probed experimentally from the expansion dynamics starting from three localized particles.

cond-mat.quant-gasCross-listedarXiv:2609.09125•Sep 9, 2026•0 citations

Anyonization of Bosons in One Dimension: An Effective Swap Model

Botao Wang, Amit Vashisht, Yanliang Guo +4 more

Anyons emerge as elementary excitations in low-dimensional quantum systems and exhibit behavior distinct from bosons or fermions. In one dimension, anyons can arise from unconventional scattering processes or density-dependent hopping on a lattice. Here, we introduce a novel framework for realizing anyonic correlations using the internal degrees of freedom of a spinor quantum gas. We propose a "swap" model, which assigns a complex phase factor to the swapping processes between two different species, referred to as "host particles" and "impurities." The anyonic characteristics are demonstrated through the one-body correlator of the impurity, using a spin-charge separation analysis. The impurity plays the role of both creating and directly probing the anyonic correlations in a quantum many-body system, which are not accessible in the conventional anyon-Hubbard model. For a single impurity, our framework can be effectively implemented by applying tilt potentials in a strongly interacting quantum gas [Dhar et al., Observing anyonization of bosons in a quantum gas, Nature (London) 642, 53 (2025).NATUAS0028-083610.1038/s41586-025-09016-9]. We further explore the dynamical properties of anyonic correlations and extend our analysis to the case of multiple impurities. Our Letter provides new avenues for engineering many-body anyonic behavior in quantum simulation platforms.

arXiv:2504.21208•Physical Review Letters•Nov 13, 2025•3 citations

Realization of one-dimensional anyons with arbitrary statistical phase

Joyce Kwan, Perrin C. Segura, Y. Li +5 more

Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of anyons in one dimension remains largely unexplored. In this work, we realize Abelian anyons in one dimension with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase through a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks and observe the anyonic Hanbury Brown-Twiss effect as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of one-dimensional anyons.

Science•Nov 28, 2024•37 citations

Realization of 1D Anyons with Arbitrary Statistical Phase

Joyce Kwan, Perrin C. Segura, Yan-Fei Li +5 more

Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase via a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks, and observe the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of 1D anyons.

arXiv:2306.01737•Jun 2, 2023•9 citations

Necessity of orthogonal basis vectors for the two-anyon problem in a one-dimensional lattice*

Cuicui Zheng, Jiahui Xie, Ming Zhang +2 more

Abstract Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. Recently, theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, resulting in non-physical degrees of freedom. In the present work, we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schrödinger equation with orthogonal and complete basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates, while the conventional (non-orthogonal) method produces many non-physical redundant eigensolutions whose components violate the anyonic commutation relations. The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes. For initial states with two anyons at the same site or two (next-)neighboring sites, we observe the same dynamical behavior in both schemes, including the revival probability, probability density function and two-body correlation. For other initial states, the conventional scheme produces erroneous states that no longer obey the anyonic relations. The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit, while these oscillations disappear at other statistical parameters. Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.

arXiv:2405.07424•Communications in Theoretical Physics•Aug 26, 2024•0 citations
In textbook physics, all particles are categorized as either bosons or fermions. When exchanging two bosons, the corresponding wavefunction is dressed with an exchange phase φ=0\varphi=0φ=0, whereas for fermions the exchange phase is φ=π\varphi=\piφ=π, reflecting the well-known symmetrization postulate of quantum mechanics. While this is true in three spatial dimensions, one- and two-dimensional systems can host particles with non-trivial exchange phase 0≤φ<2π0\leq\varphi<2\pi0≤φ<2π, so-called anyons, which exhibit exchange statistics intermediate between those of bosons and fermions. Here, we consider a Hubbard-type model for one-dimensional anyons, consisting in a discrete lattice on which anyons can tunnel and interact.\ We first address the case of two anyons on an infinite lattice and solve the Schrödinger equation analytically, deriving bound- and scattering state solutions. We demonstrate the existence of scattering resonances related to the anyonic exchange phase. We confirm this via numerical simulations of two-wavepacket scattering dynamics, where we observe Wigner time delays and lateral shifts. These two phenomena are accurately explained by studying the behavior of the scattering phase in the analytical solution. By further introducing a potential barrier, we model two-anyon interference on a beamsplitter and show that the exchange phase allows to interpolate between bosonic bunching and fermionic antibunching behaviors.\ We further examine many-anyon systems from the perspective of quantum chaos. Comparing the eigenvalue statistics, in particular the mean level-splitting-ratio with random matrix predictions, allows us to identify the non-interacting limit of the anyon-Hubbard model as chaotic, in sharp contrast to the bosonic case, which we attribute to the effective interaction mediated by the exchange phase. We further consider the collective delocalization of eigenstates in the site basis via their fractal dimensions as an additional indicator of quantum chaos. Lastly, we discuss signatures of many-body interference in the long-time average variance Δnj‾\overline{\Delta n_j}Δnj​​ of a single site's population, and the dependence of these on the exchange phase. In the chaotic regime, we find that Δnj‾\overline{\Delta n_j}Δnj​​ neither significantly depends on the initial state, nor on the exchange phase.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of one-dimensional (1D) anyons remains largely unexplored. Using ultracold bosonic Rb-87 atoms in an optical lattice, we realize and explore the anyon-Hubbard model, which hosts 1D anyons and features a rich phase diagram. We implement the model using techniques from Floquet engineering, realizing the statistical phase in the form of a density-dependent Peierls phase. Using our high-resolution imaging system, we explore both the dynamical and ground state behavior in the anyon-Hubbard model. In the first set of experiments, we probe 1D anyons via two-particle quantum walks, observing the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. In the next set of experiments, we adiabatically prepare and probe ground states in the anyon-Hubbard model. First, we observe continuous fermionization in the density profile with increasing statistical phase. Then, we probe the chirality of the bound states in the anyon-Hubbard model, drawing similarities to a continuum model of 1D anyons. This work constitutes the first experimental study of the anyon-Hubbard model, and lays the foundation for exploration in the strongly correlated many-body regime.
Quantum statistics in low-dimensional systems predicts anyonic particles with fractional exchange statistics which are neither that of bosons nor fermions. While anyons are typically found in two dimensions as excitations of topologically-ordered states of matter, anyon-like exchange statistics has also been discussed in one dimension, for instance, in the context of the anyon-Hubbard model (AHM), the physics of which has recently been observed in experiment [Kwan et al., arXiv:2306.01737; Dhar et al., arXiv:2412.21131; and Bakkali-Hassani et al., arXiv:2602.20421]. The AHM can be formulated in terms of bosons featuring density-dependent Peierls phases, described by a statistical phase angle θθθ, which controls asymmetric transport and the formation of dynamically bound pairs at finite momentum. Here, we show theoretically that the AHM also hosts exact two-body bound states in the continuum (BICs) for arbitrary θ≠0θ\neq 0θ=0, and genuine three- and four-body bound states. Unlike conventional bound states stabilized by attractive (or repulsive) interactions, which are energetically localized with a large effective mass, these clusters here are bound by a purely kinematic mechanism endowing them with fast chiral transport properties. We provide a simple variational approximation to the three-body bound states and explain their binding mechanism. Moreover, we show that the signatures of three-body bound states in the AHM can be directly probed experimentally from the expansion dynamics starting from three localized particles.
Anyons emerge as elementary excitations in low-dimensional quantum systems and exhibit behavior distinct from bosons or fermions. In one dimension, anyons can arise from unconventional scattering processes or density-dependent hopping on a lattice. Here, we introduce a novel framework for realizing anyonic correlations using the internal degrees of freedom of a spinor quantum gas. We propose a "swap" model, which assigns a complex phase factor to the swapping processes between two different species, referred to as "host particles" and "impurities." The anyonic characteristics are demonstrated through the one-body correlator of the impurity, using a spin-charge separation analysis. The impurity plays the role of both creating and directly probing the anyonic correlations in a quantum many-body system, which are not accessible in the conventional anyon-Hubbard model. For a single impurity, our framework can be effectively implemented by applying tilt potentials in a strongly interacting quantum gas [Dhar et al., Observing anyonization of bosons in a quantum gas, Nature (London) 642, 53 (2025).NATUAS0028-083610.1038/s41586-025-09016-9]. We further explore the dynamical properties of anyonic correlations and extend our analysis to the case of multiple impurities. Our Letter provides new avenues for engineering many-body anyonic behavior in quantum simulation platforms.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of anyons in one dimension remains largely unexplored. In this work, we realize Abelian anyons in one dimension with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase through a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks and observe the anyonic Hanbury Brown-Twiss effect as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of one-dimensional anyons.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase via a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks, and observe the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of 1D anyons.
Abstract Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. Recently, theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, resulting in non-physical degrees of freedom. In the present work, we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schrödinger equation with orthogonal and complete basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates, while the conventional (non-orthogonal) method produces many non-physical redundant eigensolutions whose components violate the anyonic commutation relations. The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes. For initial states with two anyons at the same site or two (next-)neighboring sites, we observe the same dynamical behavior in both schemes, including the revival probability, probability density function and two-body correlation. For other initial states, the conventional scheme produces erroneous states that no longer obey the anyonic relations. The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit, while these oscillations disappear at other statistical parameters. Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.