We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under the effect of Hamiltonians quadratic in creation and annihilation operators, also called Gaussian Hamiltonians. These anyonic models are obtained from deformations of the standard bosonic or fermionic commutation relations via the introduction of a nontrivial exchange phase between different lattice sites. We study the effects of the anyonic exchange phase on the usual bosonic and fermionic bunching behaviors. We show how to exploit the inherent Aharonov-Bohm effect exhibited by these particles to build a deterministic, entangling two-qubit gate and prove quantum computational universality in these systems. We define coherent states for bosonic anyons and study their behavior under two-mode passive, Gaussian devices. In particular we prove that, for a particular value of the exchange factor, an anyonic mirror can generate cat states, an important resource in quantum information processing with continuous variables.
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.
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, whereas for fermions the exchange phase is
φ=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<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 of a single site's population, and the dependence of these on the exchange phase. In the chaotic regime, we find that
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. 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.
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.
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.