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. 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.
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.
"Anyonic quantum statistics is an exotic phenomenon of identical particles in quantum mechanics. When particles are confined in two spatial dimensions, exchanges of identical particles can induce phase factors in the wave function of Abelian anyons or matrix valued transformations of the wave function of non-Abelian anyons. As a result, systems of anyons may have richer properties than those of bosons and fermions in three spatial dimensions. There is strong theoretical support for the existence of anyons in some engineered two-dimensional systems such as 2D electron gases, strongly correlated spin lattices and as edge modes of nanowires. In the future, anyons could be used in topological quantum computation to perform highly efficient information processing with very small error rates. The phases of matter described by dynamically interacting anyons have recently been studied in chains where anyons interact via Heisenberg-type exchange interactions. In this thesis, new kind of anyonic interactions are studied, induced purely by braiding during free evolution. Such interactions are of topological origin, and the information about the interactions is stored non-locally. A quantum walk model is used to study the effects of these braiding interactions on the dynamical behaviour of anyons. The anyonic quantum walk is a quasi-one-dimensional generalization of the discrete-time quantum walk which allows the simulation of anyonic dynamics analytically. The moving anyon and a chain of stationary anyons interact via braiding statistics, and the behaviour of the anyon is studied in three cases. Striking differences are found between particles with conventional boson or fermion statistics and non-Abelian anyonic statistics. The random walk is a dynamical model that describes the motion of a particle on a lattice. In physics, it is used to describe Brownian motion of fluids and gases. In such systems, energy transport is diffusive, and the order of the system approaches a highly mixed state without any information content. The quantum version of the random walk, the quantum walk, has nonintuitive properties. Generally, the information content in a unitarily evolving system is fixed, which leads to unexpected transport phenomena. An initially localized particle does not propagate diffusively, but escapes the starting point with ballistic speed. Most of our results for non-Abelian anyons use the Ising model anyon which is most likely to be measured in experiments. First, when each anyonic site is occupied by one Ising anyon, the propagation of the anyon becomes diffusive. More precisely, the variance of the spatial probability distribution of the particle depends linearly on the number of time steps. This is in stark contrast to bosons, fermions and Abelian anyons which propagate ballistically, and the variance depends linearly on the square of the number of time steps. The essential reason for this slowdown is that the non-Abelian anyons possess an extra degree of freedom called the fusion Hilbert space. This space can be viewed as an environment for the normal degrees of freedom of the particle, inducing decoherence in the quantum walk. This thesis opens the line for studies of this novel kind of decoherence mechanism in quantum walks. In the second case the study is extended to more general anyon models by losing some of the information about the history of the evolution. In this case the system is subject to decoherence, and the total system evolution is not unitary. The behaviour of the particle in this model is found to be diffusive for all the non-Abelian anyon models studied, while Abelian anyons behave ballistically also in this model. One peculiarity of quantum systems is their behaviour under disorder. Quantum mechanical particles moving in random local potentials are known to freeze and not move at all. Such a phenomenon is known as Anderson localization. Studies have shown that Anderson localization happens also in quantum walks with random spatial fluctuations in the coin parameters. In the third case, the transport properties of anyons are studied under topological randomness, allowing the occupations of anyons change between experiments. Bosons and fermions would propagate ballistically under such randomness, and Abelian anyons are shown to localize. The results show that non-Abelian anyons behave diffusively at short time scales, and it is argued that they do so in the long time limit as well. In all cases, non-Abelian anyons are shown to have very different dynamical properties than bosons, fermions and Abelian anyons. A possible simulation of the anyonic quantum walk in Fractional Quantum Hall systems is also discussed.
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=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.
Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of their one-dimensional (1D) counterparts remains the subject of intense debate, with renewed interest fueled by recent experimental progress. Theoretically, 1D anyons are predicted to host exotic many-body phases and quantum phase transitions, yet experimental signatures have remained elusive. Using ultracold atoms in an optical lattice, we prepare two-body ground states of the 1D anyon-Hubbard model by combining Hamiltonian engineering via quasiperiodic drives and adiabatic state manipulation. We uncover the effects of statistical interactions that lead to pseudo-fermionization and to the formation of chiral bound states when particles remain close together. Our results establish a link between lattice and continuum realizations of anyon models, and mark important steps towards the precise control of 1D anyons in both equilibrium and out-of-equilibrium settings.
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.