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.
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.
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.
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 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.
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.
Anyons are low-dimensional quasiparticles that obey fractional statistics, hence interpolating between bosons and fermions. In two dimensions, they exist as elementary excitations of fractional quantum Hall states and they are believed to enable topological quantum computing. One-dimensional (1D) anyons have been theoretically proposed, but their experimental realization has proven to be difficult. Here, we observe anyonic correlations, which emerge through the phenomenon of spin-charge separation, in a 1D strongly-interacting quantum gas. The required spin degree of freedom is provided by a mobile impurity, whose effective anyonic correlations are associated with an experimentally tunable statistical angle. These anyonic correlations are measured by monitoring the impurity momentum distribution, whose asymmetric feature demonstrates the transmutation of bosons via anyons to fermions. Going beyond equilibrium conditions, we study the dynamical properties of the anyonic correlations via dynamical fermionization of the anyons. Our work opens up the door to the exploration of non-equilibrium anyonic phenomena in a highly controllable setting.
This thesis is devoted to exploit strong correlations among ultracold atoms in order to create novel, exotic quantum states. In the first two chapters, we devise dynamical out-of-equilibrium preparation schemes which lead to intriguing final states. First of all, we propose to create the elusive supersolid state via a quantum quench protocol. Supersolids – quantum hybrids exhibiting both superflow and solidity – have been envisioned long ago, but have not been demonstrated in experiment so far. Our proposal to create a supersolid state is perfectly accessible with current technology and may clear the way to the experimental observation of supersolidity. Another out-of-equilibrium preparation scheme is discussed in the second chapter, giving rise to novel Cooper pairs of bosons. Ordinarily, Cooper pairs are composed of fermions – not so in our setup! We show that a Mott state of local bosonic Bell pairs can evolve into a Cooper-paired state of bosons, where the size of the pairs becomes macroscopic. This state can be prepared via a quick, diabatic ramp from the Mott into the superfluid regime. Furthermore, we propose to use bosons featuring conditional-hopping amplitudes in order to create Abelian anyons in one-dimensional optical lattices. We derive an exact mapping between anyons and bosons via a “fractional” Jordan-Wigner transformation. We suggest to employ a laser-assisted tunneling scheme to establish the many-particle state of “conditional-hopping bosons”, thus realizing a gas of Abelian anyons. The fractional statistics phase can be directly tuned by the lasers. The realization of non-Abelian anyons would be especially delightful, due to their significance in topological quantum computation schemes. We propose to employ strongly correlated bosons in one-dimensional optical lattices to create the Pfaffian state – which is known to host non-Abelian anyons as elementary excitations. In this setup, three-body correlations are required to dominate the system, which we model by on-site interactions of atoms with diatomic molecules. Finally, we use strong correlations in one-dimensional systems to create the effect of spin-charge separation, as formulated theoretically first in 1968. For a model of two-component bosons we compute the effective mass of a spin-flip excitation via Bethe Ansatz. In the strongly correlated regime, we show that the effective mass reaches the total mass of all particles in the system. The spin wave thus travels much more slowly than the density wave, giving rise to a strong spin-charge separation.