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arXiv:2608.05290

Exact statistical transmutation of quantum mixtures on a ring

Wayne Jordan Chetcuti, Nathan Goldman, Patrizia Vignolo, Anna Minguzzi

Published Aug 5, 2026• 0 citations
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Abstract

One-dimensional strongly repulsive quantum mixtures exhibit non-trivial exchange statistics arising from the interplay between orbital and spin degrees of freedom. Using an exact solution, we demonstrate that in the single-impurity limit the wavefunction of Fermi-Fermi and Bose-Bose mixtures on a ring threaded by an artificial gauge field display exact anyonic statistics under exchange of the impurity with the majority particles. The resulting fractional exchange phase is fixed by the angular momentum sector selected through the applied flux. We find that the impurity momentum distribution coincide exactly with the anyonic one, independently of the bosonic or fermionic nature of the mixture, with the large-momentum tails encoding a direct signature of the anyonic statistical angle. Finally, we devise a quench protocol for reversible dynamical anyonization. Our results provide a path for realizing and manipulating anyonized states with ultracold atoms.

DOI
10.48550/arxiv.2608.05290

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One-dimensional strongly repulsive quantum mixtures exhibit non-trivial exchange statistics arising from the interplay between orbital and spin degrees of freedom. Using an exact solution, we demonstrate that in the single-impurity limit the wavefunction of Fermi-Fermi and Bose-Bose mixtures on a ring threaded by an artificial gauge field display exact anyonic statistics under exchange of the impurity with the majority particles. The resulting fractional exchange phase is fixed by the angular momentum sector selected through the applied flux. We find that the impurity momentum distribution coincide exactly with the anyonic one, independently of the bosonic or fermionic nature of the mixture, with the large-momentum tails encoding a direct signature of the anyonic statistical angle. Finally, we devise a quench protocol for reversible dynamical anyonization. Our results provide a path for realizing and manipulating anyonized states with ultracold atoms.
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.
We study measurable quantities of bosonic and fermionic mixtures on a one-dimensional ring. These few-body ensembles consist of majority atoms obeying certain statistics (Fermi or Bose) and an impurity atom in a different hyperfine state. The repulsive interactions between majority-impurity and majority-majority are varied from weak to strong. We show that the majority-impurity repulsion is mainly responsible for the loss of coherence in the strongly interacting regime. The momentum distribution follows the C/p4\mathcal{C}/{p}^{4}C/p4 universal behavior for the high-momentum tail, but the contact C\mathcal{C}C is strongly dependent on the strength of the majority-impurity and in a different way on the majority-majority interactions. The static structure factor of the majority atoms exposes a low-momentum peak for strong majority-impurity repulsion, which is attributed to an effective attraction not expected for purely repulsive forces.
We establish an exact mapping between identical particles in one dimension with arbitrary exchange statistics, including bosons, anyons, and fermions, provided they share the same scattering length. This boson-anyon-fermion mapping facilitates the construction of anyons from a linear superposition of spatially symmetric and antisymmetric states. This scheme is general and has been demonstrated in a spin-1/2 Fermi gas, where both s- and p-wave bound states can be supported by manipulating spin channels. With a suitable symmetry-breaking field, these bound states are hybridized to form a fractional-wave molecule. The condensation of these molecules in a many-body system leads to anyonic superfluidity, characterized by fractional statistics upon spin exchange within a Cooper pair. These anyonic states can be detected through asymmetric momentum distributions for each spin with a chiral k − 3 tail. Our results demonstrate the inadequacy of the contact interaction model for anyons in continuum and lattices, and have also suggested a convenient route for engineering fractional phases on the platform of ultracold atoms.
Abstract Anyons 1,2 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 3–5 and are believed to enable topological quantum computing 6,7 . One-dimensional anyons have been theoretically proposed, but their experimental realization has proven to be difficult. Here we observed emergent anyonic correlations in a one-dimensional strongly interacting quantum gas, resulting from the phenomenon of spin–charge separation 8–10 . A mobile impurity provides the necessary spin degree of freedom to engineer anyonic correlations in the charge sector and simultaneously acts as a probe to reveal these correlations. Starting with bosons, we tune the statistical phase to transmute bosons through anyons to fermions and observe an asymmetric momentum distribution 11–14 , a hallmark of anyonic correlations. Going beyond equilibrium conditions, we observed dynamical fermionization of the anyons 15 . This study opens the door to the exploration of non-equilibrium anyonic phenomena in a highly controllable setting 15–17 .
We demonstrate that identical impurities immersed in a two-dimensional many-particle bath can be viewed as flux-tube-charged-particle composites described by fractional statistics. In particular, we find that the bath manifests itself as an external magnetic flux tube with respect to the impurities, and hence the time-reversal symmetry is broken for the effective Hamiltonian describing the impurities. The emerging flux tube acts as a statistical gauge field after a certain critical coupling. This critical coupling corresponds to the intersection point between the quasiparticle state and the phonon wing, where the angular momentum is transferred from the impurity to the bath. This amounts to a novel configuration with emerging anyons. The proposed setup paves the way to realizing anyons using electrons interacting with superfluid helium or lattice phonons, as well as using atomic impurities in ultracold gases.
We consider a two-component Bose–Bose mixture at infinitely strong repulsive interactions in a tightly confining, one-dimensional ring trap and subjected to an artificial gauge field. By employing the Bethe Ansatz exact solution for the many-body wavefunction, we obtain the ground state energy and the persistent currents up to four particles. For each value of the applied flux, we then determine the symmetry of the state under particles exchange. We find that the ground-state energy and the persistent currents display a reduced periodicity with respect to the case of non-interacting particles, corresponding to reaching states with fractional angular momentum per particle. We relate this effect to the change of symmetry of the ground state under the effect of the artificial gauge field. Our results generalize the ones previously reported for fermionic mixtures with both attractive and repulsive interactions and highlight the role of symmetry in this effect.