Sebastian Nagies, Botao Wang, Adam C. Knapp, André Eckardt, Nathan L. Harshman
SciPost Phys. 16, 086 (2024) ·
published 26 March 2024

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Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hardcore twobody constraints make the configuration space of particles not simplyconnected. The braid group describes how topologicallyinequivalent exchange paths can be associated to nontrivial geometric phases for abelian anyons. Braidanyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hardcore threebody constraints also make the configuration space not simplyconnected. Instead of the braid group, the topology of exchange paths and their associated nontrivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with numberdependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The groundstate of this traidanyonHubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an aposteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.
SciPost Phys. 13, 059 (2022) ·
published 21 September 2022

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We propose and investigate a scheme for engineering a synthetic thermal bath for a bosonic quantum gas in a onedimensional optical lattice based on Markovian feedback control. The performance of our scheme is quantified by the fidelity between the steady state of the system and the effective thermal state. For doublewell and triplewell systems with noninteracting particles, the steady state is found to be an exact thermal state, which is attributed to the fact that the transfer rates between all pairs of coupled eigenstates satisfy detailed balance condition. The scenario changes when there are more lattice sites, where the detailed balance condition does not hold any more, but remains an accurate approximation. Remarkably, our scheme performs very well at low and high temperature regimes, with the fidelity close to one. The performance at the intermediate temperature regime (where a crossover into a Bose condensed regime occurs) is slightly worse, and the fidelity shows a gentle decrease with increasing system size. We also discuss the interacting cases. In contrast to the noninteracting cases, the scheme is found to perform better at a higher temperature. Another difference is that the minimal temperature that can be engineered is nonzero and increases with the interaction strength.
SciPost Phys. 12, 095 (2022) ·
published 17 March 2022

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The recent progress in engineering topological band structures in opticallattice systems makes it promising to study fractional Chern insulator states in these systems. Here we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantumgas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlinlike state at filling $\nu=1/2$ can be stabilized and its fractional excitations probed. Using numerical simulations, we find an incompressible bulk density at the expected filling for systems, whose linear extent is as small as 68 sites. This is a promising result, since such small systems are favorable with respect to the required adiabatic state preparation. Moreover, we also see very clear signatures of excitations with fractional charge in response both to static pinning potentials and dynamical flux insertion. Since the compressible edges, which are found to feature chiral currents, can serve as a reservoir, these observations are robust against changes in the total particle number. Our results suggest that signatures of both a fractional Chern insulator state and its fractional excitations can be found under realistic experimental conditions.
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