Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope

Abstract

The recent progress in engineering topological band structures in optical-lattice 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 quantum-gas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlin-like state at filling \nu=1/2ν=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 6-8 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.

Recent Developments in Fractional Chern Insulators

“…The fractional statistics of quasiparticles is a characterizing feature of FCI states. One can directly simulate the generation and braiding of quasiparticles to demonstrate their fractional statistics [116][117][118][119][120][121][122][123]. Alternatively, the statistics is encoded in the so called modular matrix [124,125].…”

“…It is also possible to evaluate Hall conductance using interferometric protocols [213], randomized measurement scheme [214], or through circular-dichroic measurement [215,216]. Apart from Hall conductance measurements, other promising schemes include probing fractionalized quasiholes through density measurement [116,119,122,217] and detecting chiral edge excitation [105,218]. All of these proposals have been examined by numerical simulations in small cold-atom systems.…”

Cavity-based reservoir engineering for Floquet-engineered superconducting circuits

“…3(b)right), corresponding to hard-core bosons and a tightly bound pair, respectively. The former subspace is most interesting (as, for instance, hard-core bosons in finite two-dimensional lattices with homogeneous flux are predicted to give rise to fractional-quantum-Hall(FQH)type ground states [45][46][47]) and we can use three cavities to cool the system into the hard-core-boson ground state. Starting with two excitations localized in dif- ferent sites, achievable by exciting two atoms to state a † j a † j |0 with quick resonant pulses before launching the Floquet drives, the population build-up in time is shown in Fig.…”

“…Interesting applications are, e.g. , autonomous quantum error correction [50,51], the preparation of gapped ground states (such as FQH states [45][46][47]), and interband cooling [52]. Considering as an example a 100-site square ladder with plaquette flux Φ = 0.8π and tunneling along the rungs five times faster than along the legs, the effective spectrum features two well separated narrow bands [Fig.…”

“…Especially the combination of artificial gauge fields [1,4] or geometric frustration [9,53], as it can be achieved using Floquet engineering, with an interaction-induced hard-core constraint, is predicted to give rise to topologically ordered states of matter, such as fractional quantum Hall states or topological spin liquids. This is a promising perspective, also since clear signatures of such states can be expected already for rather small system sizes [46,47] In this section, the effective Hamiltonian of Eq. (3) in the main text and the effective master equation are derived.…”