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Experimentally Accessible Scheme for a Fractional Chern Insulator in Rydberg Atoms

Sebastian Weber, Rukmani Bai, Nastasia Makki, Johannes Mögerle, Thierry Lahaye, Antoine Browaeys, Maria Daghofer, Nicolai Lang, Hans Peter Büchler

Published Jul 5, 2022• 29 citations
Publisher

Abstract

We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and the density-matrix renormalization group. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the ν=1/2 bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking-gun signature for the fractional excitations.

DOI
10.1103/prxquantum.3.030302

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We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and the density-matrix renormalization group. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the ν=1/2 bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking-gun signature for the fractional excitations.
We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions, and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and DMRG. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the ν=1/2ν=1/2ν=1/2 bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking gun signature for the fractional excitations.
Topological nontrivial bands can be realized via Rydberg-dressed neutral atoms. We propose a two-dimensional hard-core boson model with a topological flat band on a honeycomb array, where the particle hopping is realized via van der Waals interactions that exchange the Rydberg states of two interacting atoms, while nonzero phases associated with hopping arises from the transfer of laser phase to the wave functions of Rydberg atoms. Using exactly diagonalization and infinite density matrix renormalization group simulation, we find in the system a fractional Chern insulator phase with a Chern number C=1/2C=1/2C=1/2, which can persist in the presence of weak many-body interactions. These reveal that neutral-atom arrays can emulate fractional Chern insulators. Finally, we also study the proposed two-dimensional hard-core boson model under different theoretical parameter settings; the results further support that the generated nonzero phases associated with hopping amplitudes can produce a stable fractional Chern insulator state theoretically.
Topological nontrivial bands can be realized via Rydberg-dressed neutral atoms. We propose a two-dimensional hard-core boson model with a topological ground enrgy at band on a honeycomb lattice, where the particle hopping is realized via van der Waals interaction that exchanges the Rydberg states of two interacting atoms, while nonzero phases associated with hopping is created by transferring the optical phase of laser fields to the atomic pair wave function. Using exactly diagonalization and infinite density matrix renormalization group simulation, we find in the system a fractional Chern insulator phase with a Chern number C = 1/2, which can persist in the presence of weak many-body interactions. Our studies indicate that fractional Chern insulators can be studied with neutral-atom arrays.
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=1/2 ν = 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.
Topological states of interacting many-body systems are at the focus of current research due to the exotic properties of their elementary excitations. In this paper we suggest a realistic experimental setup for the realization of a simple version of such a phase. We show how $\ensuremath{\delta}$-interacting bosons hopping on the links of a one-dimensional ladder can be used to simulate the thin-torus limit of the two-dimensional (2D) Hofstadter-Hubbard model at one-quarter magnetic flux per plaquette. Bosons can be confined to ladders by optical superlattices, and synthetic magnetic fields can be realized by laser-assisted tunneling. We show that twisted boundary conditions can be implemented, enabling the realization of a fractionally quantized Thouless pump. Using numerical density-matrix-renormalization-group calculations, we show that the ground state of our model is an incompressible symmetry-protected topological charge density wave phase at average filling $\ensuremath{\rho}=1/8$ per lattice site, related to the 1/21/21/2 Laughlin-type state of the corresponding 2D model.
Recent theoretical papers have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role in obtaining a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagome-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.