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Physical Review A

Fractional Chern insulator with Rydberg-dressed neutral atoms

Yang Zhao, Xiaofeng Shi

Published Nov 6, 2023• 6 citations
Publisher

Abstract

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 $C=1/2$, 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.

DOI
10.1103/physreva.108.053107

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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.
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.
Fractional Chern insulators arise in topologically nontrivial flat bands, characterized by an integer Chern number C that corresponds to the number of dissipationless edge states in the non-interacting regime. Higher Chern numbers can replicate the physics of higher Landau levels and often confer enhanced topological robustness. However, realizing correlated fractional phases with higher Chern numbers in such flat band systems remains challenging. Here, we propose an interlayer coupling scheme to generate higher Chern numbers in a flat-band system, where the interlayer coupling transforms two C = 1 bands in a bilayer checkerboard lattice into a single flat band with C = 2 by lifting their degeneracy and merging their topological indices. Exact diagonalization calculation reveals that this engineered band hosts two fractional Chern insulator states with C = 2/3 and 2/5, respectively. An experimental setup is proposed to simulate these states using cold alkaline-earth-like atoms in an effective bilayer optical lattice. Our work provides a general and widely applicable strategy for constructing higher Chern number flat bands, opening a pathway to explore exotic fractional quantum phases.
We demonstrate the realization of topological band structures by exploiting the intrinsic spin-orbit coupling of dipolar interactions in combination with broken time-reversal symmetry. The system is based on polar molecules trapped in a deep optical lattice, where the dynamics of rotational excitations follows a hopping Hamiltonian which is determined by the dipolar exchange interactions. We find topological bands with Chern number C=2C=2C=2 on the square lattice, while a very rich structure of different topological bands appears on the honeycomb lattice. We show that the system is robust against missing molecules. For certain parameters we obtain flat bands, providing a promising candidate for the realization of hard-core bosonic fractional Chern insulators.
The recent theoretical discovery of fractional Chern insulators (FCIs) has provided an important new way to realize topologically ordered states in lattice models. In earlier works, on-site and nearest-neighbor Hubbard-like interactions have been used extensively to stabilize Abelian FCIs in systems with nearly flat, topologically nontrivial bands. However, attempts to use two-body interactions to stabilize non-Abelian FCIs, where the ground state in the presence of impurities can be massively degenerate and manipulated through anyon braiding, have proven very difficult in uniform lattice systems. Here, we study the remarkable effect of long-range interactions in a lattice model that possesses an exactly flat lowest band with a unit Chern number. When spinless bosons with two-body long-range interactions partially fill the lowest Chern band, we find convincing evidence of gapped, bosonic Read-Rezayi (RR) phases with non-Abelian anyon statistics. We characterize these states through studying topological degeneracies, the overlap between the ground states of two-body interactions and the exact RR ground states of three- and four-body interactions, and state counting in the particle-cut entanglement spectrum. Moreover, we demonstrate how an approximate lattice form of Haldane's pseudopotentials, analogous to that in the continuum, can be used as an efficient guiding principle in the search for lattice models with stable non-Abelian phases.