String order via Floquet interactions in atomic systems

TL;DR

This paper explores how Floquet-driven interactions in atomic systems can induce and stabilize string order in the transverse-field Ising model across different dimensions, with potential experimental realizations.

Contribution

It demonstrates the emergence of string order via Floquet interactions in atomic systems and analyzes its robustness and experimental feasibility.

Findings

String order is robust to power-law interactions decaying with distance.

Higher-dimensional systems exhibit five- and seven-body interactions.

Adiabatic preparation of ground states is discussed for experimental setups.

Abstract

We study the transverse-field Ising model with interactions that are modulated in time. In a rotating frame, the system is described by a time-independent Hamiltonian with many-body interactions, similar to the cluster Hamiltonians of measurement-based quantum computing. In one dimension, there is a three-body interaction, which leads to string order instead of conventional magnetic order. We show that the string order is robust to power-law interactions that decay with the cube of distance. In two and three dimensions, there are five- and seven-body interactions. We discuss adiabatic preparation of the ground state as well as experimental implementation with trapped ions, Rydberg atoms, and polar molecules.