Experimental implementation of adiabatic passage between different topological orders

TL;DR

This paper reports an experimental quantum simulation demonstrating adiabatic transitions between different topological orders in a nuclear magnetic resonance system, confirming methods for preparing and studying complex topologically ordered states.

Contribution

It provides the first experimental implementation of adiabatic passage between distinct topological orders in a quantum simulation platform.

Findings

Successful simulation of the Wen-plaquette model with different topological phases

Observation of adiabatic transition via nonlocal Wilson loop measurements

Measurement of entanglement properties of topological orders

Abstract

Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum simulation of the Wen-plaquette spin model with different topological orders in a nuclear magnetic resonance system, and observe the adiabatic transition between two $Z_2$ topological orders through a spin-polarized phase by measuring the nonlocal closed-string (Wilson loop) operator. Moreover, we also measure the entanglement properties of the topological orders. This work confirms the adiabatic method for preparing topologically ordered states and provides an experimental tool for further studies of complex quantum systems.