Quantum simulations with complex geometries and synthetic gauge fields in a trapped ion chain

TL;DR

This paper introduces a novel method to extend quantum simulation capabilities in trapped ion chains by generating synthetic gauge fields, enabling the study of complex geometries and topologies previously inaccessible.

Contribution

The authors develop a technique using external field gradients and uniform driving to create synthetic gauge fields, expanding the range of quantum models simulatable with trapped ions.

Findings

Enables simulation of complex geometries like rings and ladders

Derives effective Hamiltonians for synthetic gauge fields

Proposes scalable implementations for larger systems

Abstract

In recent years, arrays of atomic ions in a linear RF trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.