Analog Quantum Simulation of (1+1)D Lattice QED with Trapped Ions

TL;DR

This paper proposes two methods for simulating (1+1)D lattice QED using trapped ions, enabling exploration of fundamental quantum phenomena with scalable and experimentally feasible setups.

Contribution

It introduces two novel trapped-ion schemes for simulating lattice QED, one using vibrational modes and the other employing spin-1/2 systems, with potential for larger-scale experiments.

Findings

Finite-size scaling shows the vibrational model recovers Wilson's lattice gauge theory.

Both schemes operate at energy scales above decoherence, enabling experimental study.

Simulation of phenomena like string breaking and quantum phase transitions is feasible.

Abstract

The prospect of quantum simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudo-spins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in (1+1) space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge fields by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting small-scale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.