# Quantum Simulation of the Abelian-Higgs Lattice Gauge Theory with Ultracold Atoms

## TL;DR

This paper proposes a method to simulate the Abelian-Higgs lattice gauge theory using ultracold atoms in optical lattices, enabling exploration of confinement and Higgs phenomena in a controllable quantum system.

## Contribution

It introduces a novel quantum simulation scheme that maps gauge and Higgs fields onto ultracold atomic systems, including auxiliary bosons for effective Hamiltonian realization.

## Key findings

- Demonstrates how to encode gauge symmetry via hyperfine angular momentum conservation.
- Analyzes the impact of finite boson number on simulation accuracy.
- Proposes experimental setups for studying high energy physics phenomena.

## Abstract

We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time.