Discrete Abelian Gauge Theories for Quantum Simulations of QED

Abstract

We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry ${\mathbb{Z}}_n$, approximating the $U(1)$ theory for large $n$. We analyze the role of the finiteness of the gauge fields and the properties of physical states, that satisfy a generalized Gauss's law. We finally discuss a possible implementation strategy, that involves an effective dynamics in physical space.

13 pages, 3 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Quantum Zeno dynamics: mathematical and physical aspects
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Optical Abelian Lattice Gauge Theories
• Master Equation and Control of an Open Quantum System with Leakage

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