Scalable, ab initio protocol for quantum simulating SU($N$)$\times$U(1) Lattice Gauge Theories

Abstract

We propose a protocol for the scalable quantum simulation of SU($N$)$\times$U(1) lattice gauge theories with alkaline-earth like atoms in optical lattices in both one- and two-dimensional systems. The protocol exploits the combination of naturally occurring SU($N$) pseudo-spin symmetry and strong inter-orbital interactions that is unique to such atomic species. A detailed ab initio study of the microscopic dynamics shows how gauge invariance emerges in an accessible parameter regime, and allows us to identify the main challenges in the simulation of such theories. We provide quantitative results about the requirements in terms of experimental stability in relation to observing gauge invariant dynamics, a key element for a deeper analysis on the functioning of such class of theories in both quantum simulators and computers.

16+11 pages, 4+4 figures

References in corpus (13)

• Probing many-body dynamics on a 51-atom quantum simulator
• Single-Spin Addressing in an Atomic Mott Insulator
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Controlled exchange interaction between pairs of neutral atoms in an optical lattice
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Direct observation of coherent inter-orbital spin-exchange dynamics
• Light Hadron Masses from Lattice QCD
• $Abinitio$ derivation of lattice gauge theory dynamics for cold gases in optical lattices

Cited by in corpus (7)

• Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Single-atom imaging of ${}^{173}$Yb in optical tweezers loaded by a five-beam magneto-optical trap
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• $\text{Symdyn}$: an automated algebraic solution for high-order quantum systems