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

Federica Maria Surace1, Pierre Fromholz2,3, Francesco Scazza4,5, and Marcello Dalmonte2,3

1Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
2The Abdus Salam International Centre for Theoretical Physics (ICTP), strada Costiera 11, 34151 Trieste, Italy
3International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy
4Department of Physics, University of Trieste, 34127 Trieste, Italy
5Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 34149 Basovizza-Trieste, Italy

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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.

Non-Abelian gauge theories, essential in understanding fundamental forces in particle physics, have long posed challenges for numerical simulation due to their intricate structure. Cold atom quantum simulators represent a promising tool for exploring their properties in novel, previously inaccessible regimes.

By harnessing the unique properties of alkaline-earth-like atoms in optical lattices, we propose a method for quantum simulating non-Abelian SU(N)xU(1) lattice gauge theories. Our protocol capitalizes on the inherent SU(N) pseudo-spin symmetry and strong inter-orbital interactions of these atoms. Through an ab initio study, we unveil how gauge invariance naturally emerges within experimentally feasible parameters. This not only sheds light on the behavior of such theories but also outlines the hurdles one must overcome for successful simulation.

Our results lay the groundwork for deeper insights into the study of non-Abelian gauge theories using quantum simulators.

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