Scalable, Ab Initio Protocol For Quantum Simulating SU($N$)$times$U(1) Lattice Gauge Theories

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Federica Maria Surace¹, Pierre Fromholz^2,3, Francesco Scazza^4,5, and Marcello Dalmonte^2,3

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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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.

Scalable, ab initio protocol for quantum simulating SU($N$)$times$U(1) Lattice Gauge Theories PlatoBlockchain Data Intelligence. Vertical Search. Ai.

Featured image: Scheme of the 1+1d Quantum Link Model: fermionic matter (in blue) resides on the sites of a one-dimensional lattice; the gauge field is represented by fermionic operators (rishons) that act on the two ends of a link (in orange). The matter/gauge sites correspond to the minima of an optical lattice for alkaline-earth-like atoms in the $g/e$ state respectively. The $g/e$ states correspond to the electronic ground state (${}^1S_0$) and metastable clock state (${}^3P_0$) of the atoms. There are $N_I$ nuclear spin states decoupled from the electronic degrees of freedom.

Popular summary

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.

► BibTeX data

@article{Surace2024scalableabinitio, doi = {10.22331/q-2024-05-23-1359}, url = {https://doi.org/10.22331/q-2024-05-23-1359}, title = {Scalable, ab initio protocol for quantum simulating {SU}({$N$}){$times$}U(1) {L}attice {G}auge {T}heories}, author = {Surace, Federica Maria and Fromholz, Pierre and Scazza, Francesco and Dalmonte, Marcello}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1359}, month = may, year = {2024} }

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Source: https://quantum-journal.org/papers/q-2024-05-23-1359/

Time Stamp: May 23, 2024

Time Stamp: May 14, 2024

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

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