Engineering a U(1) lattice gauge theory in classical electric circuits

Hannes Riechert, Jad C. Halimeh, Valentin Kasper, Landry Bretheau, Erez Zohar, Philipp Hauke, Fred Jendrzejewski

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9 Scopus citations


Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive experimental progress has demonstrated that they can be engineered in table-top experiments using synthetic quantum systems. However, the challenges posed by the scalability of such lattice gauge simulators are pressing, thereby making the exploration of different experimental setups desirable. Here, we realize a U(1) lattice gauge theory with five matter sites and four gauge links in classical electric circuits employing nonlinear elements connecting LC oscillators. This allows for probing previously inaccessible spectral and transport properties in a multisite system. We directly observe Gauss's law, known from electrodynamics, and the emergence of long-range interactions between massive particles in full agreement with theoretical predictions. Our paper paves the way for investigations of increasingly complex gauge theories on table-top classical setups, and demonstrates the precise control of nonlinear effects within metamaterial devices.

Original languageAmerican English
Article number205141
JournalPhysical Review B
Issue number20
StatePublished - 31 May 2022

Bibliographical note

Funding Information:
The authors are grateful for fruitful discussions with T. Gasenzer, J. Berges, and the members of the SynQS seminar. This work is part of and supported by the DFG Collaborative Research Centre SFB 1225 (ISOQUANT), the ERC Advanced Grant EntangleGen (Project-ID No. 694561), the ERC Starting Grant StrEnQTh (Project-ID No. 804305), Quantum Science and Technology in Trento (Q@TN), the Provincia Autonoma di Trento, and the Excellence Initiative of the German federal government and the state governments—funding line Institutional Strategy (Zukunftskonzept): DFG Project No. ZUK 49/Ü. ICFO group acknowledges support from: ERC AdG NOQIA; Agencia Estatal de Investigación (R&D project CEX2019-000910-S, funded by MCIN/AEI/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, FPI, QUANTERA MAQS PCI2019-111828-2, Proyectos de I+D+I “Retos Colaboración” QUSPIN RTC2019-007196-7); Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya through the European Social Fund FEDER and CERCA program (AGAUR Grant No. 2017 SGR 134, QuantumCAT/U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020); EU Horizon 2020 FET-OPEN OPTOlogic (Grant No. 899794); National Science Centre, Poland (Symfonia Grant No. 2016/20/W/ST4/00314); European Union's Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie Grant Agreement No. 101029393 (STREDCH) and No 847648 (“La Caixa” Junior Leaders fellowships ID100010434: LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, LCF/BQ/PR21/11840013). F.J. acknowledges the DFG support through the Emmy-Noether grant (Project No. 377616843). P.H. acknowledges the Google Research Scholar Award ProGauge. E.Z. was supported by the Israel Science Foundation (Grant No. 523/20). L.B. acknowledges support of Agence Nationale de la Recherche through Grant No. ANR-18-CE47-0012 (JCJC QIPHSC). V.K. received support from the La Caixa Foundation (ID No. 100010434) and from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 847648 with fellowship code No. LCF/BQ/PI20/11760031.

Publisher Copyright:
© 2022 American Physical Society.


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