Quantum simulation of an extended Dicke model with a magnetic solid

Creators: Marquez Peraca, Nicolas; Li, Xinwei; Moya, Jaime M.; Hayashida, Kenji; Kim, Dasom; Ma, Xiaoxuan; Neubauer, Kelly J.; Fallas Padilla, Diego; Huang, Chien-Lung; Dai, Pengcheng; Nevidomskyy, Andriy H.; Pu, Han; Morosan, Emilia; Cao, Shixun; Bamba, Motoaki; Kono, Junichiro

Abstract

The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO₃, where the role of atoms (photons) is played by Er³⁺ spins (Fe³⁺ magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.

Copyright and License

© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Acknowledgement

We thank Shiming Lei, Andrey Baydin, Takuma Makihara, Fuyang Tay, and Timothy Noe for useful discussions. J.K. acknowledges support from the U.S. Army Research Office (through Award No. W911NF2110157), the W. M. Keck Foundation (through Award No. 995764), the Gordon and Betty Moore Foundation (through Grant No. 11520), and the Robert A. Welch Foundation (through Grant No. C-1509). X.L. acknowledges support from the Caltech Postdoctoral Prize Fellowship and the IQIM. S.C. is grateful for financial support from the National Natural Science Foundation of China (NSFC, No. 12374116), and the Science and Technology Commission of Shanghai Municipality (No. 21JC1402600). M.B. acknowledges support from the JST PRESTO program (Grant JPMJPR1767) and Japan Society for the Promotion of Science (Grant JPJSJRP20221202). J.M.M. and E.M. were supported by NSF Grant No. DMR 1903741 and the Robert A. Welch Foundation Grant No. C-2114. A.H.N. was supported by the Robert A. Welch Foundation (through Grant No. C-1818) and the US National Science Foundation (through Grant No. DMR-1917511). P.D. was supported by U.S. DOE BES DE-SC0012311. C.-L.H. is grateful for financial support from the National Science and Technology in Taiwan (NSTC 112-2124-M-006-011).

Contributions

These authors contributed equally: Nicolas Marquez Peraca, Jaime M. Moya, Kenji Hayashida.

N.M.P. performed THz measurements and analyzed all THz data under the guidance and supervision of X.L. and J.K. J.M.M., C-L.H., and E.M. performed magnetization and MCE measurements and data analysis and discussed the results with N.M.P, X.L., D.K., and J.K. K.H. and M.B. calculated spin resonance frequencies, spin configurations, oscillator strengths, and mean-field phase diagrams. M.B. supervised K.H. in the theoretical modeling. X.M. grew, cut, and characterized the high-quality ErFeO₃ single crystals used in the experiments under the guidance of S.C. K.J.N., and P.D. performed additional Laue diffraction measurements. D.F.P., H.P., and A.H.N. contributed to the theoretical analysis. N.M.P., X.L., J.M.M., K.H., D.K., M.B., and J.K. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Data Availability

Data that support the findings of this study are available from the corresponding author upon reasonable request.

Code Availability

Codes that support the findings of this study are available from the corresponding author upon reasonable request.

Conflict of Interest

The authors declare no competing interests.

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