Theory of Fractional Quantum Hall Liquids Coupled to Quantum Light and Emergent Graviton-Polaritons

Year: 2025

Authors: Bacciconi Z., Xavier HB., Carusotto I., Chanda T., Dalmonte M.

Autors Affiliation: SISSA Int Sch Adv Studies, Via Bonomea 265, I-34136 Trieste, Italy; ICTP Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy; Univ Trento, INO CNR Pitaevskii BEC Ctr, Dipartimento Fis, I-38123 Povo, Italy; Indian Inst Technol Indore, Dept Phys, Khandwa Rd, Simrol 453552, Indore, India; Indian Inst Technol Madras, Dept Phys, Chennai 600036, India; Indian Inst Technol Madras, Ctr Quantum Informat Commun & Computat CQuICC, Chennai 600036, India.

Abstract: Recent breakthrough experiments have demonstrated how it is now possible to explore the dynamics of quantum Hall states interacting with quantum electromagnetic cavity fields. While the impact of strongly coupled nonlocal cavity modes on integer quantum Hall physics has been recently addressed, the effects on fractional quantum Hall (FQH) liquids-and, more generally, fractionalized states of matter-remain largely unexplored. In this work, we develop a theoretical framework for the understanding of FQH states coupled to quantum light. In particular, combining analytical arguments with tensor network simulations, we study the dynamics of a nu 1/4 1/3 Laughlin state in a single-mode cavity with finite electric field gradients. We find that the topological signatures of the FQH state remain robust against the nonlocal cavity vacuum fluctuations, as indicated by the endurance of the quantized Hall resistivity. The entanglement spectra, however, carry direct fingerprints of light-matter entanglement and topology, revealing peculiar polaritonic replicas of the U(1) counting. As a further response to cavity fluctuations, we also find a squeezed FQH geometry, encoded in long-wavelength correlations. By exploring the low-energy excited spectrum inside the FQH phase, we identify a new neutral quasiparticle, the graviton polariton, arising from the hybridization between quadrupolar FQH collective excitations (known as gravitons) and light. Pushing the light-matter interaction to ultrastrong-coupling regimes, we find other two important effects, a cavity vacuum-induced Stark shift for charged quasiparticles and a potential instability toward a density modulated stripe phase, competing against the phase separation driven by the Stark shift. Finally, we discuss the experimental implications of our findings and possible extension of our results to more complex scenarios.

Journal/Review: PHYSICAL REVIEW X

Volume: 15 (2)      Pages from: 21027-1  to: 21027-35

More Information: We thank G. M. Andolina, A. Asenjo-Garcia, D. Chang, G. Chiriaco, D. De Bernardis, O. Dmytruck, D. Fausti, R. Fazio, C. Mora, A. Nardin, R. Colombelli, M. Schiro, and O. Zilberberg for discussions. M. D. was partly supported by the QUANTERA DYNAMITE PCI2022-132919, by the EU-Flagship programme Pasquans2, by the PNRR MUR Project No. PE0000023-NQSTI, by the PRIN program (project CoQuS) , and by the ERC Consolidator Grant Wavenets. H. B. X. was supported by MIUR Programme FARE (MEPH) . I. C. acknowledges financial support by the PE0000023-NQSTI project by the Italian Ministry of University and Research, cofunded by the European Union – NextGeneration EU, and from Provincia Autonoma di Trento (PAT) , partly via the Q@TN initiative. Z. B., I. C., and M. D. thank the Institut Henri Poincare (UAR 839 CNRS-Sorbonne Universite) for hospitality and the group of C. Ciuti for inspiring discussions during the stay. T. C. was partly supported by the Young Faculty Initiation Grant (NFIG) at IIT Madras (Project. No. RF24250775PHNFIG009162) . T. C. acknowledges Polish high-performance computing infrastructure PLGrid (HPC Center: ACK Cyfronet AGH) for providing computer facilities and support within computational Grant No. PLG/2024/017289 for a part of the numerical simu-lations. Z. B. thanks IIT Madras for kind hospitality through the Centers of Excellence, QuCenDiEM (Project No. SP22231244CPETWOQCDHOC) and Center for Quantum Information, Communication and Computation (CQuICC) (Project No. SP22231228CPETWOCQIHOC) . MPS-based numerical calculations have been performed with the help of ITensors.jl [127] and TenNetLib.jl [128] libraries.
KeyWords: Collective Excitations; Edge Excitations; Cavity; Transition; Insulator; Excitons; States; Phase
DOI: 10.1103/PhysRevX.15.021027