Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons

TL;DR

This paper develops a theoretical framework for fractional quantum Hall states interacting with quantum light, revealing robustness of topological features, entanglement signatures, and the emergence of graviton-polaritons, with implications for ultra-strong coupling regimes.

Contribution

It introduces a novel theoretical approach combining analytical and tensor network methods to study FQH states coupled to quantum light, including the discovery of graviton-polaritons and effects of ultra-strong coupling.

Findings

Topological signatures remain robust under cavity fluctuations.

Entanglement spectra show light-matter entanglement and topology fingerprints.

Identification of a new neutral quasiparticle, the graviton-polariton.

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 non-local cavity modes on integer quantum Hall physics has been recently addressed, its 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 $\nu=1/3$ 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 non-local 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 ultra-strong coupling regimes we find other two important effects, a cavity vacuum-induced Stark shift for charged quasi-particles and a potential instability towards 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.