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arXiv:2608.20578

Nonlinear Diamagnetic Interactions in Ultrastrongly Coupled 2D Electrons

Dasom Kim, Kiran M. Kulkarni, Vaibhav Sharma, Dukhyung Lee, Geon Lee, Sunghwan Kim, Jonas Grumm, Shuang Liang, Hongjing Xu, Fuyang Tay, Andrey Baydin, Motoaki Bamba, Andreas Knorr, Christopher J. Stanton, Michael J. Manfra, Minah Seo, Stephen Hughes, Junichiro Kono

quant-phcond-mat.mes-hallSubmitted Aug 20, 2026• Announced Aug 24, 2026
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Abstract

The quantum Hopfield model is widely used to describe ultrastrong light--matter coupling between cavity photons and collective bosonic excitations in solids, where the diamagnetic interaction is conventionally assumed to be a constant. We experimentally demonstrate that the diamagnetic response of Landau polaritons is reduced under strong terahertz field excitation. We show that this behavior originates from field-driven redistribution of electrons into the nonparabolic regime of the conduction band of GaAs, which reduces the plasma frequency and consequently the diamagnetic interaction strength. A microscopic hot-electron model reproduces the observed nonlinear response. Motivated by this microscopic picture, we propose a nonlinear extension of the Hopfield model with a Kerr-like interaction. Our results establish a route toward nonlinear cavity quantum electrodynamics and driven ultrastrong light--matter coupling beyond the conventional linear Hopfield description, which is capable of creating uniquely quantum optical effects such as squeezed light generation.

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cond-mat.mes-hallCross-listedarXiv:2604.28042•May 1, 2026
The quantum Hopfield model is widely used to describe ultrastrong light--matter coupling between cavity photons and collective bosonic excitations in solids, where the diamagnetic interaction is conventionally assumed to be a constant. We experimentally demonstrate that the diamagnetic response of Landau polaritons is reduced under strong terahertz field excitation. We show that this behavior originates from field-driven redistribution of electrons into the nonparabolic regime of the conduction band of GaAs, which reduces the plasma frequency and consequently the diamagnetic interaction strength. A microscopic hot-electron model reproduces the observed nonlinear response. Motivated by this microscopic picture, we propose a nonlinear extension of the Hopfield model with a Kerr-like interaction. Our results establish a route toward nonlinear cavity quantum electrodynamics and driven ultrastrong light--matter coupling beyond the conventional linear Hopfield description, which is capable of creating uniquely quantum optical effects such as squeezed light generation.
We investigate a coherently driven exciton--photon microcavity with Kerr nonlinearity in the ultrastrong-coupling regime. When the lower and upper polariton branches are well separated in energy, the full Hopfield--Rabi--Kerr model reduces to an effective single-mode description of the lower polariton. We analyze the stability of the lower-polariton steady states. We show that the resulting bistability is qualitatively similar to that in the strong-coupling regime. However, in the ultrastrong-coupling regime counter-rotating processes and the diamagnetic A2A^{2}A2 term renormalize the polariton spectrum and composition, changing the effective detuning Δ~1\tildeΔ_{1}Δ~1​ and nonlinearity ULPU_{\mathrm{LP}}ULP​ ggg-dependency beyond the strong-coupling (RWA) picture. As a result, although the semiclassical bistability criterion keeps its standard Kerr--oscillator form, the turning points and hysteresis window are shifted relative to the strong-coupling prediction.
Dressing quantum states of matter with virtual photons can create exotic effects ranging from vacuum-field modified transport to polaritonic chemistry, and may drive strong squeezing or entanglement of light and matter modes. The established paradigm of cavity quantum electrodynamics focuses on resonant light-matter interaction to maximize the coupling strength ΩR/ωcΩ_\mathrm{R}/ω_\mathrm{c}ΩR​/ωc​, defined as the ratio of the vacuum Rabi frequency and the carrier frequency of light. Yet, the finite oscillator strength of a single electronic excitation sets a natural limit to ΩR/ωcΩ_\mathrm{R}/ω_\mathrm{c}ΩR​/ωc​. Here, we demonstrate a new regime of record-strong light-matter interaction which exploits the cooperative dipole moments of multiple, highly non-resonant magnetoplasmon modes specifically tailored by our metasurface. This multi-mode coupling creates an ultrabroadband spectrum of over 20 polaritons spanning 6 optical octaves, vacuum ground state populations exceeding 1 virtual excitation quantum for electronic and optical modes, and record coupling strengths equivalent to ΩR/ωc=3.19Ω_\mathrm{R}/ω_\mathrm{c}=3.19ΩR​/ωc​=3.19. The extreme interaction drives strongly subcycle exchange of vacuum energy between multiple bosonic modes akin to high-order nonlinearities otherwise reserved to strong-field physics, and entangles previously orthogonal electronic excitations solely via vacuum fluctuations of the common cavity mode. This offers avenues towards tailoring phase transitions by coupling otherwise non-interacting modes, merely by shaping the dielectric environment.
We investigate the nonlinearities of custom-tailored ultrastrongly light-matter coupled states by driving them with both the vacuum electromagnetic field and strong coherent THz waveforms. In this novel regime, where both the Rabi frequency induced by the coherent field and the vacuum Rabi frequency set by the cavity field are on the order of the carrier frequency of light, we observe strong subcycle pump-probe and multiwave mixing nonlinearities and nonlinear polariton correlations, violating the normal-mode approximation. Such custom-cut nonlinearities of hybridized excitations set the stage for nonlinear optical control of deep-strong coupling, exploring quantum phase transitions or nonclassical light sources.
The ultrastrong coupling regime of cavity photons and quantum materials has emerged as a pathway to modify materials properties, however definitive signatures of ultrastrong coupling remain elusive. Focusing on the quantum photon statistics of light transmitted through a cavity-embedded superconductor, we show that a two-photon Higgs polariton at strong coupling realizes a photonic nonlinearity at the single terahertz photon level. We find that as light-matter coupling increases, the photon statistics show pronounced changes due to the formation of a hybrid photon-matter dark-cavity state with finite photon occupancy, producing testable signatures of ultrastrong coupling. We derive a non-Markovian input output relation and study the cavity-embedded superconductor 2H-NbSe2 as it approaches ultrastrong light-matter coupling. Our results reveal a diagnostic for ultrastrong coupling in the two-photon coincidence statistics that is absent in total counts.
We explore the nonlinear response of tailor-cut light-matter hybrid states in a novel regime, where both the Rabi frequency induced by a coherent driving field and the vacuum Rabi frequency set by a cavity field are comparable to the carrier frequency of light. In this previously unexplored strong-field limit of ultrastrong coupling, subcycle pump-probe and multiwave mixing nonlinearities between different polariton states violate the normal-mode approximation while ultrastrong coupling remains intact, as confirmed by our mean-field model. We expect such custom-cut nonlinearities of hybridized elementary excitations to facilitate nonclassical light sources, quantum phase transitions, or cavity chemistry with virtual photons.
Deep strong light-matter coupling represents an extreme non-perturbative regime of quantum electrodynamics, in which the interaction strength exceeds the bare frequencies of the uncoupled systems. The ground state features strong quantum correlations between photons and matter excitations, and new cavity-driven phase transitions are expected to occur. Whether a superradiant quantum phase transition, marked by spontaneous dipole ordering and photon condensation, is possible has remained a long-standing and controversial question. Such phenomena have been proposed to arise in exotic electronic systems hosting Dirac and Kane fermions, owing to the formal absence of an A2A^2A2 term in their low-energy Hamiltonian. Here we exploit the ultralow effective mass of Kane fermions to realise Landau polaritons in a bulk mercury cadmium telluride layer coupled to a Fabry-Perot resonator. Using thermally tunable carrier density, we continuously tune the coupling from the weak to the deep-strong regime, achieving a record normalised coupling ratio exceeding 1.6 above room temperature. The measured polariton spectra are in excellent agreement with a rigorous, gauge-invariant microscopic theory. Despite the nonlinear Landau level structure of relativistic Kane fermions, we show that a diamagnetic A2A^2A2 term naturally emerges and precludes a superradiant phase transition. These results resolve the long-standing controversy surrounding cavity quantum electrodynamics of relativistic-like matter systems, extend deep-strong-coupling physics to Kane fermions, and open new opportunities for polaritonic semiconductor devices operating in extreme light-matter coupling regimes.