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.

Emerging theoretical frameworks suggest that physical properties of matter can be altered within an optical cavity by harnessing quantum vacuum electromagnetic fluctuations, even in the total absence of external driving fields. Among the most intriguing predictions is the potential to noninvasively manipulate superconductivity. Here, we experimentally observe modified superconductivity in niobium nitride (NbN) thin films within high-quality-factor (Q) terahertz cavities. Using terahertz time-domain spectroscopy, we characterize the NbN response both in free space and within a high-Q photonic-crystal cavity. Our analysis reveals significant cavity-induced modifications to the optical conductivity. A theoretical model indicates that these changes originate from a substantial (∼13 %) reduction in the superfluid density and a minor (∼2 %) reduction in the superconducting gap, driven by cavity vacuum fluctuations. These results demonstrate a platform for engineering ground states via vacuum–matter coupling, opening frontiers in cavity materials science.

Chiral cavities offer an intriguing way to manipulate material properties by breaking fundamental symmetries. However, only a few chiral cavity implementations exhibiting broken time-reversal symmetry have been demonstrated, with most relying on either strong magnetic fields, circularly polarized Floquet driving, or ultrastrong coupling between cavity modes and matter excitations. Here, we present a one-dimensional terahertz photonic-crystal cavity that exhibits broken time-reversal symmetry. The cavity consists of a silicon wafer sandwiched between InSb wafers. By exploiting the nonreciprocal terahertz response of a magnetoplasma and the low electron effective mass in InSb, a circularly polarized cavity mode at 0.67 THz under a modest magnetic field of 0.3 T, with a quality factor exceeding 50 is realized. Temperature-, magnetic field-, and polarization-dependent measurements and simulations demonstrate the chiral cavity with broken time-reversal symmetry, providing a robust platform for exploring chiral light–matter interactions and vacuum dressed quantum condensed matter in the terahertz regime. Researchers realized the first truly chiral terahertz cavity with time-reversal-symmetry broken vacuum fields, with near-unity ellipticity at 0.66 THz and Q>50 under a 0.3 T field, offering a robust platform for chiral light–matter interactions.

Chiral optical terahertz (THz) devices have significant technological implications for telecommunications, spectroscopy, and sensing. Engineering tunable, broadband, and cost-effective THz chiral materials has long been recognized as a challenging endeavor and a bottleneck hindering the full exploitation of the THz spectrum. Here, we present an artificial structure based on aligned carbon nanotube (CNT) films that exhibits a tunable broadband circular dichroism (CD) up to 2.8°. Its behavior is reciprocal. The theoretical simulations developed here agree with the experiments and predict a further increase in the CD signal to ∼30° as more CNT layers are added.

Optical cavities provide a powerful means to engineer light-matter hybrid states by coupling confined electromagnetic fields with matter excitations. Achieving in situ control of the coupling strength is essential for investigating how such hybridization evolves with the coupling strength. In this work, we use a symmetry-changing structural phase transition in lead halide perovskites to reversibly tune the phonon-photon coupling strength, leveraging the fact that their phonon frequencies and oscillator strengths are dictated by lattice symmetry. Terahertz time-domain spectroscopy of MAPbI3 embedded in nanoslot cavities reveals three polariton branches above the critical temperature Tc ≃ 162.5 K and the emergence of an additional branch below Tc, activated by a new phonon mode in the low-temperature phase. The full dispersion is accurately reproduced using a multimode Hopfield model, confirming that all normalized coupling strengths remain in the ultrastrong coupling regime. These results demonstrate symmetry-controlled tuning of ultrastrong light-matter coupling in optical cavities via temperature.

We study magnetic materials whose low energy physics can be effectively described by a Dicke model, which we term Dicke materials. We show how a Dicke model emerges in such materials due to a coexistence of fast-dispersing and slow-dispersing spins, which are strongly coupled. Analogous to the paradigmatic Dicke model describing light-matter interactions, these materials also exhibit signatures of a superradiant phase transition. The ground state near the superradiant phase transition is expected to be squeezed, making Dicke materials a resource for quantum metrology and witnessing entanglement in solid-state systems. However, as an entanglement measure, squeezing can be sensitive to perturbations that are otherwise irrelevant for usual correlation functions and order parameters. Motivated by the prospect of observing squeezing in such Dicke materials, we study the robustness of ground state squeezing under ubiquitous imperfections such as finite temperature, disorder, and local interactions. Using analytical and numerical techniques, we show that the squeezing obtained is perturbatively stable against these imperfections and quantitatively evaluate regimes promising for experimental observation.

The multimode ultrastrong coupling (USC) regime has emerged as a novel platform for accessing previously inaccessible phenomena in cavity quantum electrodynamics. Of particular interest are cavity-mediated correlations between local and nonlocal excitations, or equivalently, between modes at zero and finite in-plane momentum, which offer new opportunities for controlling light–matter interactions across space. However, direct experimental evidence of such interactions has remained elusive. Here, we demonstrate nonlocal multimode coupling in a Landau polariton system, where cavity photons simultaneously interact with the zero-momentum cyclotron resonance and finite-momentum magnetoplasmons of GaAs two-dimensional electron gas. Our slot cavities, with their subwavelength mode volumes, supply in-plane momentum components that enable the excitation of finite-momentum matter modes. Terahertz time-domain magnetospectroscopy measurements reveal a clear splitting of the upper-polariton branch, arising from hybridization between magnetoplasmon modes and the cavity–cyclotron-resonance hybrids. Extracted coupling strengths confirm USC of the cyclotron resonance and strong coupling of the magnetoplasmon modes to the cavity field, respectively. The experimental results are well captured by the multimode Hopfield model and finite-element simulations. These findings establish a pathway for engineering multimode light–matter interactions involving zero- and finite-momentum matter modes in the USC regime.

Landau polaritons arise when cavity photons strongly couple, or hybridize, with the cyclotron resonance of two-dimensional electrons in a strong perpendicular magnetic field. These polaritons provide a powerful platform for studying quantum electrodynamical phenomena in the ultrastrong coupling regime, where the Rabi frequency becomes a significant fraction of the bare frequencies of light and matter. Theories of Landau polaritons are well-developed under the electric-dipole approximation, including the selection rules for inter-Landau-level transitions, i.e., from the n -th to the ( n +1)-th Landau level with frequency ω c = eB / m *, where e , B , and m * are the elementary charge, magnetic field strength, and electron effective mass, respectively.

Two-level atoms ultrastrongly coupled with single-mode cavity photons are predicted to exhibit a quantum phase transition, entering a phase in which both the atomic polarization and the photonic field are finite even without external driving. However, this phenomenon, the superradiant phase transition (SRPT), is forbidden by a no-go theorem due to the existence of the diamagnetic term. Here, we present spectroscopic evidence for a magnonic SRPT in ErFeO 3 , where the role of the photonic mode (two-level atoms) in the photonic SRPT is played by an Fe 3+ magnon mode (Er 3+ spins). The absence of the diamagnetic term in the Fe 3+ -Er 3+ exchange coupling ensures that the no-go theorem does not apply. Ultrabroadband terahertz and gigahertz magnetospectroscopy experiments revealed the signatures of the SRPT in thermal equilibrium, a kink and a softening, respectively, of two spin-magnon hybridized modes at the critical point. Systems near this phase are expected to harbor large-scale squeezing, which will potentially provide a route to next-generation quantum technologies.

We present an ultrafast spin noise spectroscopy setup with wavelength tunabil-ity, enabling high-resolution detection of magnetic fluctuations. Our system can achieve $\sim 10^{-13}\text{rad}^{2}/\sqrt{\text{Hz}}$ sensitivity for spin dynamics with terahertz bandwidth. This capability opens new avenues for studying complex spin systems and phase transitions. © 2024 The Author(s)

Phonons play a central role in fundamental solid-state phenomena, including superconductivity, Raman scattering, and symmetry-breaking phases. Harnessing phonons to control these effects and enable quantum technologies is therefore of great interest. However, most existing phonon control strategies rely on external driving fields or anharmonic interactions, limiting their applicability. Here, we realize multimode ultrastrong light-matter coupling and theoretically show the modulation of phonon emission. This regime is realized by coupling two optical phonon modes in lead halide perovskites to a nanoslot array functioning as a single-mode cavity. The small mode volume of the nanoslots enables high coupling strengths in the phonon-polariton system. We show theoretically that the nanoslot resonator mediates an effective interaction between phonon modes, leading to superthermal phonon bunching in thermal equilibrium between distinct modes. Our findings are well described by a multimodal Hopfield model. This work establishes a pathway for engineering phononic properties for light-harvesting and light-emitting technologies.

Lead telluride is an important thermoelectric material due to its large Seebeck coefficient combined with its unusually low thermal conductivity that is related to the strong anharmonicity of phonons in this material. Here, we have studied the resonant and nonperturbative coupling of transverse optical phonons in lead telluride with cavity photons inside small-mode-volume metallic metasurface cavities that have photonic modes with terahertz frequencies. We observed a giant vacuum Rabi splitting on the order of the bare phonon and cavity frequencies. Through terahertz time-domain spectroscopy experiments, we systematically studied the vacuum Rabi splitting as a function of sample thickness, temperature, and cavity length. Under the strongest light-matter coupling conditions, the strength of coupling exceeded the bare phonon and cavity frequencies, putting the system into the deep-strong coupling regime. These results demonstrate that this uniquely tunable platform is promising for realizing and understanding predicted cavity-vacuum-induced ferroelectric instabilities and exploring applications of light-matter coupling in the ultrastrong and deep-strong coupling regimes in quantum technology.

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 ErFeO 3 , where the role of atoms (photons) is played by Er 3+ spins (Fe 3+ 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.

Methods for harnessing vibrational states are desired for phonon -based technologies. We realized ultrastrong coupling of two phonon modes in perovskite materials induced by ultrastrong coupling with a common photonic mode in a terahertz nanoslot cavity. (c) 2024 The Author(s)

Two-level atoms coupled with single-mode cavity photons are predicted to exhibit a quantum phase transition when the coupling strength exceeds a critical value, entering a phase in which atomic polarization and photonic field are finite even at zero temperature and without external driving. However, this phenomenon, the superradiant phase transition (SRPT), is forbidden by a no-go theorem due to the existence of the diamagnetic term in the Hamiltonian. Here, we present spectroscopic evidence for a magnonic SRPT in ErFeO$_3$, where the role of the photonic mode (two-level atoms) in the photonic SRPT is played by an Fe$^{3+}$ magnon mode (Er$^{3+}$ spins). The absence of the diamagnetic term in the Fe$^{3+}$-Er$^{3+}$ exchange coupling ensures that the no-go theorem does not apply. Terahertz and gigahertz magnetospectroscopy experiments revealed the signatures of the SRPT -- a kink and a softening, respectively, of two spin-magnon hybridized modes at the critical point.

Phonons, or vibrational quanta, are behind some of the most fundamental physical phenomena in solids, including superconductivity, Raman processes, and broken-symmetry phases. It is therefore of fundamental importance to find ways to harness phonons for controlling these phenomena and developing novel quantum technologies. However, the majority of current phonon control techniques rely on the use of intense external driving fields or strong anharmonicities, which restricts their range of applications. Here, we present a scheme for controlling the intensity fluctuations in phonon emission at room temperature based on multimode ultrastrong light–matter coupling. The multimode ultrastrong coupling regime is achieved by coupling two optical phonon modes in lead halide perovskites to an array of nanoslots, which operates as a single-mode cavity. The extremely small mode volume of the nanoslots enables unprecedented coupling strengths in a cavity phonon-polariton system. In the far-detuned, low-cavity-frequency regime, we demonstrate that the nanoslot resonator mediates an effective coupling between the phonon modes, resulting in superthermal phonon bunching in thermal equilibrium, both within the same mode and between different modes. Experimental results are in good agreement with a multimode Hopfield model. Our work paves the way for the tailoring of phonons to modify charge and energy transport in perovskite materials, with potential applications in light-collecting or emitting devices.

We demonstrated that an incident terahertz peak field amplitude below 0.01 MV/cm can trigger Zener tunneling in a semi-insulating GaAs. Moreover, a transmission decrease with an extinction ratio of 60% was observed in the semi-insulating GaAs with an electric field strength of up to 46 MV/cm (maximum incident peak field of ∼0.29 MV/cm). These experimental results were realized by taking advantage of the nonlinear effects, such as Zener tunneling, impact ionization, and metal–insulator–metal tunneling in 5 nm metallic nanogaps on the GaAs; a strong field was locally confined in the vicinity of these gaps. The 5 nm gap enabled us to lower the voltage across the gap to suppress impact ionization while allowing Zener tunneling. Simulation results indicated that the effective thickness of the semiconductor increased as a function of the gap size. The approach used in this study decreases the threshold incident electric field for nonlinear responses as well as paves the way toward ultrathin high-speed electronic devices and ultrafast light pumps.

We report ultrastrong coupling of the cyclotron resonance of a two-dimensional electron gas in a GaAs quantum well to terahertz cavity photons under extreme confinement to the nanometer scale. This was realized by an array of nano-slots fabricated close to the quantum well layer on the GaAs substrate. Our terahertz magnetospectroscopic measurements revealed two polariton branches as a function of applied magnetic field. While the photon-like part of the two polariton branches was clearly observed, the matter-like part was generally elusive. Our electromagnetic simulations quantitatively reproduce our observation for the upper-polariton branch. However, for the lower-polariton branch, our simulations predict a pronounced resonance, which was absent in experimental spectra. This discrepancy may be a consequence of the breakdown of the dipole approximation in this extreme confinement situation.

We have studied the resonant and nonperturbative coupling of transverse optical phonons in lead telluride with photons in small-mode-volume terahertz cavities, observing a giant vacuum Rabi splitting on the order of the uncoupled phonon and cavity frequencies. Our terahertz time-domain spectroscopy experimental data, systematically collected as a function of sample thickness, temperature, and cavity length, can be well reproduced by our electromagnetic simulations. These results demonstrate that this uniquely tunable platform is promising for realizing and understanding predicted cavity-vacuum-induced ferroelectric instabilities, as well as for exploring applications of light-matter coupling in the ultra-and deep-strong coupling regimes in quantum technology.

We have investigated the resonant coupling of photons with TO phonons in lead telluride in small-mode-volume terahertz cavities, observing a giant vacuum Rabi splitting on the order of the bare cavity–phonon frequency.