Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect

Landau-phonon polaritons in Dirac heterostructures

Polaritons are light-matter quasiparticles that govern the optical response of quantum materials at the nanoscale, enabling on-chip communication and local sensing. Here, we report Landau-phonon polaritons (LPPs) in magnetized charge-neutral graphene encapsulated in hexagonal boron nitride (hBN). These quasiparticles emerge from the interaction of Dirac magnetoexciton modes in graphene with the hyperbolic phonon polariton modes in hBN. Using infrared magneto-nanoscopy, we reveal the ability to completely halt the LPP propagation in real space at quantized magnetic fields, defying the conventional optical selection rules. The LPP-based nanoscopy also tells apart two fundamental many-body phenomena: the Fermi velocity renormalization and field-dependent magnetoexciton binding energies. Our results highlight the potential of magnetically tuned Dirac heterostructures for precise nanoscale control and sensing of light-matter interaction.

Extraordinary Electrical Conductance through Amorphous Nonconducting Polymers under Vibrational Strong Coupling

Enhancing the electrical conductance through amorphous nondoped polymers is challenging. Here, we show that vibrational strong coupling (VSC) of intrinsically nonconducting and amorphous polymers such as polystyrene, deuterated polystyrene, and poly(benzyl methacrylate) to the vacuum electromagnetic field of the cavity enhances the electrical conductivity by at least 6 orders of magnitude compared to the uncoupled polymers. Remarkably, the observed extraordinary conductance is vibrational mode selective and occurs only under the VSC of the aromatic C-H(D) out-of-plane bending modes of the polymers. The conductance is thermally activated at the onset of strong coupling and becomes temperature-independent as the collective strong coupling strength increases. The electrical characterizations are performed without external light excitation, demonstrating the role of vacuum electromagnetic field-matter strong coupling in enhancing long-range transport even in amorphous nonconducting polymers.

Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling

We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full nonrelativistic Pauli-Fierz problem of an ensemble of strongly coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles). Thus, collective vibrational strong coupling can alter individual molecules strongly for localized "hotspots" within the ensemble. Moreover, the discovered cavity-induced polarization pattern possesses a zero net polarization, which resembles a continuous form of a spin glass (or better polarization glass). Our findings suggest that the thorough understanding of polaritonic chemistry, requires a self-consistent treatment of dressed electronic structure, which can give rise to numerous, so far overlooked, physical mechanisms.

Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, θ≈1.05°, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately 0.8°<θ<1.3°. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the Γ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.

THz quantum gap: exploring potential approaches for generating and detecting non-classical states of THz light

Over the past few decades, THz technology has made considerable progress, evidenced by the performance of current THz sources and detectors, as well as the emergence of several THz applications. However, in the realm of quantum technologies, the THz spectral domain is still in its infancy, unlike neighboring spectral domains that have flourished in recent years. Notably, in the microwave domain, superconducting qubits currently serve as the core of quantum computers, while quantum cryptography protocols have been successfully demonstrated in the visible and telecommunications domains through satellite links. The THz domain has lagged behind in these impressive advancements. Today, the current gap in the THz domain clearly concerns quantum technologies. Nonetheless, the emergence of quantum technologies operating at THz frequencies will potentially have a significant impact. Indeed, THz radiation holds significant promise for wireless communications with ultimate security owing to its low sensitivity to atmospheric disturbances. Moreover, it has the potential to raise the operating temperature of solid-state qubits, effectively addressing existing scalability issues. In addition, THz radiation can manipulate the quantum states of molecules, which are recognized as new platforms for quantum computation and simulation with long range interactions. Finally, its ability to penetrate generally opaque materials or its resistance to Rayleigh scattering are very appealing features for quantum sensing. In this perspective, we will discuss potential approaches that offer exciting prospects for generating and detecting non-classical states of THz light, thereby opening doors to significant breakthroughs in THz quantum technologies.

Mode-multiplexing deep-strong light-matter coupling

Dressing electronic quantum states with virtual photons creates exotic effects ranging from vacuum-field modified transport to polaritonic chemistry, and squeezing or entanglement of modes. The established paradigm of cavity quantum electrodynamics maximizes the light-matter coupling strengthΩ R / ω c , defined as the ratio of the vacuum Rabi frequency and the frequency of light, by resonant interactions. Yet, the finite oscillator strength of a single electronic excitation sets a natural limit toΩ R / ω c . Here, we enter a regime of record-strong light-matter interaction which exploits the cooperative dipole moments of multiple, highly non-resonant magnetoplasmon modes tailored by our metasurface. This creates an ultrabroadband spectrum of 20 polaritons spanning 6 optical octaves, calculated vacuum ground state populations exceeding 1 virtual excitation quantum, and coupling strengths equivalent toΩ R / ω c = 3.19 . The extreme interaction drives strongly subcycle energy exchange between multiple bosonic vacuum modes akin to high-order nonlinearities, and entangles previously orthogonal electronic excitations solely via vacuum fluctuations.

Coherent Interaction of a Few-Electron Quantum Dot with a Terahertz Optical Resonator

We have investigated light-matter hybrid excitations in a quantum dot (QD) THz resonator coupled system. We fabricate a gate-defined QD near a THz split-ring resonator (SRR) by using a AlGaAs/GaAs two-dimensional electron system. By illuminating the system with THz radiation, the QD shows a current change whose spectrum exhibits coherent coupling between the electrons in the QD and the SRR as well as coupling between the two-dimensional electron system and the SRR. The latter coupling enters the ultrastrong coupling regime and the electron excitation in the QD also exhibits coherent coupling with the SRR with the remarkably large coupling constant, despite the fact that only a few electrons reside in the QD.

Ab Initio Calculations of Quantum Light-Matter Interactions in General Electromagnetic Environments

The emerging field of strongly coupled light-matter systems has drawn significant attention in recent years because of the prospect of altering both the physical and chemical properties of molecules and materials. Because this emerging field draws on ideas from both condensed-matter physics and quantum optics, it has attracted the attention of theoreticians from both fields. While the former often employ accurate descriptions of the electronic structure of the matter, the description of the electromagnetic environment is often oversimplified. In contrast, the latter often employs sophisticated descriptions of the electromagnetic environment while using oversimplified few-level approximations of the electronic structure. Both approaches are problematic because the oversimplified descriptions of the electronic system are incapable of describing effects such as light-induced structural changes in the electronic system, while the oversimplified descriptions of the electromagnetic environments can lead to unphysical predictions because the light-matter interactions strengths are misrepresented. In this work, we overcome these shortcomings and present the first method which can quantitatively describe both the electronic system and general electromagnetic environments from first principles. We realize this by combining macroscopic QED (MQED) with Quantum Electrodynamical Density-Functional Theory. To exemplify this approach, we consider the example of an absorbing spherical cavity and study the impact of different parameters of both the environment and the electronic system on the transition from weak-to-strong coupling for different aromatic molecules. As part of this work, we also provide an easy-to-use tool to calculate the cavity coupling strengths for simple cavity setups. Our work is a significant step toward parameter-free ab initio calculations for strongly coupled quantum light-matter systems and will help bridge the gap between theoretical methods and experiments in the field.

Electrical Detection of Ultrastrong Coherent Interaction between Terahertz Fields and Electrons Using Quantum Point Contacts

Light-matter interaction in the ultrastrong coupling regime is attracting considerable attention owing to its applications to coherent control of material properties by a vacuum fluctuation field. However, electrical access to such an ultrastrongly coupled system is very challenging. In this work, we have fabricated a gate-defined quantum point contact (QPC) near the gap of a terahertz (THz) split-ring resonator (SRR) fabricated on a GaAs two-dimensional (2D) electron system. By illuminating the system with external THz radiation, the QPC shows a photocurrent spectrum which exhibits significant anticrossing that arises from coupling between the cyclotron resonance of the 2D electrons and the SRR. The observed photocurrent signal can be explained by energy-selective transmission/reflection of the quantum Hall edge channels at the QPC. Furthermore, at the same gate voltage and magnetic field conditions under which the anticrossing signal was observed, the QPC exhibits anomalous conductance modulation even in the dark environment.

Vacuum-Induced Symmetry Breaking of Chiral Enantiomer Formation in Chemical Reactions

A material with symmetry breaking inside can transmit the symmetry breaking to its vicinity by vacuum electromagnetic fluctuations. Here, we show that vacuum quantum fluctuations proximate to a parity-symmetry-broken material can induce a chirality-dependent spectral shift of chiral molecules, resulting in a chemical reaction process that favors producing one chirality over the other. We calculate concrete examples and evaluate the chirality production rate with experimentally realizable parameters, showing the promise of selecting chirality with symmetry-broken vacuum quantum fluctuations.

Ultrasmall and tunable TeraHertz surface plasmon cavities at the ultimate plasmonic limit

The ability to confine THz photons inside deep-subwavelength cavities promises a transformative impact for THz light engineering with metamaterials and for realizing ultrastrong light-matter coupling at the single emitter level. To that end, the most successful approach taken so far has relied on cavity architectures based on metals, for their ability to constrain the spread of electromagnetic fields and tailor geometrically their resonant behavior. Here, we experimentally demonstrate a comparatively high level of confinement by exploiting a plasmonic mechanism based on localized THz surface plasmon modes in bulk semiconductors. We achieve plasmonic confinement at around 1 THz into record breaking small footprint THz cavities exhibiting mode volumes as low as [Formula: see text], excellent coupling efficiencies and a large frequency tunability with temperature. Notably, we find that plasmonic-based THz cavities can operate until the emergence of electromagnetic nonlocality and Landau damping, which together constitute a fundamental limit to plasmonic confinement. This work discloses nonlocal plasmonic phenomena at unprecedentedly low frequencies and large spatial scales and opens the door to novel types of ultrastrong light-matter interaction experiments thanks to the plasmonic tunability.

Weakened Topological Protection of the Quantum Hall Effect in a Cavity

We study the quantum Hall effect in a two-dimensional homogeneous electron gas coupled to a quantum cavity field. As initially pointed out by Kohn, Galilean invariance for a homogeneous quantum Hall system implies that the electronic center of mass (c.m.) decouples from the electron-electron interaction, and the energy of the c.m. mode, also known as Kohn mode, is equal to the single particle cyclotron transition. In this work, we point out that strong light-matter hybridization between the Kohn mode and the cavity photons gives rise to collective hybrid modes between the Landau levels and the photons. We provide the exact solution for the collective Landau polaritons and we demonstrate the weakening of topological protection at zero temperature due to the existence of the lower polariton mode which is softer than the Kohn mode. This provides an intrinsic mechanism for the recently observed topological breakdown of the quantum Hall effect in a cavity [F. Appugliese et al., Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect, Science 375, 1030 (2022).SCIEAS0036-807510.1126/science.abl5818]. Importantly, our theory predicts the cavity suppression of the thermal activation gap in the quantum Hall transport. Our work paves the way for future developments in cavity control of quantum materials.

Electron-Photon Chern Number in Cavity-Embedded 2D Moiré Materials

We explore theoretically how the topological properties of 2D materials can be manipulated by cavity quantum electromagnetic fields for both resonant and off-resonant electron-photon coupling, with a focus on van der Waals moiré superlattices. We investigate an electron-photon topological Chern number for the cavity-dressed energy minibands that is well defined for any degree of hybridization and entanglement of the electron and photon states. While an off-resonant cavity mode can renormalize electronic topological phases that exist without cavity coupling, we show that when the cavity mode is resonant to electronic miniband transitions, new and higher electron-photon Chern numbers can emerge.

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

Cavity-mediated thermal control of metal-to-insulator transition in 1T-TaS2

Placing quantum materials into optical cavities provides a unique platform for controlling quantum cooperative properties of matter, by both weak and strong light-matter coupling1,2. Here we report experimental evidence of reversible cavity control of a metal-to-insulator phase transition in a correlated solid-state material. We embed the charge density wave material 1T-TaS2 into cryogenic tunable terahertz cavities3 and show that a switch between conductive and insulating behaviours, associated with a large change in the sample temperature, is obtained by mechanically tuning the distance between the cavity mirrors and their alignment. The large thermal modification observed is indicative of a Purcell-like scenario in which the spectral profile of the cavity modifies the energy exchange between the material and the external electromagnetic field. Our findings provide opportunities for controlling the thermodynamics and macroscopic transport properties of quantum materials by engineering their electromagnetic environment.

Magneto-optics in a van der Waals magnet tuned by self-hybridized polaritons

Controlling quantum materials with light is of fundamental and technological importance. By utilizing the strong coupling of light and matter in optical cavities1-3, recent studies were able to modify some of their most defining features4-6. Here we study the magneto-optical properties of a van der Waals magnet that supports strong coupling of photons and excitons even in the absence of external cavity mirrors. In this material-the layered magnetic semiconductor CrSBr-emergent light-matter hybrids called polaritons are shown to substantially increase the spectral bandwidth of correlations between the magnetic, electronic and optical properties, enabling largely tunable optical responses to applied magnetic fields and magnons. Our results highlight the importance of exciton-photon self-hybridization in van der Waals magnets and motivate novel directions for the manipulation of quantum material properties by strong light-matter coupling.

Cavity Light-Matter Entanglement through Quantum Fluctuations

The hybridization between light and matter forms the basis to achieve cavity control over quantum materials. In this Letter we investigate a cavity coupled to a quantum chain of interacting spinless fermions by numerically exact solutions and perturbative analytical expansions. We draw two important conclusions about such systems: (i) Specific quantum fluctuations of the matter system play a pivotal role in achieving entanglement between light and matter; and (ii) in turn, light-matter entanglement is a key ingredient to modify electronic properties by the cavity. We hypothesize that quantum fluctuations of those matter operators to which the cavity modes couple are a general prerequisite for light-matter entanglement in the ground state. Implications of our findings for light-matter-entangled phases, cavity-modified phase transitions in correlated systems, and measurement of light-matter entanglement through Kubo response functions are discussed.

Can We Observe Nonperturbative Vacuum Shifts in Cavity QED?

We address the fundamental question of whether or not it is possible to achieve conditions under which the coupling of a single dipole to a strongly confined electromagnetic vacuum can result in nonperturbative corrections to the dipole's ground state. To do so we consider two simplified, but otherwise rather generic cavity QED setups, which allow us to derive analytic expressions for the total ground-state energy and to distinguish explicitly between purely electrostatic and genuine vacuum-induced contributions. Importantly, this derivation takes the full electromagnetic spectrum into account while avoiding any ambiguities arising from an ad hoc mode truncation. Our findings show that while the effect of confinement per se is not enough to result in substantial vacuum-induced corrections, the presence of high-impedance modes, such as plasmons or engineered LC resonances, can drastically increase these effects. Therefore, we conclude that with appropriately designed experiments it is at least in principle possible to access a regime where light-matter interactions become nonperturbative.

Electronic transport driven by collective light-matter coupled states in a quantum device

In the majority of optoelectronic devices, emission and absorption of light are considered as perturbative phenomena. Recently, a regime of highly non-perturbative interaction, ultra-strong light-matter coupling, has attracted considerable attention, as it has led to changes in the fundamental properties of materials such as electrical conductivity, rate of chemical reactions, topological order, and non-linear susceptibility. Here, we explore a quantum infrared detector operating in the ultra-strong light-matter coupling regime driven by collective electronic excitations, where the renormalized polariton states are strongly detuned from the bare electronic transitions. Our experiments are corroborated by microscopic quantum theory that solves the problem of calculating the fermionic transport in the presence of strong collective electronic effects. These findings open a new way of conceiving optoelectronic devices based on the coherent interaction between electrons and photons allowing, for example, the optimization of quantum cascade detectors operating in the regime of strongly non-perturbative coupling with light.

Field-effect bulk mobilities in polymer semiconductor films measured by sourcemeters

Semiconducting polymers inherently exhibit polydispersity in terms of molecular structure and microscopic morphology, which often results in a broad distribution of energy levels for localized electronic states. Therefore, the bulk charge mobility strongly depends on the free charge density. In this study, we propose a method to measure the charge-density-dependent bulk mobility of conjugated polymer films with widely spread localized states using a conventional field-effect transistor configuration. The gate-induced variation of bulk charge density typically ranges within ±1018 cm-3; however, this range depends significantly on the energetic dispersion width of localized states. The field-effect bulk mobility and field-effect mobility near the semiconductor-dielectric interface along with their dependence on charge density can be simultaneously extracted from the transistor characteristics using various gate voltage ranges.

Cavity Quantum Electrodynamics with Hyperbolic van der Waals Materials

The ground-state properties and excitation energies of a quantum emitter can be modified in the ultrastrong coupling regime of cavity quantum electrodynamics (QED) where the light-matter interaction strength becomes comparable to the cavity resonance frequency. Recent studies have started to explore the possibility of controlling an electronic material by embedding it in a cavity that confines electromagnetic fields in deep subwavelength scales. Currently, there is a strong interest in realizing ultrastrong-coupling cavity QED in the terahertz (THz) part of the spectrum, since most of the elementary excitations of quantum materials are in this frequency range. We propose and discuss a promising platform to achieve this goal based on a two-dimensional electronic material encapsulated by a planar cavity consisting of ultrathin polar van der Waals crystals. As a concrete setup, we show that nanometer-thick hexagonal boron nitride layers should allow one to reach the ultrastrong coupling regime for single-electron cyclotron resonance in a bilayer graphene. The proposed cavity platform can be realized by a wide variety of thin dielectric materials with hyperbolic dispersions. Consequently, van der Waals heterostructures hold the promise of becoming a versatile playground for exploring the ultrastrong-coupling physics of cavity QED materials.

Engineering random spin models with atoms in a high-finesse cavity

All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics over holographic duality in high-energy physics to annealing algorithms in quantum computing. Typically, these models are abstractions that do not find unambiguous physical realizations in nature. Here we realize an all-to-all interacting, disordered spin system by subjecting an atomic cloud in a cavity to a controllable light shift. Adjusting the detuning between atom resonance and cavity mode, we can tune between disordered versions of a central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically probing the low-energy excitations of the system, we explore the competition of interactions with disorder across a broad parameter range. We show how disorder in the central-mode model breaks the strong collective coupling, making the dark-state manifold cross over to a random distribution of weakly mixed light-matter, 'grey', states. In the Lipkin-Meshkov-Glick model, the ferromagnetic finite-sized ground state evolves towards a paramagnet as disorder is increased. In that regime, semi-localized eigenstates emerge, as we observe by extracting bounds on the participation ratio. These results present substantial steps towards freely programmable cavity-mediated interactions for the design of arbitrary spin Hamiltonians.

Quantized Fields for Optimal Control in the Strong Coupling Regime

We tailor the quantum statistics of a bosonic field to deterministically drive a quantum system into a target state. Experimentally accessible states of the field achieve good control of multilevel or multiqubit systems, notably also at coupling strengths beyond the rotating-wave approximation. This extends optimal control theory to the realm of fully quantized, strongly coupled control and target degrees of freedom.

Non-Fermi-Liquid Behavior from Cavity Electromagnetic Vacuum Fluctuations at the Superradiant Transition

We study two-dimensional materials where electrons are coupled to the vacuum electromagnetic field of a cavity. We show that, at the onset of the superradiant phase transition towards a macroscopic photon occupation of the cavity, the critical electromagnetic fluctuations, consisting of photons strongly overdamped by their interaction with electrons, can in turn lead to the absence of electronic quasiparticles. Since transverse photons couple to the electronic current, the appearance of non-Fermi-Liquid behavior strongly depends on the lattice. In particular, we find that in a square lattice the phase space for electron-photon scattering is reduced in such a way to preserve the quasiparticles, while in a honeycomb lattice the latter are removed due to a nonanalytical frequency dependence of the damping ∝|ω|^{2/3}. Standard cavity probes could allow us to measure the characteristic frequency spectrum of the overdamped critical electromagnetic modes responsible for the non-Fermi-liquid behavior.

Perspectives on weak interactions in complex materials at different length scales

Nanocomposite materials consist of nanometer-sized quantum objects such as atoms, molecules, voids or nanoparticles embedded in a host material. These quantum objects can be exploited as a super-structure, which can be designed to create material properties targeted for specific applications. For electromagnetism, such targeted properties include field enhancements around the bandgap of a semiconductor used for solar cells, directional decay in topological insulators, high kinetic inductance in superconducting circuits, and many more. Despite very different application areas, all of these properties are united by the common aim of exploiting collective interaction effects between quantum objects. The literature on the topic spreads over very many different disciplines and scientific communities. In this review, we present a cross-disciplinary overview of different approaches for the creation, analysis and theoretical description of nanocomposites with applications related to electromagnetic properties.

Vertex-Based Diagrammatic Treatment of Light-Matter-Coupled Systems

We propose a diagrammatic Monte Carlo approach for quantum impurity models, which can be regarded as a generalization of the strong-coupling expansion for fermionic impurity models. The algorithm is based on a self-consistently computed three-point vertex and a stochastically sampled four-point vertex, and it allows one to obtain numerically exact results in a wide parameter regime. The performance of the algorithm is demonstrated with applications to a spin-boson model representing an emitter in a waveguide. As a function of the coupling strength, the spin exhibits a delocalization-localization crossover at low temperatures, signaling a qualitative change in the real-time relaxation. In certain parameter regimes, the response functions of the emitter coupled to the electromagnetic continuum can be described by an effective Rabi model with appropriately defined parameters. We also discuss the spatial distribution of the photon density around the emitter.

Cavity-mediated drag in double-layer graphene

We study the frictional drag between two graphene layers placed inside a cavity. We show that the drag has two contributions: the well-known Coulomb drag, and a novel photon-mediated drag. The latter arises from a cavity-mediated interaction in which the backscattering is not suppressed and the screening is relatively weak. As a result, the photon-mediated drag resistivity in the Fermi-liquid regime acquires corrections to the usual quadratic temperature dependence, has a slow decay as the interlayer separationdincreases, and depends on the carrier densitynasρD∼1/n2. Thus, whereas for smalldandnthe Coulomb drag dominates, as these parameters increase the drag transitions to a purely photon-mediated drag. The onset of this transition depends on the electromagnetic field enhancement inside the cavity.

An ultrastrongly coupled single terahertz meta-atom

Free-space coupling to subwavelength individual optical elements is a central theme in quantum optics, as it allows the control over individual quantum systems. Here we show that, by combining an asymmetric immersion lens setup and a complementary resonating metasurface we are able to perform terahertz time-domain spectroscopy of an individual, strongly subwavelength meta-atom. We unravel the linewidth dependence as a function of the meta-atom number indicating quenching of the superradiant coupling. On these grounds, we investigate ultrastrongly coupled Landau polaritons at the single resonator level, measuring a normalized coupling ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{{\Omega }}}{\omega }=0.6$$\end{document}Ωω=0.6. Similar measurements on a lower density two dimensional electron gas yield a coupling ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{{\Omega }}}{\omega }=0.33$$\end{document}Ωω=0.33 with a cooperativity C = 94. Our findings pave the way towards the control of ultrastrong light-matter interaction at the single electron/ resonator level. The proposed technique is way more general and can be useful to characterize the complex conductivity of micron-sized samples in the terahertz domain.

By combining an asymmetric immersion lens setup and a complementary resonating metasurface, the authors are able to resolve the far-field transmission of an ultrastrongly coupled, highly subwavelength split-ring single resonator at millimeter wavelengths.