Exact solution of polaritonic systems with arbitrary light and matter frequency-dependent losses.

In this paper, we perform the exact diagonalization of a light-matter strongly coupled system taking into account arbitrary losses via both energy dissipation in the optically active material and photon escape out of the resonator. This allows us to naturally treat the cases of couplings with structured reservoirs, which can strongly impact the polaritonic response via frequency-dependent losses or discrete-to-continuum strong coupling. We discuss the emergent gauge freedom of the resulting theory and provide analytical expressions for all the gauge-invariant observables in both the Power-Zienau-Woolley and the Coulomb representations. In order to exemplify the results, the theory is finally specialized to two specific cases. In the first one, both light and matter resonances are characterized by Lorentzian linewidths, and in the second one, a fixed absorption band is also present. The analytical expressions derived in this paper can be used to predict, fit, and interpret results from polaritonic experiments with arbitrary values of the light-matter coupling and with losses of arbitrary intensity and spectral shape in both the light and matter channels. A Matlab code implementing our results is provided.

Polaritonic quantization in nonlocal polar materials.

In the Reststrahlen region, between the transverse and longitudinal phonon frequencies, polar dielectric materials respond metallically to light, and the resulting strong light-matter interactions can lead to the formation of hybrid quasiparticles termed surface phonon polaritons. Recent works have demonstrated that when an optical system contains nanoscale polar elements, these excitations can acquire a longitudinal field component as a result of the material dispersion of the lattice, leading to the formation of secondary quasiparticles termed longitudinal-transverse polaritons. In this work, we build on previous macroscopic electromagnetic theories, developing a full second-quantized theory of longitudinal-transverse polaritons. Beginning from the Hamiltonian of the light-matter system, we treat distortion to the lattice, introducing an elastic free energy. We then diagonalize the Hamiltonian, demonstrating that the equations of motion for the polariton are equivalent to those of macroscopic electromagnetism and quantize the nonlocal operators. Finally, we demonstrate how to reconstruct the electromagnetic fields in terms of the polariton states and explore polariton induced enhancements of the Purcell factor. These results demonstrate how nonlocality can narrow, enhance, and spectrally tune near-field emission with applications in mid-infrared sensing.

Engineering the Spectral and Spatial Dispersion of Thermal Emission via Polariton-Phonon Strong Coupling.

Strong coupling between optical modes can be implemented into nanophotonic design to modify the energy-momentum dispersion relation. This approach offers potential avenues for tuning the thermal emission frequency, line width, polarization, and spatial coherence. Here, we employ three-mode strong coupling between propagating and localized surface phonon polaritons, with zone-folded longitudinal optic phonons within periodic arrays of 4H-SiC nanopillars. Energy exchange, mode evolution, and coupling strength between the three polariton branches are explored experimentally and theoretically. The influence of strong coupling upon the angle-dependent thermal emission was directly measured, providing excellent agreement with theory. We demonstrate a 5-fold improvement in the spatial coherence and 3-fold enhancement of the quality factor of the polaritonic modes, with these hybrid modes also exhibiting a mixed character that could enable opportunities to realize electrically driven emission. Our results show that polariton-phonon strong coupling enables thermal emitters, which meet the requirements for a host of IR applications in a simple, lightweight, narrow-band, and yet bright emitter.

Multielectron Ground State Electroluminescence.

The ground state of a cavity-electron system in the ultrastrong coupling regime is characterized by the presence of virtual photons. If an electric current flows through this system, the modulation of the light-matter coupling induced by this nonequilibrium effect can induce an extracavity photon emission signal, even when electrons entering the cavity do not have enough energy to populate the excited states. We show that this ground state electroluminescence, previously identified in a single-qubit system [Phys. Rev. Lett. 116, 113601 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.113601] can arise in a many-electron system. The collective enhancement of the light-matter coupling makes this effect, described beyond the rotating wave approximation, robust in the thermodynamic limit, allowing its observation in a broad range of physical systems, from a semiconductor heterostructure with flatband dispersion to various implementations of the Dicke model.

Strong Coupling of Epsilon-Near-Zero Phonon Polaritons in Polar Dielectric Heterostructures.

We report the first observation of epsilon-near-zero (ENZ) phonon polaritons in an ultrathin AlN film fully hybridized with surface phonon polaritons (SPhP) supported by the adjacent SiC substrate. Employing a strong coupling model for the analysis of the dispersion and electric field distribution in these hybridized modes, we show that they share the most prominent features of the two precursor modes. The novel ENZ-SPhP coupled polaritons with a highly propagative character and deeply subwavelength light confinement can be utilized as building blocks for future infrared and terahertz nanophotonic integration and communication devices.

Strong coupling in a microcavity containing ß-carotene.

We have fabricated an open-cavity microcavity structure containing a thin film of the biologically-derived molecule ß-carotene. We show that the ß-carotene absorption can be described in terms of a series of Lorentzian functions that approximate the 0-0, 0-1, 0-2, 0-3 and 0-4 electronic and vibronic transitions. On placing this molecular material into a microcavity, we obtain anti-crossing between the cavity mode and the 0-1 vibronic transition, however other electronic and vibronic transitions remain in the intermediate or weak-coupling regime due to their lower oscillator strength and broader linewidth. We discuss the consequences of strong-coupling for the possible modification of photosynthetic processes, or a re-ordering of allowed and optically-forbidden states.

Collective Optomechanical Effects in Cavity Quantum Electrodynamics.

We investigate a cavity quantum electrodynamic effect, where the alignment of two-dimensional freely rotating optical dipoles is driven by their collective coupling to the cavity field. By exploiting the formal equivalence of a set of rotating dipoles with a polymer we calculate the partition function of the coupled light-matter system and demonstrate that it exhibits a second order phase transition between a bunched state of isotropic orientations and a stretched one with all the dipoles aligned. Such a transition manifests itself as an intensity-dependent shift of the polariton mode resonance. Our work, lying at the crossroad between cavity quantum electrodynamics and quantum optomechanics, is a step forward in the ongoing quest to understand how strong coupling can be exploited to influence matter internal degrees of freedom.

Ground State Electroluminescence.

Electroluminescence, the emission of light in the presence of an electric current, provides information on the allowed electronic transitions of a given system. It is commonly used to investigate the physics of strongly coupled light-matter systems, whose eigenfrequencies are split by the strong coupling with the photonic field of a cavity. Here we show that, together with the usual electroluminescence, systems in the ultrastrong light-matter coupling regime emit a uniquely quantum radiation when a flow of current is driven through them. While standard electroluminescence relies on the population of excited states followed by spontaneous emission, the process we describe herein extracts bound photons from the dressed ground state and it has peculiar features that unequivocally distinguish it from usual electroluminescence.

Strong and Coherent Coupling between Localized and Propagating Phonon Polaritons.

Following the recent observation of localized phonon polaritons in user-defined silicon carbide nanoresonators, here we demonstrate strong and coherent coupling between those localized modes and propagating phonon polaritons bound to the surface of the nanoresonator's substrate. In order to obtain phase matching, the nanoresonators have been fabricated to serve the double function of hosting the localized modes, while also acting as a grating for the propagating ones. The coherent coupling between long lived, optically accessible localized modes, and low-loss propagative ones, opens the way to the design and realization of phonon-polariton based coherent circuits.

Light-matter decoupling in the deep strong coupling regime: the breakdown of the Purcell effect.

Improvements in both the photonic confinement and the emitter design have led to a steady increase in the strength of the light-matter coupling in cavity quantum electrodynamics experiments. This has allowed us to access interaction-dominated regimes in which the state of the system can only be described in terms of mixed light-matter excitations. Here we show that, when the coupling between light and matter becomes strong enough, this picture breaks down, and light and matter degrees of freedom totally decouple. A striking consequence of such a counterintuitive phenomenon is that the Purcell effect is reversed and the spontaneous emission rate, usually thought to increase with the light-matter coupling strength, plummets instead for large enough couplings.

Sculpting ultrastrong light-matter coupling through spatial matter structuring.

The central theme of cavity quantum electrodynamics is the coupling of a single optical mode with a single matter excitation, leading to a doublet of cavity polaritons which govern the optical properties of the coupled structure. Especially in the ultrastrong coupling regime, where the ratio of the vacuum Rabi frequency and the quasi-resonant carrier frequency of light, ΩR/ω c, approaches unity, the polariton doublet bridges a large spectral bandwidth 2ΩR, and further interactions with off-resonant light and matter modes may occur. The resulting multi-mode coupling has recently attracted attention owing to the additional degrees of freedom for designing light-matter coupled resonances, despite added complexity. Here, we experimentally implement a novel strategy to sculpt ultrastrong multi-mode coupling by tailoring the spatial overlap of multiple modes of planar metallic THz resonators and the cyclotron resonances of Landau-quantized two-dimensional electrons, on subwavelength scales. We show that similarly to the selection rules of classical optics, this allows us to suppress or enhance certain coupling pathways and to control the number of light-matter coupled modes, their octave-spanning frequency spectra, and their response to magnetic tuning. This offers novel pathways for controlling dissipation, tailoring quantum light sources, nonlinearities, correlations as well as entanglement in quantum information processing.

Quantum phases of a multimode bosonic field coupled to flat electronic bands.

We investigate the quantum phases of systems in which a multimode bosonic field is coupled to the transitions between two flat electronic bands. In the literature, such systems are usually modeled using a single or multimode Dicke model, leading to the prediction of superradiant quantum phase transitions for large enough couplings. We show that the physics of these systems is remarkably richer than previously expected, with the system continuously interpolating between a Dicke model exhibiting a superradiant quantum phase transition and a quantum Rabi model with no phase transition.

Launching and Manipulation of Higher-Order In-Plane Hyperbolic Phonon Polaritons in Low-Dimensional Heterostructures.

Hyperbolic phonon polaritons (HPhPs) are stimulated by coupling infrared (IR) photons with the polar lattice vibrations. Such HPhPs offer low-loss, highly confined light propagation at subwavelength scales with out-of-plane or in-plane hyperbolic wavefronts. For HPhPs, while a hyperbolic dispersion implies multiple propagating modes with a distribution of wavevectors at a given frequency, so far it has been challenging to experimentally launch and probe the higher-order modes that offer stronger wavelength compression, especially for in-plane HPhPs. In this work, the experimental observation of higher-order in-plane HPhP modes stimulated on a 3C-SiC nanowire (NW)/α-MoO3 heterostructure is reported where leveraging both the low-dimensionality and low-loss nature of the polar NWs, higher-order HPhPs modes within 2D α-MoO3 crystal are launched by the 1D 3C-SiC NW. The launching mechanism is further studied and the requirements for efficiently launching of such higher-order modes are determined. In addition, by altering the geometric orientation between the 3C-SiC NW and α-MoO3 crystal, the manipulation of higher-order HPhP dispersions as a method of tuning is demonstrated. This work illustrates an extremely anisotropic low dimensional heterostructure platform to confine and configure electromagnetic waves at the deep-subwavelength scales for a range of IR applications including sensing, nano-imaging, and on-chip photonics.

Highly nonlinear dipolar exciton-polaritons in bilayer MoS2.

Realizing nonlinear optical response in the low photon density limit in solid-state systems has been a long-standing challenge. Semiconductor microcavities in the strong coupling regime hosting exciton-polaritons have emerged as attractive candidates in this context. However, the weak interaction between these quasiparticles has been a hurdle in this quest. Dipolar excitons provide an attractive strategy to overcome this limitation but are often hindered by their weak oscillator strength. The interlayer dipolar excitons in naturally occurring homobilayer MoS2 alleviates this issue owing to their formation via hybridization of interlayer charge transfer exciton with intralayer B exciton. Here we demonstrate the formation of dipolar exciton polaritons in bilayer MoS2 resulting in unprecedented nonlinear interaction strengths. A ten-fold increase in nonlinearity is observed for the interlayer dipolar excitons compared to the conventional A excitons. These highly nonlinear dipolar polaritons will likely be a frontrunner in the quest for solid-state quantum nonlinear devices.

Collective Phonon-Polaritonic Modes in Silicon Carbide Subarrays.

Localized surface phonon polaritons (LSPhPs) can be implemented to engineer light-matter interactions through nanoscale patterning for a range of midinfrared application spaces. However, the polar material systems studied to date have mainly focused on simple designs featuring a single element in the periodic unit cell. Increasing the complexity of the unit cell can serve to modify the resonant near-fields and intra- and inter-unit-cell coupling as well as to dictate spectral tuning in the far-field. In this work, we exploit more complicated unit-cell structures to realize LSPhP modes with additional degrees of design freedom, which are largely unexplored. Collectively excited LSPhP modes with distinctly symmetric and antisymmetric near-fields are supported in these subarray designs, which are based on nanopillars that are scaled by the number of subarray elements to ensure a constant unit-cell size. Moreover, we observe an anomalous mode-matching of the collective symmetric mode in our fabricated subarrays that is robust to changing numbers of pillars within the subarrays as well as to defects intentionally introduced in the form of missing pillars. This work therefore illustrates the hierarchical design of tailored LSPhP resonances and modal near-field profiles simultaneously for a variety of IR applications such as surface-enhanced spectroscopies and biochemical sensing.

Quantum Szilard engine.

The Szilard engine (SZE) is the quintessence of Maxwell's demon, which can extract the work from a heat bath by utilizing information. We present the first complete quantum analysis of the SZE, and derive an analytic expression of the quantum-mechanical work performed by a quantum SZE containing an arbitrary number of molecules, where it is crucial to regard the process of insertion or removal of a wall as a legitimate thermodynamic process. We find that more (less) work can be extracted from the bosonic (fermionic) SZE due to the indistinguishability of identical particles.

Near-Field Spectroscopy of Cylindrical Phonon-Polariton Antennas.

Surface phonon polaritons (SPhPs) are hybrid light-matter states in which light strongly couples to lattice vibrations inside the Reststrahlen band of polar dielectrics at mid-infrared frequencies. Antennas supporting localized surface phonon polaritons (LSPhPs) easily outperform their plasmonic counterparts operating in the visible or near-infrared in terms of field enhancement and confinement thanks to the inherently slower phonon-phonon scattering processes governing SPhP decay. In particular, LSPhP antennas have attracted considerable interest for thermal management at the nanoscale, where the emission strongly diverts from the usual far-field blackbody radiation due to the presence of evanescent waves at the surface. However, far-field measurements cannot shed light on the behavior of antennas in the near-field region. To overcome this limitation, we employ scattering-scanning near-field optical microscopy (sSNOM) to unveil the spectral near-field response of 3C-SiC antenna arrays. We present a detailed description of the behavior of the antenna resonances by comparing far-field and near-field spectra and demonstrate the existence of a mode with no net dipole moment, absent in the far-field spectra, but of importance for applications that exploit the heightened electromagnetic near fields. Furthermore, we investigate the perturbation in the antenna response induced by the presence of the AFM tip, which can be further extended toward situations where for example strong IR emitters couple to LSPhP modes.

Hybrid longitudinal-transverse phonon polaritons.

Phonon polaritons, hybrid light-matter quasiparticles resulting from strong coupling of the electromagnetic field with the lattice vibrations of polar crystals are a promising platform for mid-infrared photonics but for the moment there has been no proposal allowing for their electrical pumping. Electrical currents in fact mainly generate longitudinal optical phonons, while only transverse ones participate in the creation of phonon polaritons. We demonstrate how to exploit long-cell polytypes of silicon carbide to achieve strong coupling between transverse phonon polaritons and zone-folded longitudinal optical phonons. We develop a microscopic theory predicting the existence of the resulting hybrid longitudinal-transverse excitations. We then provide an experimental observation by tuning the resonance of a nanopillar array through the folded longitudinal optical mode, obtaining a clear spectral anti-crossing. The hybridisation of phonon polaritons with longitudinal phonons could represent an important step toward the development of phonon polariton-based electrically pumped mid-infrared emitters.

Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics.

Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light-matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light-matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.