Giant optical nonlinearities from Rydberg excitons in semiconductor microcavities

Cavity-Tuned Exciton Dynamics in Transition Metal Dichalcogenides Monolayers

A fully quantum, numerically accurate methodology is presented for the simulation of the exciton dynamics and time-resolved fluorescence of cavity-tuned two-dimensional (2D) materials at finite temperatures. This approach was specifically applied to a monolayer WSe2 system. Our methodology enabled us to identify the dynamical and spectroscopic signatures of polaronic and polaritonic effects and to elucidate their characteristic timescales across a range of exciton-cavity couplings. The approach employed can be extended to simulation of various cavity-tuned 2D materials, specifically for exploring finite temperature nonlinear spectroscopic signals.

Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2

The fundamental properties of an exciton are determined by the spin, valley, energy, and spatial wavefunctions of the Coulomb-bound electron and hole. In van der Waals materials, these attributes can be widely engineered through layer stacking configuration to create highly tunable interlayer excitons with static out-of-plane electric dipoles, at the expense of the strength of the oscillating in-plane dipole responsible for light-matter coupling. Here we show that interlayer excitons in bi- and tri-layer 2H-MoSe2 crystals exhibit electric-field-driven coupling with the ground (1s) and excited states (2s) of the intralayer A excitons. We demonstrate that the hybrid states of these distinct exciton species provide strong oscillator strength, large permanent dipoles (up to 0.73 ± 0.01 enm), high energy tunability (up to ~200 meV), and full control of the spin and valley characteristics such that the exciton g-factor can be manipulated over a large range (from -4 to +14). Further, we observe the bi- and tri-layer excited state (2s) interlayer excitons and their coupling with the intralayer excitons states (1s and 2s). Our results, in good agreement with a coupled oscillator model with spin (layer)-selectivity and beyond standard density functional theory calculations, promote multilayer 2H-MoSe2 as a highly tunable platform to explore exciton-exciton interactions with strong light-matter interactions.

Nonlinear Rydberg exciton-polaritons in Cu2O microcavities

Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu2O-filled microresonator. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as ∝ n4.4±1.8 for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly correlated photonic (polaritonic) states in a solid state system.

Highly-excited Rydberg excitons in synthetic thin-film cuprous oxide

Cuprous oxide ([Formula: see text]) has recently emerged as a promising material in solid-state quantum technology, specifically for its excitonic Rydberg states characterized by large principal quantum numbers (n). The significant wavefunction size of these highly-excited states (proportional to [Formula: see text]) enables strong long-range dipole-dipole (proportional to [Formula: see text]) and van der Waals interactions (proportional to [Formula: see text]). Currently, the highest-lying Rydberg states are found in naturally occurring [Formula: see text]. However, for technological applications, the ability to grow high-quality synthetic samples is essential. The fabrication of thin-film [Formula: see text] samples is of particular interest as they hold potential for observing extreme single-photon nonlinearities through the Rydberg blockade. Nevertheless, due to the susceptibility of high-lying states to charged impurities, growing synthetic samples of sufficient quality poses a substantial challenge. This study successfully demonstrates the CMOS-compatible synthesis of a [Formula: see text] thin film on a transparent substrate that showcases Rydberg excitons up to [Formula: see text] which is readily suitable for photonic device fabrications. These findings mark a significant advancement towards the realization of scalable and on-chip integrable Rydberg quantum technologies.

An Inverse-Designed Nanophotonic Interface for Excitons in Atomically Thin Materials

Efficient nanophotonic devices are essential for applications in quantum networking, optical information processing, sensing, and nonlinear optics. Extensive research efforts have focused on integrating two-dimensional (2D) materials into photonic structures, but this integration is often limited by size and material quality. Here, we use hexagonal boron nitride (hBN), a benchmark choice for encapsulating atomically thin materials, as a waveguiding layer while simultaneously improving the optical quality of the embedded films. When combined with a photonic inverse design, it becomes a complete nanophotonic platform to interface with optically active 2D materials. Grating couplers and low-loss waveguides provide optical interfacing and routing, tunable cavities provide a large exciton-photon coupling to transition metal dichalcogenide (TMD) monolayers through Purcell enhancement, and metasurfaces enable the efficient detection of TMD dark excitons. This work paves the way for advanced 2D-material nanophotonic structures for classical and quantum nonlinear optics.

Rydberg Excitons and Trions in Monolayer MoTe2

Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances, which serve as a microscopic, noninvasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS₂, MoSe₂, WS₂, and WSe₂), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe₂). Here, we report an experimental investigation of excitonic luminescence properties of monolayer MoTe₂ to understand the excitonic Rydberg series, up to 3s. We report a significant modification of emission energies with temperature (4 to 300 K), thereby quantifying the exciton-phonon coupling. Furthermore, we observe a strongly gate-tunable exciton-trion interplay for all the Rydberg states governed mainly by free-carrier screening, Pauli blocking, and band gap renormalization in agreement with the results of first-principles GW plus Bethe-Salpeter equation approach calculations. Our results help bring monolayer MoTe₂ closer to its potential applications in near-infrared optoelectronics and photonic devices.

Near-field enhancement of optical second harmonic generation in hybrid gold-lithium niobate nanostructures

Nanophotonics research has focused recently on the ability of nonlinear optical processes to mediate and transform optical signals in a myriad of novel devices, including optical modulators, transducers, color filters, photodetectors, photon sources, and ultrafast optical switches. The inherent weakness of optical nonlinearities at smaller scales has, however, hindered the realization of efficient miniaturized devices, and strategies for enhancing both device efficiencies and synthesis throughput via nanoengineering remain limited. Here, we demonstrate a novel mechanism by which second harmonic generation, a prototypical nonlinear optical phenomenon, from individual lithium niobate particles can be significantly enhanced through nonradiative coupling to the localized surface plasmon resonances of embedded gold nanoparticles. A joint experimental and theoretical investigation of single mesoporous lithium niobate particles coated with a dispersed layer of ~10 nm diameter gold nanoparticles shows that a ~32-fold enhancement of second harmonic generation can be achieved without introducing finely tailored radiative nanoantennas to mediate photon transfer to or from the nonlinear material. This work highlights the limitations of current strategies for enhancing nonlinear optical phenomena and proposes a route through which a new class of subwavelength nonlinear optical platforms can be designed to maximize nonlinear efficiencies through near-field energy exchange.

Exciton Dynamics and Time-Resolved Fluorescence in Nanocavity-Integrated Monolayers of Transition-Metal Dichalcogenides

We have developed an ab initio-based, fully quantum, numerically accurate methodology for the simulation of the exciton dynamics and time- and frequency-resolved fluorescence spectra of the cavity-controlled two-dimensional materials at finite temperatures and applied this methodology to the single-layer WSe₂ system. Specifically, the multiple Davydov D₂ Ansatz has been employed in combination with the method of thermofield dynamics for the finite-temperature extension of accurate time-dependent variation. This allowed us to establish dynamical and spectroscopic signatures of the polaronic and polaritonic effects as well as uncover their characteristic time scales in the relevant range of temperatures. Our study reveals the pivotal role of multidimensional conical intersections in controlling the many-body dynamics of highly intertwined excitonic, phononic, and photonic modes.

Rydberg polaritons in ReS2 crystals

Rhenium disulfide belongs to group VII transition metal dichalcogenides (TMDs) with attractive properties such as exceptionally high refractive index and remarkable oscillator strength, large in-plane birefringence, and good chemical stability. Unlike most other TMDs, the peculiar optical properties of rhenium disulfide persist from bulk to the monolayer, making this material potentially suitable for applications in optical devices. In this work, we demonstrate with unprecedented clarity the strong coupling between cavity modes and excited states, which results in a strong polariton interaction, showing the interest of these materials as a solid-state counterpart of Rydberg atomic systems. Moreover, we definitively clarify the nature of important spectral features, shedding light on some controversial aspects or incomplete interpretations and demonstrating that their origin is due to the interesting combination of the very high refractive index and the large oscillator strength expressed by these TMDs.

Self-Kerr Effect across the Yellow Rydberg Series of Excitons in Cu_{2}O

We investigate the nonlinear refraction induced by Rydberg excitons in Cu_{2}O. Using a high-precision interferometry imaging technique that spatially resolves the nonlinear phase shift, we observe significant shifts at extremely low laser intensity near each exciton resonance. From this, we derive the nonlinear index n_{2}, present the n_{2} spectrum for principal quantum numbers n≥5, and report large n_{2} values of order 10^{-3}  mm^{2}/mW. Moreover, we observe a rapid saturation of the Kerr nonlinearity and find that the saturation intensity I_{sat} decreases as n^{-7}. We explain this with the Rydberg blockade mechanism, whereby giant Rydberg interactions limit the exciton density, resulting in a maximum phase shift of 0.5 rad in our setup.

Rydberg exciton-polaritons in a Cu2O microcavity

Giant Rydberg excitons with principal quantum numbers as high as n = 25 have been observed in cuprous oxide (Cu₂O), a semiconductor in which the exciton diameter can become as large as ∼1 μm. The giant dimension of these excitons results in excitonic interaction enhancements of orders of magnitude. Rydberg exciton-polaritons, formed by the strong coupling of Rydberg excitons to cavity photons, are a promising route to exploit these interactions and achieve a scalable, strongly correlated solid-state platform. However, the strong coupling of these excitons to cavity photons has remained elusive. Here, by embedding a thin Cu₂O crystal into a Fabry-Pérot microcavity, we achieve strong coupling of light to Cu₂O Rydberg excitons up to n = 6 and demonstrate the formation of Cu₂O Rydberg exciton-polaritons. These results pave the way towards realizing strongly interacting exciton-polaritons and exploring strongly correlated phases of matter using light on a chip.

Experimental Realization of Reconfigurable Photonic Lattices in Coherent Rydberg Atomic Vapors

We experimentally demonstrated the formation of a one-dimensional electromagnetically induced optical lattice in coherently prepared three-level 85Rb Rydberg atomic vapors with electromagnetically induced transparency (EIT). The one-dimensional photonic lattice was optically induced by a coupling field with a spatially periodical intensity distribution deriving from the interference of two strong Gaussian beams from the same laser source (~480 nm). Under the Rydberg-EIT condition, the incident weak probe beam can feel a tunable spatially modulated susceptibility, which is verified by the controllable discrete diffraction pattern observed at the output plane of the vapor cell. This investigation not only opens the door for experimentally introducing the strong interaction between Rydberg atoms to govern the beam dynamics in photonic lattices based on atomic coherence but also provides an easily accessible periodic environment for exploring Rydberg-atom physics and related applications.

Beam steering at the nanosecond time scale with an atomically thin reflector

Techniques to mold the flow of light on subwavelength scales enable fundamentally new optical systems and device applications. The realization of programmable, active optical systems with fast, tunable components is among the outstanding challenges in the field. Here, we experimentally demonstrate a few-pixel beam steering device based on electrostatic gate control of excitons in an atomically thin semiconductor with strong light-matter interactions. By combining the high reflectivity of a MoSe₂ monolayer with a graphene split-gate geometry, we shape the wavefront phase profile to achieve continuously tunable beam deflection with a range of 10°, two-dimensional beam steering, and switching times down to 1.6 nanoseconds. Our approach opens the door for a new class of atomically thin optical systems, such as rapidly switchable beam arrays and quantum metasurfaces operating at their fundamental thickness limit.

Andersen et al. have demonstrated a new type of beam steering device based on the excitonic response of an atomically thin semiconductor. Using electrostatic gates, the authors achieved tunable steering with switching times on the nanosecond scale.

Giant enhancement of THz-frequency optical nonlinearity by phonon polariton in ionic crystals

The field of nonlinear optics has grown substantially in past decades, leading to tremendous progress in fundamental research and revolutionized applications. Traditionally, the optical nonlinearity for a light wave at frequencies beyond near-infrared is observed with very high peak intensity, as in most materials only the electronic nonlinearity dominates while ionic contribution is negligible. However, it was shown that the ionic contribution to nonlinearity can be much larger than the electronic one in microwave experiments. In the terahertz (THz) regime, phonon polariton may assist to substantially trigger the ionic nonlinearity of the crystals, so as to enhance even more the nonlinear optical susceptibility. Here, we experimentally demonstrate a giant second-order optical nonlinearity at THz frequency, orders of magnitude higher than that in the visible and microwave regimes. Different from previous work, the phonon-light coupling is achieved under a phase-matching setting, and the dynamic process of nonlinear THz generation is directly observed in a thin-film waveguide using a time-resolved imaging technique. Furthermore, a nonlinear modification to the Huang equations is proposed to explain the observed nonlinearity enhancement. This work brings about an effective approach to achieve high nonlinearity in ionic crystals, promising for applications in THz nonlinear technologies.

Optical nonlinearity in the THz range is of interest for scientific applications. Here the authors show that THz nonlinearity in ionic crystals can be enhanced by orders of magnitude through phonon polaritons, which is also described by nonlinear modified Huang equations.

Enhanced nonlinear interaction of polaritons via excitonic Rydberg states in monolayer WSe2

Strong optical nonlinearities play a central role in realizing quantum photonic technologies. Exciton-polaritons, which result from the hybridization of material excitations and cavity photons, are an attractive candidate to realize such nonlinearities. While the interaction between ground state excitons generates a notable optical nonlinearity, the strength of such interactions is generally not sufficient to reach the regime of quantum nonlinear optics. Excited states, however, feature enhanced interactions and therefore hold promise for accessing the quantum domain of single-photon nonlinearities. Here we demonstrate the formation of exciton-polaritons using excited excitonic states in monolayer tungsten diselenide (WSe2) embedded in a microcavity. The realized excited-state polaritons exhibit an enhanced nonlinear response ∼[Formula: see text] which is ∼4.6 times that for the ground-state exciton. The demonstration of enhanced nonlinear response from excited exciton-polaritons presents the potential of generating strong exciton-polariton interactions, a necessary building block for solid-state quantum photonic technologies.

Attractive and Repulsive Exciton-Polariton Interactions Mediated by an Electron Gas

Realizing strong photon-photon interactions in a solid-state setting is a major goal with far reaching potential for optoelectronic applications. Using Landau's quasiparticle framework combined with a microscopic many-body theory, we explore the interactions between exciton-polaritons and trions in a two-dimensional semiconductor injected with an electron gas inside a microcavity. We show that particle-hole excitations in the electron gas mediate an attractive interaction between the polaritons, whereas the interaction between trions and polaritons mediated by the exchange of an electron can be either repulsive or attractive. These mediated interactions are intrinsic to the quasiparticles and are also present in the absence of light. Importantly, they can be tuned to be more than an order of magnitude stronger than the direct polariton-polariton interaction in the absence of the electron gas, thereby providing a promising outlook for nonlinear optical components. Finally, we compare our theoretical predictions to two recent experiments.

Controlling Exciton-Phonon Interactions via Electromagnetically Induced Transparency

Highly excited Rydberg states of excitons in Cu_{2}O semiconductors provide a promising approach to explore and control strong particle interactions in a solid-state environment. A major obstacle has been the substantial absorption background that stems from exciton-phonon coupling and lies under the Rydberg excitation spectrum, weakening the effects of exciton interactions. Here, we demonstrate that two-photon excitation of Rydberg excitons under conditions of electromagnetically induced transparency (EIT) can be used to control this background. Based on a microscopic theory that describes the known single-photon absorption spectrum, we analyze the conditions under which two-photon EIT permits separating the optical Rydberg excitation from the phonon-induced absorption background, and even suppressing it entir7ely. Our findings thereby pave the way for the exploitation of Rydberg blockade with Cu_{2}O excitons in nonlinear optics and other applications.

Plasma-Enhanced Interaction and Optical Nonlinearities of Cu_{2}O Rydberg Excitons

We theoretically investigate the nonlinear optical transmission through a cuprous oxide crystal for wavelengths that cover the series of highly excited excitons, observed in recent experiments. Since such Rydberg excitons have strong van der Waals interactions, they can dynamically break the conditions for resonant exciton creation and dramatically modify the refractive index of the material in a nonlinear manner. We explore this mechanism theoretically and determine its effects on the optical properties of a semiconductor for the case of degenerate pair-state asymptotes of Rydberg excitons in Cu_{2}O. Upon analyzing the additional effects of a dilute residual electron-hole plasma, we find quantitative agreement with previous transmission measurements, which provides strong indications for the enhancement of Rydberg-induced nonlinearities by surrounding free charges.

Superfluid Flow of Polaron Polaritons above Landau's Critical Velocity

We develop a theory for the interaction of light with superfluid optical media, describing the motion of quantum impurities that are created and dragged through the liquid by propagating photons. It is well known that a mobile impurity suffers dissipation due to phonon emission as soon as it moves faster than the speed of sound in the superfluid-Landau's critical velocity. Surprisingly we find that in the present hybrid light-matter setting, polaritonic impurities can be protected against environmental decoherence and be allowed to propagate well above the Landau velocity without jeopardizing the superfluid response of the medium.

Electromagnetically Induced Transparency in Media with Rydberg Excitons 1: Slow Light

In this paper, we show that Electromagnetically Induced Transparency (EIT) can be realized in mediums with Rydberg excitons. With realistic, reliable parameters which show good agreement with optical and electro-optical experiments, as well as the proper choice of Rydberg exciton states in the Cu₂O crystal, we indicate how the EIT can be performed. The calculations show that, due to a large group index, one can expect the slowing down of a light pulse by a factor of about 104 in this medium.

Electromagnetically Induced Transparency in Media with Rydberg Excitons 2: Cross-Kerr Modulation

By mapping photons into the sample of cuprous oxide with Rydberg excitons, it is possible to obtain a significant optical phase shift due to third-order cross-Kerr nonlinearities realized under the conditions of electromagnetically induced transparency. The optimum conditions for observation of the phase shift over π in Rydberg excitons media are examined. A discussion of the application of the cross-phase modulations in the field of all-optical quantum information processing in solid-state systems is presented.

Controlling Excitons in an Atomically Thin Membrane with a Mirror

We demonstrate a new approach for dynamically manipulating the optical response of an atomically thin semiconductor, a monolayer of MoSe_{2}, by suspending it over a metallic mirror. First, we show that suspended van der Waals heterostructures incorporating a MoSe_{2} monolayer host spatially homogeneous, lifetime-broadened excitons. Then, we interface this nearly ideal excitonic system with a metallic mirror and demonstrate control over the exciton-photon coupling. Specifically, by electromechanically changing the distance between the heterostructure and the mirror, thereby changing the local photonic density of states in a controllable and reversible fashion, we show that both the absorption and emission properties of the excitons can be dynamically modulated. This electromechanical control over exciton dynamics in a mechanically flexible, atomically thin semiconductor opens up new avenues in cavity quantum optomechanics, nonlinear quantum optics, and topological photonics.

Observation of Rydberg exciton polaritons and their condensate in a perovskite cavity

The condensation of half-light half-matter exciton polaritons in semiconductor optical cavities is a striking example of macroscopic quantum coherence in a solid-state platform. Quantum coherence is possible only when there are strong interactions between the exciton polaritons provided by their excitonic constituents. Rydberg excitons with high principal value exhibit strong dipole-dipole interactions in cold atoms. However, polaritons with the excitonic constituent that is an excited state, namely Rydberg exciton polaritons (REPs), have not yet been experimentally observed. Here, we observe the formation of REPs in a single crystal CsPbBr₃ perovskite cavity without any external fields. These polaritons exhibit strong nonlinear behavior that leads to a coherent polariton condensate with a prominent blue shift. Furthermore, the REPs in CsPbBr₃ are highly anisotropic and have a large extinction ratio, arising from the perovskite's orthorhombic crystal structure. Our observation not only sheds light on the importance of many-body physics in coherent polariton systems involving higher-order excited states, but also paves the way for exploring these coherent interactions for solid-state quantum optical information processing.

Solid-state pulsed microwave emitter based on Rydberg excitons

We theoretically demonstrate how the cuprous oxide Cu ₂O could be used as a gain medium in a solid-state maser. By taking advantage of radiative microwave transitions between highly excited Rydberg states, one can achieve population inversion and masing in a wide range of wavelengths. In the pulsed emission regime, the considered excitonic system is characterized by intricate and rich dynamics, which are investigated numerically, taking into account several key features of the medium, such as strong Stark shift of energy levels and the presence of the Rydberg blockade effect.

Beating the Rayleigh Limit Using Two-Photon Interference

Multiparameter estimation theory offers a general framework to explore imaging techniques beyond the Rayleigh limit. While optimal measurements of single parameters characterizing a composite light source are now well understood, simultaneous determination of multiple parameters poses a much greater challenge that in general requires implementation of collective measurements. Here we show, theoretically and experimentally, that Hong-Ou-Mandel interference followed by spatially resolved detection of photons provides precise information on both the separation and the centroid for a pair of point emitters, avoiding trade-offs inherent to single-photon measurements.

Proposal of tunable Rydberg exciton maser

We propose a continuous-mode solid-state maser based on Cu₂O, where ensemble of highly excited Rydberg exciton states serves as a gain medium. We show that the system is highly tunable with an external electric field, allowing for a wide range of emission frequencies within terahertz range. Numerical simulations of the system dynamics are performed to optimize the conditions for efficient masing and estimate the emission power.