Quasi-2D halide perovskites are chemically synthesized realizations of quantum well stacks with giant exciton oscillator strengths, tunable emission spectra, and very large exciton binding energies. While these features render quasi-2D halide perovskites a promising platform for room-temperature polaritonics, bosonic condensation and polariton lasing in quasi-2D perovskites have so far remained elusive at ambient conditions. Here, we demonstrate room-temperature cavity exciton-polariton condensation in mechanically exfoliated crystals of the quasi-2D Ruddlesden-Popper iodide perovskite (BA)2(MA)2Pb3I10 in an open optical microcavity. We observe a polariton condensation threshold of 0.41 µJ cm−2 per pulse and detect a strong non-linear response. Interferometric measurements confirm the spontaneous emergence of spatial coherence across the condensate with an associated first-order autocorrelation reaching 0.6 with 1 ps coherence time and an effective de Broglie wavelength of 13 µm. Our results lay the foundation for a new class of room-temperature polariton lasers based on quasi-2D halide perovskites with great potential for hetero-integration with other van-der-Waals materials and combination with photonic crystals or waveguides. The authors report the experimental observation of room-temperature condensation of exciton polaritons in quasi-2D layered crystals of halide perovskite, integrated into an open optical microcavity. These materials combine van-der-Waals properties with dominant exciton physics at room temperature.

Transition metal dichalcogenides represent a versatile platform to study strong light-matter interactions based on excitons and electrons in ordered lattices. Twist-engineering of moiré structures further enables the manipulation of the polaritonic nonlinearities via engineering the exciton landscape on the nanoscale. In this work, we demonstrate in-situ control of the optical saturation-based nonlinearity of moiré exciton-polaritons by phase space restriction via charge doping. Strong exciton-photon coupling is established in a gate-controllable MoTe_2-MoSe_2 heterobilayer, embedded in a spectrally-tunable open cavity. A small gate voltage can effectively lower the necessary polariton density by one order of magnitude to achieve a similar nonlinear saturation effect as in the charge-neutral case. Our microscopic description successfully explains the observed phenomena in the framework of Pauli blocking for the moiré superlattices with charge preoccupation.

We develop a microscopic theory for nonlinear optical response of moiré exciton polaritons in bilayers of transition metal dichalcogenides (TMDs). Our theory allows us to study the tunnel-coupled intralayer and interlayer excitonic modes for a wide range of twist angles (θ), external electric field, and light-matter coupling, providing insights into the hybridization regime inaccessible before. Specifically, we account for the umklapp scattering processes of two exciton polaritons responsible for enhanced nonlinearity, and show that it is crucial for describing interactions at strong hybridization. We reveal a regime of attractive nonlinearity for moiré polaritons, stemming from the anisotropic Coulomb interactions, which can explain some of experimental features of optical response in TMD bilayers. Furthermore, within our theory we demonstrate that the attractive nonlinearity can be tuned into repulsive by applying an external electric field. Our findings show that nonlinear moiré polaritons offer a controllable platform nonlinear polaritonic devices.

Layered perovskites are an emergent class of materials, which feature extraordinarily large light-matter coupling, driven by excitons with binding energies significantly beyond the thermal energy at room-temperature. In this work, widely tunable room-temperature cavity exciton polaritons are demonstrated at the cross-over from the strong coupling to the very strong coupling regime in mechanically exfoliated crystals of quasi-2D Ruddlesden-Popper iodide perovskite (BA)2(MA)2Pb3I10 embedded in an open microcavity. The coupled exciton-cavity system features a Rabi-splitting up to Omega R similar or equal to 155 meV, exceeding the experimentally determined exciton binding energy of E b = 100 +/- 10 meV and thus operates at the onset of the very strong coupling regime, in which the light-matter coupling alters the interaction of electron and hole. This combined experimental-theoretical effort provides a consistent microscopic picture successfully describing the observed peculiar scaling of the Rabi-splitting with an increasing effective cavity length. These findings provide a foundation for future on-chip applications involving tunable polaritonic and nonlinear optical devices based on strongly coupled perovskite systems.

Ultrafast all-optical logic devices based on nonlinear light-matter interactions hold the promise to overcome the speed limitations of conventional electronic devices. Strong coupling of excitons and photons inside an optical resonator enhances such interactions and generates new polariton states which give access to unique nonlinear phenomena, such as Bose-Einstein condensation, used for all-optical ultrafast polariton transistors. However, to reach the threshold for condensation high quality factors and high pulse energies are required. Here we demonstrate all-optical switching exploiting the ultrafast transition from the strong to the weak coupling regime in low-Q microcavities embedding bilayers of transition metal dichalcogenides with high optical nonlinearities and fast exciton relaxation times. We observe a collapse of polariton gaps as large as 55 meV, and their revival, lowering the threshold for optical switching below 4 pJ per pulse, while retaining ultrahigh switching frequencies. As an additional degree of freedom, the switching can be triggered pumping either the intra- or the interlayer excitons of the bilayers at different wavelengths, speeding up the polariton dynamics, owing to unique interspecies excitonic interactions. Our approach will enable the development of compact ultrafast all-optical logical circuits and neural networks, showcasing a new platform for polaritonic information processing based on manipulating the light-matter coupling.

Van der Waals magnets are an emergent material class of paramount interest for fundamental studies in coupling light with matter excitations, which are uniquely linked to their underlying magnetic properties. Among these materials, the magnetic semiconductor CrSBr is possibly a first playground where we can study simultaneously the interaction of photons, magnons, and excitons at the quantum level. Here we demonstrate a coherent macroscopic quantum phase, the bosonic condensation of exciton-polaritons, which emerges in a CrSBr flake embedded in a fully tunable cryogenic open optical cavity. The Bose condensate is characterized by a highly non-linear threshold-like behavior, and coherence manifests distinctly via its first and second order quantum coherence. We find that the condensate's non-linearity is highly susceptible to the magnetic order in CrSBr, and encounters a sign change depending on the antiferro- and ferromagnetic ordering. Our findings open a route towards magnetically controllable quantum fluids of light, and optomagnonic devices where spin magnetism is coupled to on-chip Bose-Einstein condensates.

Layered 2D halide perovskites are chemically synthesized realizations of quantum well stacks with giant exciton oscillator strengths, tunable emission spectra and very large exciton binding energies. While these features render 2D halide perovskites a promising platform for room-temperature polaritonics, bosonic condensation and polariton lasing in 2D perovskites have so far remained elusive at ambient conditions. Here, we demonstrate room-temperature cavity exciton-polariton condensation in mechanically exfoliated crystals of the 2D Ruddlesden-Popper iodide perovskite (BA)_2(MA)_2Pb_3I_10 in an open optical microcavity. We observe a polariton condensation threshold of P_th=6.76 fJ per pulse and detect a strong non-linear response. Interferometric measurements confirm the spontaneous emergence of spatial coherence across the condensate with an associated first-order autocorrelation reaching g^(1)≈ 0.6. Our results lay the foundation for a new class of room-temperature polariton lasers based on 2D halide perovskites with great potential for hetero-integration with other van-der-Waals materials and combination with photonic crystals or waveguides.

We develop a full microscopic theory for a nonlinear phase space filling (NPSF) in strongly coupled two-dimensional polaritonic lattices. Ubiquitous in polaritonic experiments, the theoretical description of NPSF, remains limited to perturbative treatment and homogeneous samples. In this study, we go beyond the existing theoretical description and discover the broad scope of regimes where NPSF crucially modifies the optical response. Studying the quantum effects of non-bosonicity, cooperative light-matter coupling, and Coulomb blockade, we reveal several regimes for observing the nonlinear Rabi splitting quench due to the phase space filling. Unlike prior studies, we derive nonlinear Rabi frequency scaling all the way to the saturation limit and show that the presence of a lattice potential leads to qualitatively distinct nonlinearity. We concentrate on three regimes of NPSF: 1) planar; 2) fractured; and 3) ultralocalized. In planar saturation, the Rabi frequency decreases exponentially as a function of exciton density. For the fractured case, where excitons form a lattice with sites exceeding the exciton size, we discover fast NPSF at low occupation in the lattice. This is followed by slower NPSF as the medium becomes fully saturated. This behavior is particularly pronounced in the presence of Coulomb (or Rydberg) blockade, where regions of fast and slow NPSF depend on the strength of repulsion. For the ultralocalized NPSF, we observe the square-root saturation typical to the collection of two-level systems. Our findings can help describing recent observations of strong nonlinearity in heterobilayers of transition metal dichalcogenides where Moir{\'e} lattices emerge naturally [Nature \textbf{591}, 61 (2021)]. The theory also opens the prospects for engineering strongly nonlinear responses of polaritonic lattices with patterned samples, driving polaritonics into the quantum regime.

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 ∝ n 4.4 ± 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.

We theoretically investigate the nonlinearity of trion-polaritons in a two-dimensional material that arises from Coulomb interaction between quasiparticles. To evaluate the interaction constant, we solve a three-body Wannier equation precisely by expanding trion wavefunctions into a Gaussian basis. Using these wavefunctions, we calculate the trion-polariton interaction energies for the exchange processes, resolving the outstanding question of trion-trion scattering. We find that the nonlinearity is the result of the competition between different scattering channels. Such a cancellation effect is sensitive to wavefunction overlaps and depends on material parameters. Most importantly, our result shows that the nonlinear interaction between trion-polaritons is attractive, and is fivefold stronger than exciton-polariton interaction. Our work thus describes the regime where trion-polaritons offer the prospects for attractive fluids of light in monolayers of transition metal dichalcogenides.

We construct a microscopic model based on superexchange theory for a moir\'e bilayer in chromium trihalides (Cr$X_3$, $X=$Br, I). In particular, we derive analytically the interlayer Heisenberg exchange and the interlayer Dzyaloshinskii-Moriya interaction with arbitrary distances (x) between spins. Importantly, our model takes into account sliding and twisting geometries in the interlayer $X$-$X$ hopping processes. Our approach can directly access the $x$-dependent interlayer exchange without large unit-cell calculations. We argue that deducing interlayer exchange by various sliding bilayers may lead to an incomplete result in a moir\'e bilayer. Using the \textit{ab initio} tight-binding Hamiltonian, we numerically evaluate the exchange interactions in CrI$_3$. We find that our analytical model agrees with previous comprehensive density functional theory studies. Furthermore, our findings reveal the important role of the correlation effects in the $X$'s $p$ orbitals, which gives rise to a rich interlayer magnetic interaction with remarkable tunability.

We develop a theoretical description of Coulomb interactions between trions (charged excitons) that define a nonlinear optical response in doped two-dimensional semiconductors. First, we formulate a microscopic theory of trion-trion interactions based on composite nature of these particles, and account for all possible exchange processes. Next, we calculate numerically the trion binding energies and corresponding three-body wavefunctions using a basis set with high expressivity. Then, using the obtained wavefunctions we calculate the matrix elements of two-trion scattering, and compare the contributions coming from direct and exchange terms. Finally, we find that the considered scattering gives significant contribution to the optical nonlinearity in monolayers of transition metal dichalcogenides. In particular, this can lead to an attractive interaction in doped monolayers. Our theory opens a route for studying nonlinear properties of trion-polaritons inaccessible before.

We perform a $\mathbf{k \cdot p}$ theory analysis of the spectra of the lowest energy and excited states of the excitons in few-layer atomically thin films of InSe taking into account in-plane electric polarizability of the film and the influence of the encapsulation environment. For the thinner films, the lowest-energy state of the exciton is weakly indirect in momentum space, with its dispersion showing minima at a layer-number-dependent wave number, due to an inverted edge of a relatively flat topmost valence band branch of the InSe film spectrum and we compute the activation energy from the momentum dark exciton ground state into the bright state. For the films with more than seven In$_2$Se$_2$ layers, the exciton dispersion minimum shifts to $\Gamma$-point.

We investigate the influence of Landau quantization on the superconducting instability for a pure layered superconductor in the magnetic field directed perpendicular to the layers. We demonstrate that the quantization corrections to the Cooper-pairing kernel with finite Zeeman spin splitting promote the formation of the nonuniform state in which the order parameter is periodically modulated along the magnetic field, i.e., between the layers (Fulde-Ferrell-Larkin-Ovchinnikov [FFLO] state). The conventional uniform state experiences such a quantization-induced FFLO instability at low temperatures even in a common case of predominantly orbital suppression of superconductivity when the Zeeman spin splitting is expected to have a relatively weak effect. The maximum relative FFLO temperature is given by the ratio of the superconducting transition temperature and the Fermi energy. This maximum is realized when the ratio of the spin-spitting energy and the Landau-level separation is half-integer. These results imply that the FFLO states may exist not only in the Pauli-limited superconductors but also in very clean materials with small Zeeman spin-splitting energy. We expect that the described quantization-promoted FFLO instability is a general phenomenon, which may be found in materials with different electronic spectra and order-parameter symmetries.

Spontaneous rotational-symmetry breaking in the superconducting state of doped $\mathrm{Bi}_2\mathrm{Se}_3$ has attracted significant attention as an indicator for topological superconductivity. In this paper, high-resolution calorimetry of the single-crystal $\mathrm{Sr}_{0.1}\mathrm{Bi}_2\mathrm{Se}_3$ provides unequivocal evidence of a two-fold rotational symmetry in the superconducting gap by a \emph{bulk thermodynamic} probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the material's low carrier concentration proving bulk superconductivity. The large basal-plane anisotropy of $H_{c2}$ is attributed to a nematic phase of a two-component topological gap structure $\vec{\eta} = (\eta_{1}, \eta_{2})$ and caused by a symmetry-breaking energy term $\delta (|\eta_{1}|^{2} - |\eta_{2}|^{2}) T_{c}$. A quantitative analysis of our data excludes more conventional sources of this two-fold anisotropy and provides the first estimate for the symmetry-breaking strength $\delta \approx 0.1$, a value that points to an onset transition of the second order parameter component below 2K.

Sr_xBi_2Se_3 and the related compounds Cu_xBi_2Se_3 and Nb_xBi_2Se_3 have attracted considerable interest, as these materials may be realizations of unconventional topological superconductors. Superconductivity with T_c 3 K in Sr_xBi_2Se_3 arises upon intercalation of Sr into the layered topological insulator Bi_2Se_3. Here we elucidate the anisotropy of the normal and superconducting state of Sr_0.1Bi_2Se_3 with angular dependent magnetotransport and thermodynamic measurements. High resolution x-ray diffraction studies underline the high crystalline quality of the samples. We demonstrate that the normal state electronic and magnetic properties of Sr_0.1Bi_2Se_3 are isotropic in the basal plane while we observe a large two-fold in-plane anisotropy of the upper critical field in the superconducting state. Our results support the recently proposed odd-parity nematic state characterized by a nodal gap of E_u symmetry in Sr_xBi_2Se_3.