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Exciton-polariton laser is a promising source of coherent light for low-energy applications due to its low-threshold operation. However, a detailed experimental study of its spectral purity, which directly affects its coherence properties is still missing. Here}, we present a high-resolution spectroscopic investigation of the energy and linewidth of an exciton-polariton laser in the single-mode regime, which derives its coherent emission from an optically pumped and confined exciton-polariton condensate. We report an ultra-narrow linewidth of 56~MHz or 0.24~$\mu$eV, corresponding to a coherence time of 5.7~ns. The narrow linewidth is consistently achieved by using an exciton-polariton condensate with a high photonic content confined in an optically induced trap. Contrary to previous studies, we show that the excitonic reservoir created by the pump and responsible for creating the trap does not strongly affect the emission linewidth as long as the condensate is trapped and the pump power is well above the condensation (lasing) threshold. \red{The long coherence time of the exciton-polariton system uncovered here opens up opportunities for manipulating its macroscopic quantum state, which is essential for applications in classical and quantum computing.

According to the principles of quantum mechanics the Hamiltonian describing a closed system's energies must be Hermitian. This leads to an avoided crossing on resonance, as coupling between states causes the energy levels to repel. This concept lies at the heart of exciton-polariton physics, where coherent exciton-photon interaction causes polariton branches to repel in momentum dispersion. However, non-Hermitian physics predicts an opposite effect: level attraction, which occurs when significant energy dissipation is present in the system. Here, we show a manifestation of dissipative coupling in a high-quality AlGaAs-based polariton microcavity, where two polariton branches attract, resulting in an anomalous, inverted dispersion of the lower branch in momentum dispersion. We observe the evolution of the level attraction with exciton-photon detuning, leading to changes in anomalous dispersion shape within a single sample. The dissipative coupling is explained by the interaction with an indirect exciton, acting as a highly dissipative channel in our system, and the observed dispersions are well captured within a phenomenological model. Our results present a new mechanism of dissipative coupling in light-matter systems and offer a tunable and well-controlled AlGaAs-based platform for engineering the non-Hermitian and negative mass effects in polariton systems.

We present an experimental study on optical properties and dynamics of direct and spatially and momentum indirect excitons in AlGaAs/AlAs quantum wells near the crossover between $\varGamma$- and $X$-valley confined electron states. The time-integrated photoluminescence experiment at $T=$4.8 K revealed three simultaneously observed optical transitions resulting from (a) a direct exciton recombination, involving an electron and a hole states both located in the $\varGamma$-valley in the quantum well layer, and (b) two spatially and momentum indirect excitons, comprising of the confined electron states in the $X$-valley in the AlAs barrier with different effective masses and quantum well holes in the $\varGamma$-valley. The measured spatial extent, density dependence and temperature dependence of the structure photoluminescence revealed characteristics necessary to pinpoint the states' nature and provided their characterization crucial in future device design. Temporal dynamics observed in the time-resolved photoluminescence measurement showed the complexity of the capture and recombination dynamics, largely affected by nonradiative processes, what is additionally critical in the system's use. This solid state platform hosting both direct and indirect excitons in a highly tunable monolithic system can benefit and underline the operation principles of novel electronic and photonic devices.

Many bosons can occupy a single quantum state without a limit. This state is described by quantum-mechanical Bose-Einstein statistics, which allows the formation of a Bose-Einstein condensate at low temperatures and high particle densities. Photons, historically the first considered bosonic gas, were late to show this phenomenon, which was observed in rhodamine-filled microlaser cavities and doped fiber cavities. These more recent findings have raised the natural question as to whether condensation is common in laser systems, with potential technological applications. Here, we show the Bose-Einstein condensation of photons in a broad-area vertical-cavity surface-emitting laser with positive cavity mode-gain peak energy detuning. We observed a Bose-Einstein condensate in the fundamental transversal optical mode at the critical phase-space density. The experimental results follow the equation of state for a two-dimensional gas of bosons in thermal equilibrium, although the extracted spectral temperatures were lower than those of the device. This is interpreted as originating from the driven-dissipative nature of the device and the stimulated cooling effect. In contrast, non-equilibrium lasing action is observed in the higher-order modes in a negatively detuned device. Our work opens the way for the potential exploration of superfluid physics of interacting photons mediated by semiconductor optical non-linearities. It also shows great promise for enabling single-mode high-power emission from a large aperture device., Comment: 9 pages, 4 figures

Optical trapping has been proven to be an effective method of separating exciton-polariton condensates from the incoherent high-energy excitonic reservoir located at the pumping laser position. This technique has significantly improved the coherent properties of exciton-polariton condensates, when compared to a quasi-homogeneous spot excitation scheme. Here, we compare two experimental methods on a sample, where a single spot excitation experiment allowed only to observe photonic lasing in the weak coupling regime. In contrast, the ring-shaped excitation resulted in the two-threshold behavior, where an exciton-polariton condensate manifests itself at the first and photon lasing at the second threshold. Both lasing regimes are trapped in an optical potential created by the pump. We interpret the origin of this confining potential in terms of repulsive interactions of polaritons with the reservoir at the first threshold and as a result of the excessive free-carrier induced refractive index change of the microcavity at the second threshold. This observation offers a way to achieve multiple phases of photonic condensates in samples, e.g., containing novel materials as an active layer, where two-threshold behavior is impossible to achieve with a single excitation spot., Comment: 19 pages, 5 figures

The classic Bogoliubov theory of weakly interacting Bose gases rests upon the assumption that nearly all the bosons condense into the lowest quantum state at sufficiently low temperatures. Here we develop a generalized version of Bogoliubov theory for the case of a driven-dissipative exciton-polariton condensate with a large incoherent uncondensed component, or excitonic reservoir. We argue that such a reservoir can consist of both excitonic high-momentum polaritons and optically dark superpositions of excitons across different optically active layers, such as multiple quantum wells in a microcavity. In particular, we predict interconversion between the dark and bright (light-coupled) excitonic states that can lead to a dynamical equilibrium between the condensate and reservoir populations. We show that the presence of the reservoir fundamentally modifies both the energy and the amplitudes of the Bogoliubov quasiparticle excitations due to the non-Galilean-invariant nature of polaritons. Our theoretical findings are supported by our experiment, where we directly detect the Bogoliubov excitation branches of an optically trapped polariton condensate in the high-density regime. By analyzing the measured occupations of the excitation branches, we extract the Bogoliubov amplitudes across a range of momenta and show that they agree with our generalized theory., Comment: 16 pages, 7 figures

The integration of two-dimensional transition metal dichalcogenide crystals (TMDCs) into a dielectric environment is critical for optoelectronic and photonic device applications. Here, we investigate the effects of direct deposition of different dielectric materials (Al$_2$O$_3$, SiO$_2$, SiN$_x$) onto atomically thin (monolayer) TMDC WS$_2$ on its optical response. Atomic layer deposition (ALD), electron beam evaporation (EBE), plasma enhanced chemical vapour deposition (PECVD), and magnetron sputtering methods of material deposition are investigated. The photoluminescence (PL) measurements reveal quenching of the excitonic emission after all deposition processes. The reduction in neutral exciton PL is linked to the increased level of charge doping and associated rise of the trion emission, and/or the localized (bound) exciton emission. Furthermore, Raman spectroscopy allows us to clearly correlate the observed changes of excitonic emission with the increased levels of lattice disorder and defects. Overall, the EBE process results in the lowest level of doping and defect densities and preserves the spectral weight of the exciton emission in the PL, as well as the exciton oscillator strength. Encapsulation with ALD appears to cause chemical changes, which makes it distinct from all other techniques. Sputtering is revealed as the most aggressive deposition method for WS$_2$, fully quenching its optical response. Our results demonstrate and quantify the effects of direct deposition of dielectric materials onto monolayer WS$_2$, which can provide a valuable guidance for the efforts to integrate monolayer TMDCs into functional optoelectronic devices.

Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterised by topological invariants. In energy-conserving (Hermitian) systems, these invariants are determined by the winding of eigenstates in momentum space. In non-Hermitian systems, a novel topological invariant is predicted to emerge from the winding of the complex eigenenergies. Here, we directly measure the non-Hermitian topological invariant arising from exceptional points in the momentum-resolved spectrum of exciton polaritons. These are hybrid light-matter quasiparticles formed by photons strongly coupled to electron-hole pairs (excitons) in a halide perovskite semiconductor at room temperature. We experimentally map out both the real (energy) and imaginary (linewidth) parts of the spectrum near the exceptional points and extract the novel topological invariant - fractional spectral winding. Our work represents an essential step towards realisation of non-Hermitian topological phases in a condensed matter system.

Monolayer transition metal dichalcogenides are a promising platform to investigate many-body interactions of excitonic complexes. In monolayer tungsten diselenide, the ground-state exciton is dark (spin-indirect), and the valley degeneracy allows low-energy dark momentum-indirect excitons to form. Interactions between the dark exciton species and the optically accessible bright exciton (X) are likely to play significant roles in determining the optical properties of X at high power, as well as limiting the ultimate exciton densities that can be achieved, yet so far little is known about these interactions. Here, we demonstrate long-lived dense populations of momentum-indirect intervalley ($X_K$) and spin-indirect intravalley (D) dark excitons by time-resolved photoluminescence measurements (Tr-PL). Our results uncover an efficient inter-state conversion between X to D excitons through the spin-flip process and the one between D and $X_K$ excitons mediated by the exchange interaction (D + D to $X_K$ + $X_K$). Moreover, we observe a persistent redshift of the X exciton due to strong excitonic screening by $X_K$ exciton with a response time in the timescale of sub-ns, revealing a non-trivial inter-state exciton-exciton interaction. Our results provide a new insight into the interaction between bright and dark excitons, and point to a possibility to employ dark excitons for investigating exciton condensation and the valleytronics.

Atomically thin transition metal dichalcogenide crystals (TMDCs) have extraordinary optical properties that make them attractive for future optoelectronic applications. Integration of TMDCs into practical all-dielectric heterostructures hinges on the ability to passivate and protect them against necessary fabrication steps on large scales. Despite its limited scalability, encapsulation of TMDCs in hexagonal boron nitride (hBN) currently has no viable alternative for achieving high performance of the final device. Here, we show that the novel, ultrathin Ga$_2$O$_3$ glass is an ideal centimeter-scale coating material that enhances optical performance of the monolayers and protects them against further material deposition. In particular, Ga$_2$O$_3$ capping of commercial grade WS$_2$ monolayers outperforms hBN in both scalability and optical performance at room temperature. These properties make Ga$_2$O$_3$ highly suitable for large scale passivation and protection of monolayer TMDCs in functional heterostructures.

The property of superfluidity, first discovered in liquid 4He, is closely related to Bose-Einstein condensation (BEC) of interacting bosons. However, even at zero temperature, when one would expect the whole bosonic quantum liquid to become condensed, a fraction of it is excited into higher momentum states via interparticle interactions and quantum fluctuations -- the phenomenon of quantum depletion. Quantum depletion of weakly interacting atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This is even more challenging in driven-dissipative systems such as exciton-polariton condensates(photons coupled to electron-hole pairs in a semiconductor), since their nonequilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of an optically trapped high-density exciton-polariton condensate by directly detecting the spectral branch of elementary excitations populated by this process. Analysis of the population of this branch in momentum space shows that quantum depletion of an exciton-polariton condensate can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the fraction of matter (exciton) in an exciton-polariton. Our results reveal the effects of exciton-polariton interactions beyond the mean-field description and call for a deeper understanding of the relationship between equilibrium and nonequilibrium BECs., Comment: 18 pages, 5 figures, with supplementary information

We demonstrate an experimental approach to create dissipative solitons in a microcavity laser. In particular, we shape the spatial gain profile of a quasi-one-dimensional microcavity laser with a nonresonant, pulsed optical pump to create spatially localised structures, called gain-pinned dissipative solitons that exist due to the balance of gain and nonlinear losses and are confined to a diffraction-limited volume. The ultrafast formation dynamics and decay of the gain-pinned solitons are probed directly, showing that they are created on a picosecond timescale, orders of magnitude faster than laser cavity solitons. All of the experimentally observed features and dynamics are reconstructed by using a standard complex Ginzburg-Landau model., Comment: 10 pages, 3 figures

We provide an analytical and numerical description of relaxation oscillations in the nonresonantly pumped polariton condensate. The presented considerations are based on the open dissipative Gross-Pitaevskii equation coupled to a pair of rate equations. The evolution of the condensate density can be explained qualitatively by studying the topology of the trajectory in phase space. We use a fixed points analysis for the classification of the different regimes of condensate dynamics, including fast stabilization, slow oscillations and ultrashort pulse emission. We obtain an analytical condition for the occurrence of relaxation oscillations. Continuous and pulsed condensate excitation considered and we demonstrate that in the latter case the existence of the second reservoir is necessary for the emergence of oscillations. We show that relaxation oscillations should be expected to occur in systems with relatively short polariton lifetime.

We study theoretically the emission of dark solitons induced by a moving defect in a nonresonantly pumped exciton-polariton condensate. The number of created dark solitons per unit of time is found to be strongly dependent on the pump power. We relate the observed dynamics of this process to the oscillations of the drag force experienced by the condensate. We investigate the stability of the polariton quantum fluid and present various types of dynamics depending on the condensate and moving obstacle parameters. Furthermore, we provide analytical expressions for dark soliton dynamics using the variational method adapted to the non-equilibrium polariton system. The determined dynamical equations are found to be in excellent agreement with the results of numerical simulations.

Semiconductor microcavities are often influenced by structural imperfections, which can disturb the flow and dynamics of exciton-polariton condensates. Additionally, in exciton-polariton condensates there is a variety of dynamical scenarios and instabilities, owing to the properties of the incoherent excitonic reservoir. We investigate the dynamics of an exciton-polariton condensate which emerges in semiconductor microcavity subject to disorder, which determines its spatial and temporal behaviour. Our experimental data revealed complex burst-like time evolution under non-resonant optical pulsed excitation. The temporal patterns of the condensate emission result from the intrinsic disorder and are driven by properties of the excitonic reservoir, which decay in time much slower with respect to the polariton condensate lifetime. This feature entails a relaxation oscillation in polariton condensate formation, resulting in ultrafast emission pulses of coherent polariton field. The experimental data can be well reproduced by numerical simulations, where the condensate is coupled to the excitonic reservoir described by a set of rate equations. Theory suggests the existence of slow reservoir temporarily emptied by stimulated scattering to the condensate, generating ultrashort pulses of the condensate emission., Comment: 14 pages, 4 figures

An expanding polariton condensate is investigated under pulsed nonresonant excitation with a small laser pump spot. Far above the condensation threshold we observe a pronounced increase in the dispersion curvature with a subsequent linearization of the spectrum and strong luminescence from a ghost branch orthogonally polarized with respect to the linearly polarized condensate emission. The presence of the ghost branch has been confirmed in time-resolved measurements. The dissipative and nonequilibrium effects in the photoluminescence of polariton condensates and their excitations are discussed., Comment: 13 pages, 4 figures