Macroscopic Two-Dimensional Polariton Condensates

Ultrafast exciton fluid flow in an atomically thin MoS2 semiconductor

Excitons (coupled electron-hole pairs) in semiconductors can form collective states that sometimes exhibit spectacular nonlinear properties. Here, we show experimental evidence of a collective state of short-lived excitons in a direct-bandgap, atomically thin MoS2 semiconductor whose propagation resembles that of a classical liquid as suggested by the nearly uniform photoluminescence through the MoS2 monolayer regardless of crystallographic defects and geometric constraints. The exciton fluid flows over ultralong distances (at least 60 μm) at a speed of ~1.8 × 107 m s-1 (~6% the speed of light). The collective phase emerges above a critical laser power, in the absence of free charges and below a critical temperature (usually Tc ≈ 150 K) approaching room temperature in hexagonal-boron-nitride-encapsulated devices. Our theoretical simulations suggest that momentum is conserved and local equilibrium is achieved among excitons; both these features are compatible with a fluid dynamics description of the exciton transport.

Observation of Zitterbewegung in photonic microcavities

We present and experimentally study the effects of the photonic spin-orbit coupling on the real space propagation of polariton wavepackets in planar semiconductor microcavities and polaritonic analogues of graphene. In particular, we demonstrate the appearance of an analogue Zitterbewegung effect, a term which translates as 'trembling motion' in English, which was originally proposed for relativistic Dirac electrons and consisted of the oscillations of the centre of mass of a wavepacket in the direction perpendicular to its propagation. For a planar microcavity, we observe regular Zitterbewegung oscillations whose amplitude and period depend on the wavevector of the polaritons. We then extend these results to a honeycomb lattice of coupled microcavity resonators. Compared to the planar cavity, such lattices are inherently more tuneable and versatile, allowing simulation of the Hamiltonians of a wide range of important physical systems. We observe an oscillation pattern related to the presence of the spin-split Dirac cones in the dispersion. In both cases, the experimentally observed oscillations are in good agreement with theoretical modelling and independently measured bandstructure parameters, providing strong evidence for the observation of Zitterbewegung.

Modified Bose-Einstein condensation in an optical quantum gas

Open quantum systems can be systematically controlled by making changes to their environment. A well-known example is the spontaneous radiative decay of an electronically excited emitter, such as an atom or a molecule, which is significantly influenced by the feedback from the emitter's environment, for example, by the presence of reflecting surfaces. A prerequisite for a deliberate control of an open quantum system is to reveal the physical mechanisms that determine its state. Here, we investigate the Bose-Einstein condensation of a photonic Bose gas in an environment with controlled dissipation and feedback. Our measurements offer a highly systematic picture of Bose-Einstein condensation under non-equilibrium conditions. We show that by adjusting their frequency Bose-Einstein condensates naturally try to avoid particle loss and destructive interference in their environment. In this way our experiments reveal physical mechanisms involved in the formation of a Bose-Einstein condensate, which typically remain hidden when the system is close to thermal equilibrium.

Measurement of the quantum geometric tensor and of the anomalous Hall drift

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor¹-comprising the Berry curvature² (crucial for topological matter)³ and the quantum metric⁴, which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands⁵, orbital magnetic susceptibility^6,7, the exciton Lamb shift⁸ and the non-adiabatic anomalous Hall effect^6,9. However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium-a high-finesse planar microcavity¹⁰-together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton-photon modes (exciton polaritons) that are subject to photonic spin-orbit coupling¹¹ from which Dirac cones emerge¹², and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics^13-15. These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands^9,16. The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems.

Observation of quantum depletion in a non-equilibrium exciton-polariton condensate

Superfluidity, first discovered in liquid ⁴He, is closely related to Bose–Einstein condensation (BEC) phenomenon. However, even at zero temperature, a fraction of the quantum liquid is excited out of the condensate into higher momentum states via interaction-induced fluctuations—the phenomenon of quantum depletion. Quantum depletion of atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This measurement is even more challenging in driven-dissipative exciton–polariton condensates, since their non-equilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of a high-density exciton–polariton condensate by detecting the spectral branch of elementary excitations populated by this process. Analysis of this excitation branch shows that quantum depletion of exciton–polariton condensates can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the exciton fraction in an exciton polariton. Our results reveal beyond mean-field effects of exciton–polariton interactions and call for a deeper understanding of the relationship between equilibrium and non-equilibrium BECs.

Many aspects of polariton condensate behaviour can be captured by mean-field theories but interactions introduce additional quantum effects. Here the authors observe quantum depletion in a driven-dissipative condensate and find that deviations from equilibrium predictions depend on the excitonic fraction.

Directional Goldstone waves in polariton condensates close to equilibrium

Quantum fluids of light are realized in semiconductor microcavities using exciton-polaritons, solid-state quasi-particles with a light mass and sizeable interactions. Here, we use the microscopic analogue of oceanographic techniques to measure the excitation spectrum of a thermalised polariton condensate. Increasing the fluid density, we demonstrate the transition from a free-particle parabolic dispersion to a linear, sound-like Goldstone mode characteristic of superfluids at equilibrium. Notably, we reveal the effect of an asymmetric pumping by showing that collective excitations are created with a definite direction with respect to the condensate. Furthermore, we measure the critical sound speed for polariton superfluids close to equilibrium.

Polariton polarization rectifier

We propose a novel photonic device, the polariton polarization rectifier, intended to transform polariton pulses with arbitrary polarization into linearly polarized pulses with controllable orientation of the polarization plane. It is based on the interplay between the orbital motion of the polariton wave packet and the dynamics of the polariton pseudospin governed by the spatially dependent effective magnetic field. The latter is controlled by the TE-TM splitting in a harmonic trap. We show that the unpolarized polariton pulse acquires linear polarization in the course of propagation in a harmonic trap. This gives the considered structure an extra function as a linear polarizer of polariton pulses.

Self-Trapping of Exciton-Polariton Condensates in GaAs Microcavities

The self-trapping of exciton-polariton condensates is demonstrated and explained by the formation of a new polaronlike state. Above the polariton lasing threshold, local variation of the lattice temperature provides the mechanism for an attractive interaction between polaritons. Because of this attraction, the condensate collapses into a small bright spot. Its position and momentum variances approach the Heisenberg quantum limit. The self-trapping does not require either a resonant driving force or a presence of defects. The trapped state is stabilized by the phonon-assisted stimulated scattering of excitons into the polariton condensate. While the formation mechanism of the observed self-trapped state is similar to the Landau-Pekar polaron model, this state is populated by several thousands of quasiparticles, in a striking contrast to the conventional single-particle polaron state.

Spatiotemporal Evolution of Coherent Polariton Modes in ZnO Microwire Cavities at Room Temperature

Tunable waveguides for propagating coherent quantum states are demanded for future applications in quantum information technology and optical data processing. We present coherent whispering gallery mode polariton states in ZnO-based hexagonal microwires at room temperature. We observed their propagation over the field of view of about 20 μm by picosecond time-resolved real space imaging using a streak camera. Spatial coherence was proven by time integrated Michelson interferometry superimposing the inverted spatial emission pattern with its original one. We furthermore show that the real and momentum space evolution of the coherent states can not only be described by the commonly used model developed for ballistically propagating Bose-Einstein condensates based on the Gross-Pitaevskii equation but equivalently by classical ray optics considering a spatially varying particle density dependent refractive index of the cavity material, not yet considered in literature so far. By changing the excitation spot size, the refractive index gradient and thus the propagation velocity is changed.

Generation of Quantized Polaritons below the Condensation Threshold

Exciton polaritons in high quality semiconductor microcavities can travel long macroscopic distances (>100  μm) due to their ultralight effective mass. The polaritons are repelled from optically pumped exciton reservoirs where they are formed; however, their spatial dynamics is not as expected for pointlike particles. Instead we show polaritons emitted into waveguides travel orthogonally to the repulsive potential gradient and can only be explained if they are emitted as macroscopic delocalized quantum particles, even before they form Bose condensates.

Single-shot condensation of exciton polaritons and the hole burning effect

A bosonic condensate of exciton polaritons in a semiconductor microcavity is a macroscopic quantum state subject to pumping and decay. The fundamental nature of this driven-dissipative condensate is still under debate. Here, we gain an insight into spontaneous condensation by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in a single-shot optical excitation regime, without averaging over multiple condensate realisations. We demonstrate that condensation is strongly influenced by an incoherent reservoir and that the reservoir depletion, the so-called spatial hole burning, is critical for the transition to the ground state. Condensates of photon-like polaritons exhibit strong shot-to-shot fluctuations and density filamentation due to the effective self-focusing associated with the reservoir depletion. In contrast, condensates of exciton-like polaritons display smoother spatial density distributions and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study fundamental properties of non-equilibrium condensation in the presence of a reservoir.

Negative-Mass Effects in Spin-Orbit Coupled Bose-Einstein Condensates

Negative effective masses can be realized by engineering the dispersion relation of a variety of quantum systems. A recent experiment with spin-orbit coupled Bose-Einstein condensates has shown that a negative effective mass can halt the free expansion of the condensate and lead to fringes in the density [M. A. Khamehchi et al., Phys. Rev. Lett. 118, 155301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.155301]. Here, we show that the underlying cause of these observations is the self-interference of the wave packet that arises when only one of the two effective mass parameters that characterize the dispersion of the system is negative. We show that spin-orbit coupled Bose-Einstein condensates may access regimes where both mass parameters controlling the propagation and diffusion of the condensate are negative, which leads to the novel phenomenon of counterpropagating self-interfering packets.

Topological order and thermal equilibrium in polariton condensates

The Berezinskii-Kosterlitz-Thouless phase transition from a disordered to a quasi-ordered state, mediated by the proliferation of topological defects in two dimensions, governs seemingly remote physical systems ranging from liquid helium, ultracold atoms and superconducting thin films to ensembles of spins. Here we observe such a transition in a short-lived gas of exciton-polaritons, bosonic light-matter particles in semiconductor microcavities. The observed quasi-ordered phase, characteristic for an equilibrium two-dimensional bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. This is made possible thanks to long polariton lifetimes in high-quality samples and in a reservoir-free region. Our results show that the joint measurement of coherence both in space and time is required to characterize driven-dissipative phase transitions and enable the investigation of topological ordering in open systems.

Relaxation Oscillations and Ultrafast Emission Pulses in a Disordered Expanding Polariton Condensate

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.