Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence, we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of this structure which holds massless, massive, and infinitely massive particles opens the route towards studies of the interplay of dispersion, interactions, and frustration in a novel and controlled environment.

The coupling of two macroscopic quantum states through a tunnel barrier gives rise to Josephson phenomena 1 such as Rabi oscillations 2 , the a.c. and d.c. effects 3 , or macroscopic self-trapping, depending on whether tunnelling or interactions dominate 4 . Nonlinear Josephson physics was first observed in superfluid helium 5 and atomic condensates 6,7 , but it has remained inaccessible in photonic systems because it requires large photon-photon interactions. Here we report on the observation of nonlinear Josephson oscillations of two coupled polariton condensates confined in a photonic molecule formed by two overlapping micropillars etched in a semiconductor microcavity 8 . At low densities we observe coherent oscillations of particles tunnelling between the two sites. At high densities, interactions quench the transfer of particles, inducing the macroscopic self-trapping of polaritons in one of the micropillars 9,10 . The finite lifetime results in a dynamical transition from self-trapping to oscillations with π phase. Our results open the way to the experimental study of highly nonlinear regimes in photonic systems, such as chaos 11-13 or symmetry-breaking bifurcations 14,15 .A bosonic Josephson junction is a device in which two macroscopic ensembles of bosons, each of them occupying a single quantum state, are coupled by a tunnel barrier. The system can be described by the following coupled nonlinear Schrödinger equations 1 :where ψ L,R are the bosonic wavefunctions with particle densities |ψ L,R | 2 localized to the left (L) and to the right (R) of the barrier, E 0 L,R is the single particle energy of the quantum states, U is the particle-particle interaction strength and J is the tunnel coupling constant. In the absence of interactions, equations (1a) and (1b) can be diagonalized in a basis of bonding (). An initial state prepared in a linear combination of these two (for instance, all particles in the left site) will result in density oscillations between the two sites. This is the main principle of the bosonic Josephson effect, which manifests in an ensemble of oscillatory regimes. In the absence of interactions, sinusoidal oscillations take place 4,7 with a frequencȳ Josephson physics shows the most spectacular phenomena in the nonlinear regime, when the interaction energy (U |ψ| 2 ) is greater than the coupling J . The transfer of particles from one site to the other gives rise to a dynamical renormalization of the energy in each site, resulting in anharmonic oscillations. If interactions are strong enough (U |ψ| 2 J ), the self-induced energy renormalization quenches the tunnelling, and most of the particles remain localized in one of the sites. This out of equilibrium metastable regime is called macroscopic quantum self-trapping.A number of bosonic systems have demonstrated Josephson physics. Harmonic oscillations in the linear regime have been observed in superconductor junctions 2 or in nanoscale apertures connecting superfluid helium vessels 5 . Bose-Einstein condensates of ultracold atoms in cou...

We use coupled micropillars etched out of a semiconductor microcavity to engineer a spin-orbit Hamiltonian for photons and polaritons in a microstructure. The coupling between the spin and orbital momentum arises from the polarization-dependent confinement and tunneling of photons between adjacent micropillars arranged in the form of a hexagonal photonic molecule. It results in polariton eigenstates with distinct polarization patterns, which are revealed in photoluminescence experiments in the regime of polariton condensation. Thanks to the strong polariton nonlinearities, our system provides a photonic workbench for the quantum simulation of the interplay between interactions and spin-orbit effects, particularly when extended to two-dimensional lattices.

We report on polariton condensation in photonic molecules formed by two coupled micropillars. We show that the condensation process is strongly affected by the interaction with the cloud of uncondensed excitons. Depending on the spatial position of these excitons within the molecule, condensation can be triggered on both binding and anti-binding polariton states of the molecule, on a metastable state or a total transfer of the condensate into one of the micropillars can be obtained. Our results highlight the crucial role played by relaxation kinetics in the condensation process.PACS numbers: 71.36.+c, 67.85.Hj, 78.67.Pt, 78.55.Cr Most of the experimental studies in atomic Bose condensates have explored conditions of thermodynamic equilibrium since typical condensate lifetimes are much longer than interaction times. Recent theoretical proposals have shown that out of equilibrium bosonic systems present qualitatively new behaviors [1]. One proposed way to reach this regime is the use of photonic systems with effective photon-photon interactions and dissipation provided by inherent optical losses [2]. Localized to delocalized phase transitions [3,4], highly entangled states [5], or fermionisation effects in a ring of coupled sites [6] are predicted in such systems.Microcavity polaritons are a model system for the investigation of the physics of driven-dissipative boson condensates [7][8][9][10][11][12][13]. They are the quasi-particules arising from the strong coupling between excitons confined in quantum wells and the optical mode of a microcavity. Because of their light-matter nature, polaritons present peculiar properties: they interact efficiently with their environment through their excitonic part [14,15] while their photonic part enables efficient coupling with the free space optical modes. Polariton condensates can be generated in zero dimensional micropillars [11] or in arrays of pillars with fully controlled coupling [16,17]. In this configuration, the non-equilibrium nature of polariton condensates should allow the realization of metastable collective states, such as the self-trapped states in a bosonic Josephson junction [18][19][20].In the present paper we investigate polariton condensation in photonic molecules obtained by coupling two micropillars. We demonstrate that polariton interactions strongly affect the way condensation occurs in such coupled system, not only modifying the wavefunction of the polariton condensate, but also the relaxation dynamics. This effect, specific to an out-of-equilibrium bosonic system, is illustrated by considering different positions of the non resonant excitation within the molecule. When the excitation spot is placed at the center of the molecule, polariton condensation is observed on both binding and anti-binding states. Interactions induce strong changes in the condensate wavefunction, the most important one being the change in its spatial anisotropy.When the excitation spot is positioned on one of the two coupled micropillars, condensation occurs in a very diffe...

Great suppression of fine-structure splitting (FSS) is demonstrated in self-assembled GaAs quantum dots (QDs) grown on AlGaAs(111)A surface. Due to the three-fold rotational symmetry of the growth plane, highly symmetric excitons with significantly reduced FSS are achieved. Scanning tunneling microscopy and cross-sectional transmission microscopy demonstrate a laterally symmetric dot shape with abrupt interface. Polarized photoluminescence spectra confirm excitonic transition with FSS smaller than ∼20 µeV, a substantial reduction from that of QDs grown on (100).

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Subwavelength-sized dielectric Mie resonators have recently emerged as a promising photonic platform, as they combine the advantages of dielectric microstructures and metallic nanoparticles supporting surface plasmon polaritons. Here, we report the capabilities of a dewetting-based process, independent of the sample size, to fabricate Si-based resonators over large scales starting from commercial silicon-on-insulator (SOI) substrates. Spontaneous dewetting is shown to allow the production of monocrystalline Mie-resonators that feature two resonant modes in the visible spectrum, as observed in confocal scattering spectroscopy. Homogeneous scattering responses and improved spatial ordering of the Si-based resonators are observed when dewetting is assisted by electron beam lithography. Finally, exploiting different thermal agglomeration regimes, we highlight the versatility of this technique, which, when assisted by focused ion beam nanopatterning, produces monocrystalline nanocrystals with ad hoc size, position, and organization in complex multimers.

We report polarization-resolved high spectral resolution photoluminescence measurements in self-assembled strain-free GaAs/Al0.3Ga0.7As quantum dots designed and realized in order to reduce as much as possible strain and segregation, which affected previous finestructure splitting FSS experiments. Photoluminescence from isolated quantum dots exhibits a linearly polarized FSS. FSS clearly shows a quantum size effect monotonically decreasing from 90 to 20 eV by decreasing the quantum dot size increasing emission energy . While this finding is similar to that observed in strained In Ga As/GaAs quantum dots, clearly it requires a different explanation, being our quantum dots not affected by strain-induced piezoelectricity. We ascribed the observed FSS to a size dependent reduction in dot shape anisotropy as evidenced by structural data analysis. Moreover the linear polarization in dots with shape close to cylindrical symmetry is not along the 110 crystallographic axis but it turns out randomly distributed, highlighting the role of extrinsic effects.