We study the condensation of exciton-polaritons in a two-dimensional Lieb lattice of micropillars. We show selective polariton condensation into the flatbands formed by S and Px,y orbital modes of the micropillars under non-resonant laser excitation. The real space mode patterns of these condensates are accurately reproduced by the calculation of related Bloch modes of S-and Pflatbands. Our work emphasizes the potential of exciton-polariton lattices to emulate Hamiltonians of advanced potential landscapes. Furthermore, the obtained results provide a deeper inside into the physics of flatbands known mostly within the tight-binding limit.Dispersionless energy bands or flatbands (FBs) appear in a large variety of condensed matter systems and are linked to a wide range of topological many-body phenomena such as graphene edge modes [1], the fractional quantum Hall effect [2][3][4][5] and flat band ferromagnetism [6][7][8].There is a variety of two-dimensional lattices that support flat energy bands [9][10][11], with the so-called Lieb lattice being on of the most straightforward examples [12]. Lieb lattices have been studied extensively in recent years and flatband states have been observed in photonic [13][14][15] as well as cold atom systems [16]. Creating artificial lattices in order to emulate and simulate complex many-body systems with additional degrees of freedom has attracted considerable scientific interest [17][18][19]. Exciton-polariton gases in periodic lattice potential landscapes have emerged as a very promising solid state system to emulate many-body physics [20,21]. Polaritons are eigenstates resulting of strong coupling between a quantum well exciton and a photonic cavity mode. The excitonic fraction provides a strong nonlinearity while the photonic part results in a low effective mass, allowing the formation of driven-dissipative BoseEinstein condensation [22,23]. These so-called quantum fluids of light [24] can be placed in an artificial lattice potential landscape using a variety of well developed semiconductor etching techniques [9,25,26], thin metal films [27], surface acoustic waves [28], or optically imprinted lattices [29,30]. In this work we investigate the polariton photoluminescence (PL) emission in a two-dimensional Lieb lattice ( Fig. 1(a)). Due to destructive interference of next neighbor tunneling J, flatbands form. Fig. 1(b) shows a tightbinding calculation of the first Brillouin zone (BZ) band structure, with the flatband dispersion highlighted in red. High symmetry points of the BZ are found in the inset.The two-dimensional polaritonic Lieb lattice was fabricated using an electron beam lithography process * sebastian.klembt@physik.uni-wuerzburg.de and a consecutive reactive ion etching step on an AlAs λ/2-cavity with three stacks of four 13 nm wide GaAs quantum wells (QWs) placed in the antinode of the electric field, with a 32.5 (36) fold AlAs/Al 0.20 Ga 0.80 As top (bottom) distributed Bragg reflector (DBR) (Fig. 1(c,d)). The Rabi splitting of the sample is 9.5 meV. Only the top D...

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Two-dimensional electronic materials such as graphene and transition metal dichalgenides feature unique electrical and optical properties due to the conspirative effect of band structure, orbital coupling, and crystal symmetry. Synthetic matter, as accomplished by artificial lattice arrangements of cold atoms, molecules, electron patterning, and optical cavities, has emerged to provide manifold intriguing frameworks to likewise realize such scenarios. Exciton-polaritons have recently been added to the list of promising candidates for the emulation of system Hamiltonians on a semiconductor platform, offering versatile tools to engineer the potential landscape and to access the non-linear electro-optical regime. In this work, we introduce an electronically driven square and honeycomb lattice of exciton-polaritons, paving the way towards real world devices based on polariton lattices for on-chip applications. Our platform exhibits laser-like emission from high-symmetry points under direct current injection, hinting at the prospect of electrically driven polariton lasers with possibly topologically non-trivial properties.

We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.

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