Topological insulators are a striking example of materials in which topological invariants are manifested in robustness against perturbations [1,2]. Their most prominent feature is the emergence of topological edge states with reduced dimension at the boundary between areas with distinct topological invariants. The observable physical effect is unidirectional robust transport, unaffected by defects or disorder. Topological insulators were originally observed in the integer quantum Hall effect [3], and subsequently suggested [4-6] and observed [7] even in the absence of magnetic field. These were fermionic systems of correlated electrons. However, during the past decade the concepts of topological physics have been introduced into numerous fields beyond condensed matter, ranging from microwaves [8,9] and photonic systems [10-12] to cold atoms [13,14], acoustics [15,16] and even mechanics [17,18]. Recently, topological insulators were proposed [19-21] in exciton-polariton systems organized as honeycomb (graphene-like) lattices, under the influence of a magnetic field. Topological phenomena in polaritons are fundamentally different from all topological effects demonstrated experimentally thus far: exciton-polaritons are part-light part-matter quasiparticles emerging from the strong coupling of quantum well excitons and cavity photons [22]. Here, we demonstrate experimentally the first exciton-polariton topological insulator. This constitutes the first symbiotic light-matter topological insulators. Our polariton lattice is excited non-resonantly, and the chiral topological polariton edge mode is populated by a polariton condensation mechanism. We use scanning imaging techniques in real-space and in Fourier-space to measure photoluminescence, and demonstrate that the topological edge mode avoids defects, and that the propagation direction of the mode can be reversed by inverting the applied magnetic field. Our exciton-polariton topological insulator paves the way for a variety of new topological phenomena, as they involve light-matter interaction, gain, and perhaps most importantly -exciton-polaritons interact with one another as a nonlinear many-body system.Microcavity exciton-polaritons (polaritons) are composite bosons originating from the strong coupling of quantum well excitons to microcavity photons. While the excitonic fraction provides a strong non-linearity, the photonic part results in a low effective mass, allowing the formation of a driven-dissipative Bose-Einstein condensate [23,24] and a superfluid phase [25], making polaritons being referred to as "quantum fluids of light" [26]. For the epitaxially well-controlled III-V semiconductor material system, a variety of techniques are available to micropattern such cavities in order to precisely engineer the potential landscapes of polaritons [27]. With the recent advances of bringing topological effects to the realms of photonics [8][9][10][11][12]28], several avenues to realize topological edge propagation with polaritons have been suggested [19][20][21], wi...

The lower branch of the dispersion relation of exciton polaritons in semiconductor microcavities, operating in the strong-coupling regime, contains sections of both positive and negative curvature along one spatial direction. We show that this leads to the existence of stable one-dimensional bright microcavity solitons supported by the repulsive polariton nonlinearity. To achieve localization along the second transverse direction we propose to create a special soliton waveguide by changing the cavity detuning and hence the boundary of the soliton existence in such a way that the solitons are allowed only within the stripe of the desired width.

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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...

Interacting Bosons in artificial lattices have emerged as a modern platform to explore collective manybody phenomena and exotic phases of matter as well as to enable advanced on-chip simulators. On chip, exciton–polaritons emerged as a promising system to implement and study bosonic non-linear systems in lattices, demanding cryogenic temperatures. We discuss an experiment conducted on a polaritonic lattice at ambient conditions: We utilize fluorescent proteins providing ultra-stable Frenkel excitons. Their soft nature allows for mechanically shaping them in the photonic lattice. We demonstrate controlled loading of the coherent condensate in distinct orbital lattice modes of different symmetries. Finally, we explore the self-localization of the condensate in a gap-state, driven by the interplay of effective interaction and negative effective mass in our lattice. We believe that this work establishes organic polaritons as a serious contender to the well-established GaAs platform for a wide range of applications relying on coherent Bosons in lattices.

We study, theoretically and numerically, the onset and development of modulational instability in an incoherently pumped spatially homogeneous polariton condensate. Within the framework of mean-field theory, we identify regimes of modulational instability in two cases: 1) Strong feedback between the condensate and reservoir, which may occur in scalar condensates, and 2) Parametric scattering in the presence of polarization splitting in spinor condensates. In both cases we investigate the instability induced textures in space and time including non-equilibrium dynamics of phase dislocations and vortices. In particular we discuss the mechanism of vortex destabilization and formation of spiraling waves. We also identify the presence of topological defects, which take the form of half-vortex pairs in the spinor case, giving an "eyelet" structure in intensity and dipole type structure in the spin polarization. In the modulationally stable parameter domains, we observe formation of the phase defects in the process of condensate formation from an initially spatially incoherent low-density state. In analogy to the Kibble-Zurek type scaling for nonequilibrium phase transitions, we find that the defect density scales with the pumping rate.

We report the existence of dark polariton solitons and study their stability and symmetry breaking in semiconductor microcavities operating in the strong-coupling regime. These half-light half-matter solitons are potential candidates for applications in all-optical signal processing. Their excitation time and required pump powers are a few orders of magnitude less than those of their weakly coupled light-only counterparts.

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