We create a large exciton-polariton condensate and employ a Michelson interferometer setup to characterize the short-and longdistance behavior of the first order spatial correlation function. Our experimental results show distinct features of both the twodimensional and nonequilibrium characters of the condensate. We find that the gaussian short-distance decay is followed by a powerlaw decay at longer distances, as expected for a two-dimensional condensate. The exponent of the power law is measured in the range 0.9-1.2, larger than is possible in equilibrium. We compare the experimental results to a theoretical model to understand the features required to observe a power law and to clarify the influence of external noise on spatial coherence in nonequilibrium phase transitions. Our results indicate that Berezinskii-KosterlitzThouless-like phase order survives in open-dissipative systems.quantum well excitons | semiconductor microcavities T he spatial correlation function quantifies the coherence properties of a system (1). In a 3D Bose-condensed gas, long range order is observed, and the correlation function decays toward a plateau at large distances (2, 3). In the homogeneous 2D Bose gas (4), however, no long range order can be established (5). Instead, Berezinskii-Kosterlitz-Thouless (BKT) theory of the equilibrium interacting gas predicts a transition to a low-temperature superfluid phase, which shows a power-law decay of the correlation function (6, 7). Unfortunately, it is frequently hard to directly measure this, and only very recently (8) was indication of the power-law decay of coherence seen in a 2D atomic gas. It has been theoretically predicted (9, 10) that power-law decay of coherence survives in the nonequilibrium problem, and it is this prediction that the current experiment sets out to test.Exciton polaritons are short-lived quasiparticles formed in a semiconductor quantum well strongly coupled to a planar microcavity (11). Each one is a superposition of a quantum well exciton and a microcavity photon, and they behave as 2D bosons below the Mott density. Above a threshold particle density, condensation is observed (12). Due to the nonequilibrium nature of polariton condensation, understanding its coherence properties is quite revealing regarding the different roles of fluctuations in the equilibrium and nonequilibrium problems.Previous measurements on polariton condensates have demonstrated coherence at large distances but were limited by large experimental uncertainties (13) or highly disordered samples (14,15), and the long-distance behavior could not be fully extracted. Recently, the correlation function at large distances was studied in 1D condensates confined in a quantum wire (16) and in a valley of the disorder potential (17). In ref. 16, the data was energy-resolved so that excited states were filtered out, while in ref. 17 a rare area on the sample was chosen in which a single mode condensate is seen. The purpose of both those experiments was to investigate how long the coherence length o...

In this letter, we present a study of the condensation of exciton-polaritons in large etched pillar structures that exhibit shallow edge trapping. The ≈ 100 µm ×100 µm pillars were fabricated using photolithography and a BCl 3 /Cl 2 reactive ion etch. A low energy region emerged along the etched edge, with the minima ≈ 7 µm from the outer edge. The depth of the trap was 0.5 − 1.5 meV relative to the level central region, with the deepest trapping at the corners. We were able to produce a Bose-Einstein condensate in the trap near the edges and corners by pumping non-resonantly in the middle of the pillar. This condensate began as a set of disconnected condensates at various points along the edges, but then became a single mono-energetic condensate as the polariton density was increased. Similar edge traps could be used to produce shallow 1D traps along edges or other more complex traps using various etch geometries and scales. In the past two decades, many experiments have used polaritons resulting from strong coupling between trapped microcavity photons and quantum well (QW) excitons. These bosonic particles have a very light mass (∼ 10 −4 m e) due to being partially photonic, but also strong particle-particle interactions from being partially excitonic. 1 This combination of a light mass and strong interactions leads to the formation of Bose-Einstein con-densates (BECs) at relatively high temperatures (∼ 10 K). 2-4 Polaritons provide a promising system for studying bosonic particles at even higher temperatures, and polariton lasing has been observed at room temperature in both GaN 5 and organic 6 systems. Many methods of confinement have been used to study polariton dynamics in a variety of geometries. Applying stress to a thin (≈ 100 µm) GaAs sample can be used to shift the exciton energy, resulting in a harmonic trap. 4,7 Pumping such a stress trap non-resonantly in the center forms a repulsive barrier and can be used to form a ring geometry. 8 Complex pumping geometries can also be used to confine polaritons, including the use of two or more pump spots in various arrangements or using a ring-shaped pump spot. 9-13 More permanent methods of confinement include producing a spacer in certain regions of the cavity during the growth process, 14-16 using sub-wavelength gratings as the top mirror, 17,18 depositing metal strips onto the top mirror, 19 and etching the sample after growth to form 1D wires, 2D pillars, and 2D arrays of coupled pillars. 20-25 While optically induced trapping potentials have the advantage of being easily reconfigured, etched trapping allows the confinement to be somewhat independent of the pump laser. Post-growth etching also produces much higher potential barriers at the etched edges than the a) Electronic mail: dmm154@pitt.edu b) J. K. Wuenschell is now at Physical Sciences Laboratory, The Aerospace Corporation, El Segundo, CA 90245, USA deposition of metal strips, and it is compatible with our existing sample materials and growth methods, unlike sub-wavelength gratings or modulating t...

We observe quasi-long-range coherence in a two-dimensional condensate of exciton-polaritons. Our measurements confirm that the spatial correlation algebraically decays with a slow power law, whose exponent quantitatively behaves as predicted by the Berezinskii-Kosterlitz-Thouless theory. The exciton-polaritons are created by nonresonant optical pumping of a microcavity sample with embedded GaAs quantum wells at liquid helium temperature. Michelson interference is used to measure the coherence of the photons emitted by decaying exciton-polaritons.

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