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.
Polaritons are quasiparticles arising from the strong coupling of electromagnetic waves in cavities and dipolar oscillations in a material medium. In this framework, localized surface plasmon in metallic nanoparticles defining optical nanocavities have attracted increasing interests in the last decade. This interest results from their subdiffraction mode volume, which offers access to extremely high photonic densities by exploiting strong scattering cross-sections. However, high absorption losses in metals have hindered the observation of collective coherent phenomena, such as condensation. arXiv:1709.04803v2 [cond-mat.mtrl-sci]
We report a record-size polariton condensate of a fraction of a millimeter. This macroscopically occupied state of macrosopic size is not constrained to the excitation spot and is free from the usual complications brought by high-energy reservoir excitons, which strongly alter the physics of polaritons, including their mobility, energy distribution and particle interactions. The density of this trap-free condensate is lower than 1 polariton/µm 2 , reducing the phase noise induced by the interaction energy. Experimental findings are backed up by numerical simulations using a hydrodynamic model which takes into account both the polariton expansion and the phonon-assisted relaxation towards the lowest energy state. These results propel polariton condensates at the fundamental level set by their cold-atomic counterparts by getting rid of several solid-state difficulties, while still retaining their unique driven/dissipative features.PACS numbers: 71.36.+c, 63.20.Ls, 67.25.dg, 42.50.Ct Under suitable conditions, light-matter interaction can be strong enough to drive the coherent exchange of energy between photonic and electronic modes [1]. This is the paradigm of microcavity exciton-polaritons: quasiparticles created by the strong coupling between the photonic mode of a microcavity and the excitonic transition of semiconductor quantum wells [2]. Polaritons manifest their composite nature with a combination of photonic and excitonic properties [3]. Thanks to their photonic component, polaritons can ballistically propagate in the plane of the microcavity with velocities up to a few percent of the speed of light [4]. On the other hand, the exciton component results in strong optical nonlinearities and induces an energy renormalization of the polariton dispersion at high densities [5]. This energy shift can be much larger than the linewidth and is at the foundation of most polaritonic effects and applications [6][7][8]. As bosonic quasiparticles, polaritons experiment final-state stimulated scattering, which results, above a density threshold, in a laser-like emission without population inversion, a collective phenomenon that is explained in the framework of Bose-Einstein condensation [9][10][11]. A unique feature of polariton condensates is their driven/dissipative nature, in which the steady state is reached through a dynamical balance of pumping and dissipation.Polariton condensate have been experimentally observed in different materials, both inorganic [12][13][14][15] and organic semiconductors [16,17], and thanks to their light mass, condensation is achieved also at room temperature [18]. However, differently from their atomic counterpart, these condensates suffer from dephasing and density fluctuations induced by the interactions with the exciton reservoir, effectively resulting in multimode condensates [19][20][21]. The exciton reservoir also acts as a trapping mechanism, if the polariton lifetime is too short, confining the condensation process within the region of the excitation spot [22][23][24][25]. Moreov...
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