Excitons, bound pairs of electrons and holes, form a model system to explore the quantum physics of cold bosons in solids. Cold exciton gases can be realized in a system of indirect excitons, which can cool down below the temperature of quantum degeneracy due to their long lifetimes. Here, we report on the measurement of spontaneous coherence in a gas of indirect excitons. We found that extended spontaneous coherence of excitons emerges in the region of the macroscopically ordered exciton state and in the region of vortices of linear polarization. The coherence length in these regions is much larger than in a classical gas, indicating a coherent state with a much narrower than classical exciton distribution in momentum space, characteristic of a condensate. We also observed phase singularities in the coherent exciton gas. Extended spontaneous coherence and phase singularities emerge when the exciton gas is cooled below a few Kelvin. Spontaneous coherence of excitonsIf bosonic particles are cooled down below the temperature of quantum degeneracy they can spontaneously form a coherent state in which individual matter waves synchronize and combine. Spontaneous coherence of matter waves forms the basis for a number of fundamental phenomena in physics, including superconductivity, superfluidity, and Bose-Einstein condensation (BEC) [1][2][3][4][5]. Spontaneous coherence is the key characteristic of condensation in momentum space [6].Excitons are hydrogen-like bosons at low densities [7] and Cooper-pair-like bosons at high densities [8]. The bosonic nature of excitons allows for condensation in momentum space, i.e. emergence of spontaneous coherence. Designing semiconductor structures with required characteristics and controlling the parameters of the exciton system gives an opportunity to study various types of exciton condensates.A condensate of exciton-polaritons was recently realized in semiconductor microcavities [9][10][11][12][13]. This condensate is characterized by a strong coupling of excitons to the optical field and a short lifetime of the polaritons. Unlike BEC, equilibrium is not required for the polariton condensation and coherence in the polariton condensate forms due to a coherent optical field similar to coherence in lasers [14].There are intriguing theoretical predictions for a range of coherent states in cold exciton systems, including BEC [7], BCS-like condensation [8], charge-density-wave formation [15], and condensation with spontaneous timereversal symmetry breaking [16]. In these condensates, spontaneous coherence of exciton matter waves emerges below the temperature of quantum degeneracy.Since excitons are much lighter than atoms, quantum degeneracy can be achieved in excitonic systems at temperatures orders of magnitude higher than the microKelvin temperatures needed in atomic vapors [1, 2]. Exciton gases need be cooled down to a few Kelvin to enter the quantum regime. Although the temperature of the semiconductor crystal lattice T lat can be lowered well below 1 K in He-refrigerators, lower...

In order to explain and model the inner ring in photoluminescence (PL) patterns of indirect excitons in GaAs/AlGaAs quantum wells (QWs), we develop a microscopic approach formulated in terms of coupled nonlinear equations for the diffusion, thermalization and optical decay of the particles. The origin of the inner ring is unambiguously identified: it is due to cooling of indirect excitons in their propagation from the excitation spot. We infer that in our high-quality structures the in-plane diffusion coefficient D (2d) x ≃ 10 − 30 cm 2 /s and the amplitude of the disorder potential U 0 /2 ≃ 0.45 meV.

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We study transport of indirect excitons in GaAs/AlGaAs coupled quantum wells in linear lattices created by laterally modulated gate voltage. The localization-delocalization transition for transport across the lattice was observed with reducing lattice amplitude or increasing exciton density. The exciton interaction energy at the transition is close to the lattice amplitude. These results are consistent with the model, which attributes the localization-delocalization transition to the interaction-induced percolation of the exciton gas through the external potential. We also discuss applications of the lattice potentials for estimating the strength of disorder and exciton interaction.

Spin currents and spin textures are observed in a coherent gas of indirect excitons. Applied magnetic fields bend the spin current trajectories and transform patterns of linear polarization from helical to spiral and patterns of circular polarization from four-leaf to bell-like-with-inversion.Studies of electron spin currents in semiconductors led to the discoveries of the spin Hall effect [1][2][3][4][5][6], persistent spin helix [7], and spin drift, diffusion, and drag [8][9][10]. There is also considerable interest in developing semiconductor (opto)electronic devices based on spin currents. An important role in spin current phenomena is played by spin-orbit (SO) coupling. It is the origin of the spin Hall effect and persistent spin helix. It also creates spin structures with the spin vector perpendicular to the momentum of the electrons in metals [11] and topological insulators [12][13][14]. While phenomena caused by SO coupling are ubiquitous in fermionic systems, they have yet to be explored in bosonic matter. Available experimental data for bosons include the optical spin Hall effect in photonic systems [10,16,17] and spin patterns in atomic condensates [18,19]. Here, we report the observation of spin currents and associated rich variety of polarization patterns in a coherent gas of indirect excitons. Applied magnetic fields bend the spin current trajectories and transform patterns of linear polarization from helical to spiral and patterns of circular polarization from four-leaf to bell-like-with-inversion. We also present a theory of exciton transport with spin precession that reproduces the observed exciton polarization patterns and indicates trajectories of spin currents.Excitons -bound pairs of electrons and holes -form a model system to study spin currents of bosons [20]. SO coupling for an exciton originates from the combined Dresselhaus and Rashba effects for the electron and the hole [21][22][23]. An indirect exciton can be formed by an electron and a hole confined in separate quantum-well (QW) layers arXiv:1302.3852v1 [cond-mat.mes-hall]