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...