Résumé
It is well known that a two-dimensional gas of dipolar bosons can form a supersolid with fluctuating phase (quasicondensate) at low enough temperatures. Recently, periodical density modulation has been observed in a cold gas of indirect excitons in semiconductor nanostructures. The photoluminescence ring of a 2D exciton gas squeezes and fragments into an array of beads having macroscopic sizes (10 mkm) below some critical temperature. Surprisingly, shift-interferometry measurements reveal build up of long-range order (ODLRO) in each bead. In other words, each bead represents a true Bose-Einstein condensate of excitons. The fact that a 2D cloud having macroscopic size (10 mkm) is fully coherent suggests that this cloud is trapped. In this talk I argue that the localization of excitons on the ring is due to the macroscopic charge separation. In these conditions strong dipolar repulsive interaction between the excitons results in further localization - the beads localize themselves along the ring. Such "autolocalization" alters dramatically the exciton DOS, making it possible to observe true second order phase transition (the build up of order parameter) in the thermodynamic limit. This is the crucial difference between the observed ordering of the exciton system and the well-known transition of a 2D gas to a supersolid with algebraic decay in the density matrix. Considering the fragmented exciton ring as an array of Bose-Einstein condensates, I analyze its coherent properties and find the number of beads in equilibrium. The latter is determined by the balance between the kinetic energy due to autolocalization and the entropy of the Josephson junctions between the adjacent condensates.