Low temperature kinetics of 2 D exciton gas cooling in quantum well bilayer

We study the kinetics of 2D Bose gas cooling provided Bose particles interact with 3D phonons. At low temperatures phonon emission is prohibited by the energy and the momentum conservation. We show that both particle-particle scattering and impurity scattering assist the Bose gas cooling. The temporal relaxation of temperature follows the law T ∼ 1/ √ t above the Berezinski-Kosterlitz-Thouless phase transition point and T ∼ 1/t after a Bose-Einstein 2D quasi-condensate develops. Exciton gas in GaAs bilayer quantum well represents a system where a 2D Bose-Einstein quasi-condensation (BEqC) is possible at low temperatures. Experimental efforts [1, 2] have been directed to produce such an exciton gas and to cool it down to a BEqC temperature. A short laser photo-illumination pulse excites electron and hole pairs. The so-called indirect exciton technique is used where a perpendicular electric field drags electrons and holes apart into two spatially separated layers. Then an electron and a hole bind themselves into an indirect exciton particle. This experimental setup suppresses the electron-hole recombination giving rise to a relatively long exciton life time. During the initial photoexcitation pulse newly born excitons are hot and form a non-equilibrium state. In short time after the pulse ends the exciton gas reaches an equilibrium at some effective exciton temperature which is much higher than the lattice temperature of the cold GaAs crys