Large-scale coherence of the bose condensate of spatially indirect excitons

The Bose condensation of spatially indirect (dipolar) excitons in a wide single quantum well in an electric field transverse to the heterolayers is analyzed. Voltage is applied between a metallic film on the surface (Schottky gate) and a conducting electron layer inside a heterostructure (integrated electrode). The excitation of dipolar excitons and observation of their luminescence are performed through circle windows in a metallic mask 5 μm in diameter. Excitons are collected in a ring lateral trap, which is formed along the window perimeter owing to the strongly inhomogeneous electric field. When the critical condensation conditions in pump and temperature are reached, a narrow line of dipolar excitons corresponding to the exciton condensate appears stepwise in the luminescence spectrum. Under these conditions, a spatially periodic structure of equidistant luminescence spots appears in the luminescence pattern that is observed through a window with a resolution of about 1 μm and is selected by means of an interference filter. An in situ optical Fourier transform of spatially periodic structures from the real space to the k space is derived. The resulting Fourier transforms reproducing the pattern of the luminescence intensity distribution in the far field exhibit the result of the destructive and constructive interference, as well as the fact that the luminescence is directed along the normal to the heterolayers. These results are consequences of the large-scale coherence of the condensed exciton state in the ring lateral trap. Direct measurements of double-beam interference from pairs of luminescence spots in the ring show that the spatial coherence length is no less than 4 μm. Such a large scale means that the experimentally observed periodic luminescence structures are described by a common wavefunction under the condition of the Bose condensation of dipolar excitons.