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The transition of atomic, electronic, or e-h systems to quantum phases is anextraordinary process when both microscopic and macroscopic properties of thesystem undergo fundamental changes. Bose-Einstein condensation, has beenobserved in a number of physical systems, including super-cold atomic gases andsolid- state quasiparticles. The most typical example of equilibriumcondensation is the superconducting state of Cooper pairs in metals. However,in many cases the lifetime of particles or quasiparticles under study isfinite, ranging from picoseconds to milliseconds. And even in this casecondensation is possible. It is generally understood at present that coherenceand off-diagonal long-range order in the density matrix are the most importantcharacteristic features of condensed quantum states. Phase coherenceestablished over microscopic distances is an intrinsic property of all Bosecondensates. Experiments featuring interference between either two condensatesor two separate parts of the same condensate are often considered as moreconvincing than observation of the macroscopic occupation of the ground state.The formation of long-range order and spatial phase coherence can be measuredby studying interference patterns using either a Michelson interferometer orYoung double slit arrangement. Here we present experimental results ofobservation of long-range temporal and spatial coherence of a macroscopicallyordered state of a high-density e-h system in GaAs during the generation offemtosecond superradiant emission at room temperature

Observation of the formation of long-range order during superradiant emission in a high-density e-h system