  The transition of atomic, electronic, or e-h systems to quantum phases is an
extraordinary process when both microscopic and macroscopic properties of the
system undergo fundamental changes. Bose-Einstein condensation, has been
observed in a number of physical systems, including super-cold atomic gases and
solid- state quasiparticles. The most typical example of equilibrium
condensation is the superconducting state of Cooper pairs in metals. However,
in many cases the lifetime of particles or quasiparticles under study is
finite, ranging from picoseconds to milliseconds. And even in this case
condensation is possible. It is generally understood at present that coherence
and off-diagonal long-range order in the density matrix are the most important
characteristic features of condensed quantum states. Phase coherence
established over microscopic distances is an intrinsic property of all Bose
condensates. Experiments featuring interference between either two condensates
or two separate parts of the same condensate are often considered as more
convincing than observation of the macroscopic occupation of the ground state.
The formation of long-range order and spatial phase coherence can be measured
by studying interference patterns using either a Michelson interferometer or
Young double slit arrangement. Here we present experimental results of
observation of long-range temporal and spatial coherence of a macroscopically
ordered state of a high-density e-h system in GaAs during the generation of
femtosecond superradiant emission at room temperature
