  Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity
is a macroscopically populated coherent quantum state subject to concurrent
pumping and decay. Debates about the fundamental nature of the condensed phase
in this open quantum system still persist. Here, we gain a new insight into the
spontaneous condensation process by imaging long-lifetime exciton polaritons in
a high-quality inorganic microcavity in the single-shot optical excitation
regime, without averaging over multiple condensate realisations. In this highly
non-stationary regime, a condensate is strongly influenced by the `hot'
incoherent reservoir, and reservoir depletion is critical for the transition to
the ground energy and momentum state. Condensates formed by more photonic
exciton polaritons exhibit dramatic reservoir-induced density filamentation and
shot-to-shot fluctuations. In contrast, condensates of more excitonic
quasiparticles display smooth density and are second-order coherent. Our
observations show that the single-shot measurements offer a unique opportunity
to study formation of macroscopic phase coherence during a quantum phase
transition in a solid state system.
