  Quantum gases of light, as photons or polariton condensates in optical
microcavities, are collective quantum systems enabling a tailoring of
dissipation from e.g. cavity loss. This makes them a tool to study dissipative
phases, an emerging subject in quantum manybody physics. Here we experimentally
demonstrate a non-Hermitian phase transition of a photon Bose-Einstein
condensate to a new dissipative phase, characterized by a biexponential decay
of the condensate's second-order coherence. The phase transition occurs due to
the emergence of an exceptional point in the quantum gas. While Bose-Einstein
condensation is usually connected to ordinary lasing by a smooth crossover, the
observed phase transition separates the novel, biexponential phase from both
lasing and an intermediate, oscillatory condensate regime. Our findings pave
the way for studies of a wide class of dissipative quantum phases, for instance
in topological or lattice systems.
