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 condensates 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.
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