The Berezinskii–Kosterlitz–Thouless phase transition from a disordered to a quasi-ordered state, mediated by the proliferation of topological defects in two dimensions, governs seemingly remote physical systems ranging from liquid helium, ultracold atoms and superconducting thin films to ensembles of spins. Here we observe such a transition in a short-lived gas of exciton-polaritons, bosonic light–matter particles in semiconductor microcavities. The observed quasi-ordered phase, characteristic for an equilibrium two-dimensional bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. This is made possible thanks to long polariton lifetimes in high-quality samples and in a reservoir-free region. Our results show that the joint measurement of coherence both in space and time is required to characterize driven–dissipative phase transitions and enable the investigation of topological ordering in open systems.

Berezinskii–Kosterlitz–Thouless相变从无序状态过渡到准有序状态，这是由二维缺陷的扩散所介导的，它似乎控制着从液氦，超冷原子和超导薄膜到自旋集合体的遥远物理系统。在这里，我们观察到半导体微腔中的激子-极化子，硼光物质粒子的短命气体中的这种过渡。用随机动力学的数值解再现了观测到的准序相，该准序相是平衡二维玻色气的特征，在时域和时域都具有相同的代数指数，并且具有相干性衰减。拓扑缺陷（涡旋）是过渡到代数阶的原因。这归功于高质量样品和无储层区域中的极化子寿命长。我们的结果表明，需要对空间和时间的相干性进行联合测量，以表征驱动-耗散相变，并能够研究开放系统中的拓扑顺序。