Direct evaluation of coherence in a Magnon Bose-Einstein Condensate

The spontaneous emergence of coherence is a defining feature of multi-body quantum systems, underlying phenomena from superconductivity to quantum information processing. While Bose-Einstein condensates (BECs) provide a unique setting for exploring this process, yet direct observation of how a condensate acquires a coherent global phase has remained out of reach. Here, we present the first time-resolved measurement of spontaneous phase formation in a magnon BEC. Using a phase-referenced detection technique, we track the phase of the condensate coherent state relative to an external reference, revealing how an initially incoherent magnon gas thermalizes and undergoes a spontaneous transition into a coherent quantum state with a well-defined macroscopic phase.This observation provides direct evidence of spontaneous symmetry breaking in a quasiparticle condensate, confirming a central prediction of BEC theory that extends across diverse quantum systems.