We examine the phase evolution of a Bose-Einstein condensate of photons generated in a dye microcavity by temporal interference with a phase reference. The photoexcitable dye molecules constitute a reservoir of variable size for the condensate particles, allowing for grand canonical statistics with photon bunching, as in a lamptype source. We directly observe phase jumps of the condensate associated with the large statistical number fluctuations and find a separation of correlation timescales.For large systems, our data reveals phase coherence and a spontaneously broken symmetry, despite the statistical fluctuations.At the heart of Bose-Einstein condensation, the phase transition of a cold and dense gas of integer spin (bosonic) particles to a macroscopically populated ground state, is its phase coherence [1,2]. While for a thermal, incoherent ensemble each particle evolves individually, in a Bose-Einstein condensate the macroscopic ground state occupation leads to the whole condensate acting as a single, giant quantum wave. Each individual measurement will then yield a fixed, though random phase, as expected from spontaneous symmetry breaking [3,4,33]. The macroscopic phase of Bose-Einstein condensates has been verified in interference experiments with ultracold atomic gases [6]. For condensates of polaritons, mixed states of matter and light, polarization symmetry breaking was reported [7,8], while polariton arrays have shown phase locking [9]. Further, spatial coherence has been reported for equilibrium photon condensates [10], and also in a nonequilibrium regime [11]. Both atomic and polariton condensates are usually assumed to emit a single wave train of constant amplitude [1,12].They operate with an essentially fixed number of particles, corresponding to a description in the microcanonical or canonical ensemble limit. Such sources have both first and second-order * Present address: Institute for Quantum Electronics, ETH Zürich, Auguste-Piccard-Hof 1, 8093 Zürich, Switzerland arXiv:1512.07148v1 [cond-mat.quant-gas]

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Bose-Einstein condensation is a phenomenon well known for material particles as cold atomic gases, and this concept has in recent years been extended to photons confined in microscopic optical cavities. Essential for the operation of such a photon condensate is a thermalization mechanism that conserves the average particle number, as in the visible spectral regime can be realized by subsequent absorption re-emission processes in dye molecules.Here we report on the status of an experimental effort aiming at the extension of the concept of Bose-Einstein condensation of photons towards the vacuum ultraviolet spectral regime, with gases at high pressure conditions serving as a thermalization medium for the photon gas. We have recorded absorption spectra of xenon gas at up to 30 bar gas pressure of the 5p 6 − 5p 5 6s transition with a wavelength close to 147 nm. Moreover, spectra of ethylene noble gas mixtures between 155 nm and 180 nm wavelength are reported.

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