Abstract
Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. Correlations allow the quantification of the degree of order and the classification of different phases. Here we report measurements of first-order spatial correlations in a harmonically trapped two-dimensional photon gas below, at and above the critical particle number for Bose–Einstein condensation, using interferometric measurements of the emission of a dye-filled optical microcavity. For the uncondensed gas, the transverse coherence decays on a length scale determined by the thermal de Broglie wavelength of the photons, which shows the expected scaling with temperature. At the onset of Bose–Einstein condensation, true long-range order emerges, and we observe quantum statistical effects as the thermal wave packets overlap. The excellent agreement with equilibrium Bose gas theory prompts microcavity photons as promising candidates for studies of critical scaling and universality in optical quantum gases.
Highlights
Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples
A gas of massive particles at high temperatures or low densities, for example, exhibits short-range spatial first-order correlations as inherited by its classical single-particle properties[2,3,4]. The latter are determined by the thermal de Broglie wave descpribffiffiiffinffiffiffigffiffiffiffiaffiffiffipffiffiffiarticle of mass m, which is defined as λth1⁄4h= 2πmkBT, where T denotes the temperature, equaling the de Broglie wavelength of a particle at an average thermal velocity[5]
We report on a quantitative study of the first-order spatial correlations of a two-dimensional harmonically trapped photon gas at equilibrium conditions, both in the classical and in the Bose–Einstein condensed phase using optical interferometry
Summary
Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. As the photon number is increased, long-range order, as indicated by a significant increase of the transverse coherence length, emerges when the mean distance between the optical wave packets approaches the measured thermal de Broglie wavelength.
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