The Planck distribution of photons emitted by a black body led to the development of quantum theory. An analogous distribution of phonons should exist in a Bose-Einstein condensate. We observe this Planck distribution of thermal phonons in a 3D conde
nsate. This observation provides an important confirmation of the basic nature of the condensates quantized excitations. In contrast to the bunching effect, the density fluctuations are seen to increase with increasing temperature. This is due to the non-conservation of the number of phonons. In the case of rapid cooling, the phonon temperature is out of equilibrium with the surrounding thermal cloud. In this case, a Bose-Einstein condensate is not as cold as previously thought. These measurements are enabled by our in situ k-space technique.
By a novel reciprocal space analysis of the measurement, we report a calibrated in situ observation of the bunching effect in a 3D ultracold gas. The calibrated measurement with no free parameters confirms the role of the exchange symmetry and the Ha
nbury Brown-Twiss effect in the bunching. Also, the enhanced fluctuations of the bunching effect give a quantitative measure of the increased isothermal compressibility. We use 2D images to probe the 3D gas, using the same principle by which computerized tomography reconstructs a 3D image of a body. The powerful reciprocal space technique presented is applicable to systems with one, two, or three dimensions.
