Figure 1

The measured far-field density of particle momenta from two trap configurations (black and magenta). Three regions are shown: At low k the parabolic distribution of the BEC dominates. For larger k, the thermal parts (fits shown by dashed lines) decay super-exponentially as \(e^{-k^2}\). For even larger k, these give way to the surmised quantum depletion region. A combined fit of the form \(n_T(k) + C_4/k^4\) (green dot-dash lines) yields temperatures consistent with the thermal fit and also an amplitude \(C_4\) of the depleted tail. The grey dotted line is a guide to the eye showing a \(k^{-4}\) decay. Due to constraints of the detector geometry (see Supplementary Materials for details), these profiles were integrated over two spherical segments, each subtending an angle of \(\pi /6\) radians with the \(\pm z\) axes (see also Fig. 5). The detector shows signs of saturation for low \(k (\lesssim 1.5~\mu {{\text {m}}}^{-1}\)). These factors imply the total area under the curves is less than the average number of trapped atoms.