Quantum critical region of ultracold Bose gases exhibiting universal density-probability distribution after free expansion

We report the observation of a universal behavior of ultracold quantum critical (QC) Bose gases trapped in a one-dimensional optical lattice. We extract the density probability distributions from the measured atomic density of the rubidium Bose gases after a free expansion time. The density probability is found to follow a simple exponential law once the lattice system has entered the QC region above the Berezinskii-Kosterlitz-Thouless transition. We show that, in addition to relative phase fluctuations between the subcondensates in different lattice wells, there also exist spatial phase fluctuations within single lattice wells in this QC region. The universal density-probability distribution can thus be well understood by a simple theoretical model taking into account these two kinds of phase fluctuations.