Two dimensional dilute Bose gas exhibits a scale-invariant behavior throughout its phase diagram and universality near the Berezinskii-Kosterlitz-Thouless (BKT) phase transition between the normal and quasi-condensate states, where fluctuations dominate, and mean-field description fails. In this regime, the system is similar to a resonant Fermi gas and is  described by a generic scale-invariant equation of state, which only depends on the thermal de Broglie wavelength as the sole length scale.

We study this scaling behavior of ultracold Cs atoms in a 2D optical trap based on high resolution in situ imaging, revealing both density profiles and fluctuations at varied temperature and chemical potential. We confirm the scale invariance throughout the normal, fluctuation and superfluid phases, and identify BKT transition points. By investigating the equation of state at different atomic interactions near a magnetic Feshbach resonance, we observe universal scaling behavior of density and fluctuations throughout the fluctuation-dominated region. We show that universality can be used as a
powerful tool to test thermodynamical theorems in the critical regime and outline future efforts to explore quantum criticality near the superfluid-Mott insulator transition in a 2D optical lattice.