  We have measured the critical atom number in an array of harmonically trapped
two-dimensional (2D) Bose gases of rubidium atoms at different temperatures. We
found this number to be about five times higher than predicted by the
semi-classical theory of Bose-Einstein condensation (BEC) in the ideal gas.
This demonstrates that the conventional BEC picture is inapplicable in an
interacting 2D atomic gas, in sharp contrast to the three-dimensional case. A
simple heuristic model based on the Berezinskii-Kosterlitz-Thouless theory of
2D superfluidity and the local density approximation accounts well for our
experimental results.
