Is a multiple excitation of a single atom equivalent to a single excitation of an ensemble of atoms?

Recent technological advances have enabled to isolate, control and measure the properties of a single atom, leading to the possibility to perform statistics on the behavior of single quantum systems. These experiments have enabled to check a question which was out of reach previously: Is the statistics of a multiple excitation of an atom N times equivalent to a single excitation of an ensemble of N atoms? We present a new method to analyze quantum measurements which leads to the conclusion that the answer is most probably no. We discuss the merits of the analysis and its conclusion.