Photocount statistics of the Josephson parametric amplifier

Parametric amplifiers are known to squeeze the vacuum state of the electromagnetic field, thus the statistics of the photocounts at their output should be that of squeezed vacuum. However, several theoretical works predict a very different statistical distribution. We have measured the photocount statistics of a Josephson parametric amplifier and recover the expected squeezed vacuum statistics. We explain this discrepancy by showing theoretically how the photocount statistics is dictated by the detection process. Namely, most experiments will naturally measure a single mode of the electromagnetic field, while the aforementioned theoretical works implicitly describe massively multimode detection.