Interference of macroscopic beams on a beam splitter: phase uncertainty converted into photon-number uncertainty

Squeezed-vacuum twin beams, commonly generated through parametric down-conversion, are known to have perfect photon-number correlations. According to the Heisenberg principle, this is accompanied by a huge uncertainty in their relative phase. By overlapping bright twin beams on a beam splitter, we convert phase fluctuations into photon-number fluctuations and observe this uncertainty as a typical `U-shape' of the output photon-number distribution. This effect, although reported for atomic ensembles and giving hope for phase super-resolution, has been never observed for light beams. The shape of the normalized photon-number difference distribution is similar to the one that would be observed for high-order Fock states. It can be also mimicked by classical beams with artificially mixed phase, but without any perspective for phase super-resolution. The probability distribution at the beam splitter output can be used for filtering macroscopic superpositions at the input.