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Role of particle-number statistics in interference of independent Bose fields

We elucidate generally the interference of independent Bose fields in view of the conditional probability for the particle number measurements, and clarify its relation to the source number statistics. Despite lack of intrinsic phases, the interference phase can be inferred from the particle number registered at one detector by using the classical mean fields. If the conditional number distributions for the other detectors, given the outcome of the first detector, exhibit sufficiently narrow peaks around the values specified by the estimated phases, the mean field description is valid in a single run of interference. The widths in the conditional distribution are determined by the number statistics of the sources, among which notable scaling behavior is found depending on the detector configurations with the boundary at the Poissonian. The mean field description is found to be applicable to Poissonian and sub-Poissonian sources, whereas for super-Poissonian sources it is likely invalidated with the rather broad conditional distribution.