Characterization of Noninteracting Bosons, with Applications

Abstract: Boson sampling is the task of producing samples from the number-basis distribution of many bosons traveling through a passive linear optical network. It is believed to be extremely difficult to accomplish classically, and has been the motivation for many "quantum advantage" demonstrations. Here we discuss the characterization tools that were developed to interpret the results of a boson sampling experiment performed at JILA, using atoms instead of photons. We measured the indistinguishability of the atoms using a Hong-Ou-Mandel style measurement, and found that it was $99.5^{+0.5}_{-1.6}\%$. We then showed that the indistinguishability of the atoms was a good predictor of the multiparticle bunching features, which in turn was a measure of multiparticle indistinguishability itself. To make this latter connection explicit, we introduce the weak generalized bunching conjecture and show it is equivalent to an existing mathematical conjecture. For the purpose of characterizing the dynamics that were present in the experiment, we discuss how to optimize the experimental design for inferring the single-particle unitary from Fock basis measurements. We showed that having very cold atoms was necessary to perform the inference of the dynamics in a reasonable amount of time. We then partially characterized the single particle unitary via direct measurements using one and two atoms, and compared our measurements to a separate characterization using a new statistic that describes the deviation between the two characterization methods while being insensitive to uninferable parameters.