Sparse interferometry for measuring multiphoton collective phase

A multiphoton collective phase is a multiphoton-scattering feature that cannot be reduced to a sequence of two-photon scattering events, and the three-photon “triad phase” is the smallest nontrivial example. Observing a higher-order collective phase is experimentally challenging, and only triad and four-photon tetrad collective phases have been observed. We introduce a scheme to make higher-order multiphoton collective-phase observations feasible by designing a sparse interferometer, which significantly reduces complexity compared with the current best scheme for observing a multiphoton collective phase. Specifically, our scheme reduces the optical depth from logarithmic to constant and reduces the number of beam splitters from O(nlogn) to linear scaling with respect to the collective-phase order n. As constant depth reduces loss and dispersion to a fixed rate regardless of collective-phase order, a major obstacle to observing large-scale collective phases is removed.