Observation of genuine three-mode interference produced by higher order spontaneous parametric downconversion

Parametric processes are well recognized as key elements for various quantum protocols. Advancing to higher-order parametric processes has been an on-going challenge. In particular, a long-sought goal in quantum optics has been third-order spontaneous parametric down-conversion (SPDC), where photons are directly created in triplets. We report the generation of microwave signals from third-order SPDC in a multimode parametric cavity when pumping both a single mode and three coupled modes. By pumping at the triple frequency of a single mode, we observe a phase-space distribution with a non-Gaussian profile which shows strong skewness in the quadrature amplitude distribution. By pumping at the sum frequency of three modes, we observe non-zero coskewness between the quadrature amplitudes of the modes. These phase-dependent three-mode correlations are observed even though the two-mode covariance between any two of the three modes is zero. This suggest the existence of a nontrivial three-mode continuous variable interference. These types of non-Gaussian states have been suggested as a resource enabling universal quantum computation with continuous variables. The multimode states may also be useful for three-party quantum communication protocols such as quantum secret sharing.