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Optical quantum states defined in temporal modes, especially non-Gaussianstates like photon-number states, play an important role in quantum computingschemes. In general, the temporal-mode structures of these states arecharacterized by one or more complex functions called temporal-mode functions(TMFs). Although we can calculate TMF theoretically in some cases, experimentalestimation of TMF is more advantageous to utilize the states with high purity.In this paper, we propose a method to estimate complex TMFs. This method can beapplied not only to arbitrary single-temporal-mode non-Gaussian states but alsoto two-temporal-mode states containing two photons. This method is implementedby continuous-wave (CW) dual homodyne measurement and doesn't need priorinformation of the target states nor state reconstruction procedure. Wedemonstrate this method by analyzing several experimentally creatednon-Gaussian states.

Complete temporal mode characterization of non-Gaussian states by dual homodyne measurement