Multiphoton interference outperforms pairwise overlaps for distinguishability characterization

Abstract

We propose a protocol that characterizes the pairwise overlaps of the internal modes of single photons more efficiently than pairwise Hong-Ou-Mandel characterization experiments. This protocol exploits multiphoton interference. We experimentally implement this protocol to characterize three photons. We show that our implementation of the characterization protocol outperforms the pairwise Hong-Ou-Mandel characterization, even if the Hong-Ou-Mandel characterization would have been performed in a noiseless, perfect experiment. We demonstrate this via the Fisher information matrix.

Figures (4)

• Figure 1: Improved characterization protocol. (a) The linear optical circuit consists of a balanced beamsplitter (indicated as a red horizontal stripe), followed by a beamsplitter with a splitting ratio that is dependent on the quality of the photons. The balanced beamsplitter effectively performs a HOM-characterization, in which information is gained about the pairwise overlap of the uppermost two photons. The second beamsplitter is then used to gain additional information about the pairwise overlaps. (b) The relation between the splitting ratio of the second beamsplitter and the quality of the photons.
• Figure 2: Generalization of multiphoton characterization experiments that will outperform HOM-characterization. (a) A cascade of beamsplitters, each new beamsplitter is attached to the output arm of the previous beam splitter and to a 'fresh' photon. We expect the splitting ratios of the beamsplitters in the cascade to match values such that forbidden outcomes are a result of destructive quantum interference for the dominant contribution to the output state of the previous beamsplitter. (b) Balanced beampslitters in the first layer perform many HOM-characterization experiments in parallel. The second layer is used to perform additional interference experiments to extract additional information about the pairwise overlaps. We leave the output mode of at least one balanced beamsplitter untouched (the upper one in our schematic) to determine whether a bunching or anti-bunching event occurred at each beamsplitter in the first layer.
• Figure 3: Experimental setup. A Ti:Sapph laser pumps two single-photon sources in parallel. The beam is focused onto a ppKTP crystal to produce pairs of single photons (red wave-packets) via type-II SPDC, then filtered with a high-pass filter (HPF). The two photons are split at a polarizing beam splitter (PBS), filtered with bandpass filters (BPF), and coupled into optical fibers. Linear stages control the path lengths and thus the relative delays of the photons, to optimize temporal opverlap of the photons. The first three photons are sent to the photonic chip for the experiments, while the fourth is used as a herald. The scatterig matrixa presented in Fig. (\ref{['fig1: better than HOM']}) is programmed in the top-left corner of the chip. A picture of the photonic chip is included as an inset. The output state is detected using a bank of quasi-photon-number-resolving superconducting nanowire single-photon detectors (qPNR SNSPDs).
• Figure 4: Experimental results. (a) The probability mass function corresponding to the scattering matrix of Fig. (\ref{['fig1: better than HOM']}a), experimentally measured (blue) and modeled (red). (b) The determinant of the inverse of the observed Fisher information matrix is plot against the number of samples (blue circles). The value is compared with the fisher information corresponding to a perfectly executed noiseless HOM-characterization experiment (purple squares) and with a perfectly executed noiseless experiment of our improved characterization protocol (orange triangles). We see that the our experiment consistently outperforms the HOM-characterization.