For advanced quantum information technology, sources of photon pairs in quantum mechanically factorable states are of great importance for realizing high-fidelity photon-photon quantum gate operations. Here we experimentally demonstrate a technique to produce spectrally factorable photon pairs utilizing multi-order quasi-phase-matching (QPM) conditions in spontaneous parametric downconversion (SPDC). In our scheme, a spatial nonlinearity profile of a nonlinear optical crystal is shaped with current standard poling techniques, and the associated phase-matching function can be approximated to a Gaussian form. By the measurement of a phase-matching function and the second-order autocorrelation function, we demonstrate that telecom-band photon pairs produced by our custom-poled crystal are highly factorable with > 95% single-photon purity. I. INTRODUCTIONQuantum photonics technology plays an important role in various quantum applications such as quantum computing [1, 2], quantum communication [3,4], quantum metrology [5], and bridging solid and atomic quantum systems at a distance [6]. One of the central requirements in the quantum photonics technology is to produce pure single photons. Most multi-photon applications rely on interference of independent single photons [7], and only pure and indistinguishable photons can exhibit perfect interference. Photon-pair generation via spontaneous parametric downconversion (SPDC) has been widely accepted in quantum optics and photonic quantum information experi-

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An NMR (Nuclear Magnetic Resonance) imaging technique was employed to visualize the convective motion in a horizontally vibrated granular bed. The size segregation phenomena are observed for a binary mixture of larger and smaller particles. Temporal progress of the size segregation was evaluated for three different combinations of binary mixture. The convective motion was clearly observed by MRI, that is, the smaller particles tended to fall down along the side wall, while the larger particles tended to rise through the central region. The convective motion is observed even in the plane perpendicular to the vibration direction as well as in the plane parallel to the vibration direction for all combinations of binary mixture. It was suggested that the size ratio of larger to smaller particles and of vessel to particle affected the segregation phenomena.

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