在量子資訊的領域，操控糾纏光子的物理特性是一門相當重要的學問，這不論改變光子的波形又或是賦予其不同的糾纏特性。實驗中，先以單一極化的KTP晶體產生Type2同軸的糾纏光子，並探討晶體加入極化反轉的調製時，糾纏光子會如何改變。我們觀察到當極化的長度有偏差時，糾纏光子頻譜的變化，並給出先對應的理論模擬，而運用KTP晶體原先就能產生糾纏光子為前提來設計極化反轉，也使得我們成功地發展出一套微型化產生高純度的偏振糾纏光子的方法。

In quantum information science, how to control single photons and biphotons is an important issue, which includes how we shape the wavepacket of biphotons or let them obtain other entanglement properties. In our experiment, we first use a single domain KTP crystal to generate collinear Type-2 phase matched biphotons. Then, we discuss how the poling on the crystal will change the biphotons. We observed that the spectrum of biphoton is modulated by the random poling error and confirmed them by our theory. We also design the poling grating to reach an easy way of generating polarization entangled photons.

[1] Robert W. Boyd, Nonlinear Optics, Third Edition, Academic Press, 2008
[2] Fejer, Martin M., et al. "Quasi-phase-matched second harmonic generation: tuning and tolerances." IEEE Journal of Quantum Electronics 28.11 (1992): 2631-2654.
[3] Kimble, H. Jeff. "The quantum internet." Nature 453.7198 (2008): 1023.15
[4] Cirac, Juan Ignacio, et al. "Quantum state transfer and entanglement distribution among distant nodes in a quantum network." Physical Review Letters 78.16 (1997): 3221.
[5] Zhang, Shanchao, et al. "Coherent control of single-photon absorption and reemission in a two-level atomic ensemble." Physical review letters 109.26 (2012): 263601.
[6] Su, Wei-Ming, et al. "Shaping single photons and biphotons by inherent losses." Physical Review A 94.3 (2016): 033805.
[7] Bennett, Charles H., and Gilles Brassard. "Quantum cryptography: Public key distribution and coin tossing." Theor. Comput. Sci. 560.P1 (2014): 7-11.
[8] Inoue, Kyo, Edo Waks, and Yoshihisa Yamamoto. "Differential phase shift quantum key distribution." Physical Review Letters 89.3 (2002): 037902.
[9] Bennett, Charles H., Gilles Brassard, and N. David Mermin. "Quantum cryptography without Bell’s theorem." Physical Review Letters 68.5 (1992): 557.
[10] Yang, Chun-Yao, et al. "Parametric down-conversion with nonideal and random quasi-phase-matching." Scientific reports 6 (2016): 26079.
[11] Rubin, Morton H., et al. "Theory of two-photon entanglement in type-II optical parametric down-conversion." Physical Review A50.6 (1994): 5122.
[12] Kim, Yoon-Ho, et al. "Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion." Physical Review A 63.6 (2001): 062301.
[13] C.-S. Chuu, ABCD Formulism for Spontaneous Parametric Down Conversion, Physics Department, National Tsing Hua University, Taiwan
[14] Kato, Kiyoshi, and Eiko Takaoka. "Sellmeier and thermo-optic dispersion formulas for KTP." Applied optics 41.24 (2002): 5040-5044.
[15] Fox, Mark. Quantum optics: an introduction. Vol. 15. OUP Oxford, 2006.
[16] Pearson, Brett J., and David P. Jackson. "A hands-on introduction to single photons and quantum mechanics for undergraduates." American Journal of Physics 78.5 (2010): 471-484.
[17] Franson, James D. "Bell inequality for position and time." Physical review letters 62.19 (1989): 2205.
[18] Kwiat, P. G., et al. "Correlated two-photon interference in a dual-beam Michelson interferometer." Physical Review A 41.5 (1990): 2910.
[19] Chen, Yu-Ao, et al. "Memory-built-in quantum teleportation with photonic and atomic qubits." Nature Physics 4.2 (2008): 103.
[20] Ren, Ji-Gang, et al. "Ground-to-satellite quantum teleportation." Nature 549.7670 (2017): 70.
[21] Pan, Jian-Wei, et al. "Experimental demonstration of four-photon entanglement and high-fidelity teleportation." Physical Review Letters 86.20 (2001): 4435.
[22] De Riedmatten, Hugues, et al. "Long-distance entanglement swapping with photons from separated sources." Physical Review A 71.5 (2005): 050302.
[23] Pan, Jian-Wei, et al. "Experimental demonstration of four-photon entanglement and high-fidelity teleportation." Physical Review Letters 86.20 (2001): 4435.
[24] Hamel, Deny R., et al. "Direct generation of three-photon polarization entanglement." Nature Photonics 8.10 (2014): 801.
[25] Chen, Luo-Kan, et al. "Observation of ten-photon entanglement using thin BiB 3 O 6 crystals." Optica 4.1 (2017): 77-83.
[26] Kwiat, Paul G., et al. "New high-intensity source of polarization-entangled photon pairs." Physical Review Letters 75.24 (1995): 4337.
[27] Fedrizzi, Alessandro, et al. "Anti-symmetrization reveals hidden entanglement." New Journal of Physics 11.10 (2009): 103052.
[28] Kwiat, Paul G., et al. "Ultrabright source of polarization-entangled photons." Physical Review A 60.2 (1999): R773.
[29] Pelton, Matthew, et al. "Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP." Optics Express 12.15 (2004): 3573-3580.
[30] Fiorentino, Marco, et al. "Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints." Physical Review A 69.4 (2004): 041801.
[31] Kim, Taehyun, Marco Fiorentino, and Franco NC Wong. "Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer." Physical Review A 73.1 (2006): 012316.
[32] Fedrizzi, Alessandro, et al. "A wavelength-tunable fiber-coupled source of narrowband entangled photons." Optics Express 15.23 (2007): 15377-15386.
[33] Ueno, Wakana, et al. "Entangled photon generation in two-period quasi-phase-matched parametric down-conversion." Optics Express 20.5 (2012): 5508-5517.
[34] Gong, Yan-Xiao, et al. "Compact source of narrow-band counterpropagating polarization-entangled photon pairs using a single dual-periodically-poled crystal." Physical Review A 84.5 (2011): 053825.
[35] Hong, Chong-Ki, Zhe-Yu Ou, and Leonard Mandel. "Measurement of subpicosecond time intervals between two photons by interference." Physical review letters 59.18 (1987): 2044.
[36] Ou, Z. Y., and L. Mandel. "Observation of spatial quantum beating with separated photodetectors." Physical review letters61.1 (1988): 54.
[37] Grice, Warren P., and Ian A. Walmsley. "Spectral information and distinguishability in type-II down-conversion with a broadband pump." Physical Review A 56.2 (1997): 1627.
[38] Steinberg, A. M., P. G. Kwiat, and R. Y. Chiao. "Dispersion cancellation in a measurement of the single-photon propagation velocity in glass." Physical review letters 68.16 (1992): 2421.
[39] Legero, Thomas, et al. "Quantum beat of two single photons." Physical review letters 93.7 (2004): 070503.
[40] Kim, Yoon-Ho. "Quantum interference with beamlike type-II spontaneous parametric down-conversion." Physical Review A68.1 (2003): 013804.
[41] Lee, Sang Min, et al. "Polarization-entangled photon-pair source obtained via type-II non-collinear SPDC process with PPKTP crystal." Optics Express 24.3 (2016): 2941-2953.