频率非简并第I类自发参量下转换纠缠光子对量子特性
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摘要
理论研究了频率非简并第I类自发参量下转换过程中产生的纠缠光子对的量子特性,且与频率简并的情况做了对比.通过纠缠光子对的联合谱强度分析了纠缠光子对的光谱特性及纠缠特性;通过洪-区-曼德尔干涉仪和马赫-曾德尔干涉仪分析了纠缠光子对的量子干涉特性.结果表明:脉冲泵浦作用下,由于频率非兼并使得相位匹配函数不对称,导致两纠缠光子可区分,量子干涉可见度减小.随着泵浦脉冲频宽的增加,这种效应更加明显.连续激光泵浦时,相位匹配函数是对称的,得到最大的纠缠度和量子干涉可见度.该研究为频率非简并纠缠光子源在各种量子信息方案中的应用提供理论指导.
The quantum properties of entangled biphotons generated via frequency-nondegenerate type-I Spontaneous Parametric Down-Conversion(SPDC)were studied in theory,and compared with that of frequency-degenerate type-I SPDC.The properties of spectrum and entanglement of entangled biphotons in both cases were analyzed by the joint spectral intensity;the property of quantum interference was given by the results of Hong-Ou-Mandel interferometer and Mach-Zehnder interferometer.The results show that,for pulse pumping,the phase-matching function is shown to be asymmetric as a result of frequencynondegenerate,which leads to entangled biphotons distinguishable and quantum interference visibility was reduced. As the pump bandwidth is increased,this effect becomes more pronounced.For monochromatic pumping,the phase-matching function is shown to be symmetric,which results in maximum entanglement and quantum interference visibility.These results provide a theoretical basis for the applications of frequency-nondegenerate entangled photon source in various quantum information schemes.
The quantum properties of entangled biphotons generated via frequency-nondegenerate type-I Spontaneous Parametric Down-Conversion(SPDC)were studied in theory,and compared with that of frequency-degenerate type-I SPDC.The properties of spectrum and entanglement of entangled biphotons in both cases were analyzed by the joint spectral intensity;the property of quantum interference was given by the results of Hong-Ou-Mandel interferometer and Mach-Zehnder interferometer.The results show that,for pulse pumping,the phase-matching function is shown to be asymmetric as a result of frequencynondegenerate,which leads to entangled biphotons distinguishable and quantum interference visibility was reduced. As the pump bandwidth is increased,this effect becomes more pronounced.For monochromatic pumping,the phase-matching function is shown to be symmetric,which results in maximum entanglement and quantum interference visibility.These results provide a theoretical basis for the applications of frequency-nondegenerate entangled photon source in various quantum information schemes.
引文
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[2] GIOVANNETTI V,LLOYD S,MACCONE L.Advances in quantum metrology[J].Nature Photonics,2011,5:222-229.
[3] LI Yong-fang,WANG Zhao-hua,LI Bai-hong,et al.Experimental scheme design and analysis for the quantum spatial positioning with pulse laser[J].Acta Photonica Sinica,2010,39(10):1811-1815.李永放,王兆华,李百宏等.脉冲激光作用下的量子定位实验方案的设计及分析[J].光子学报,2010,39(10):1811-1815.
[4] PITTMAN T B,SHIH Y H,STREKALOV D V,et al.Optical imaging by means of two-photon quantum entanglement[J].Physical Review A,1995,52(5):R3429-R3432.
[5] ANGELO M D,KIM Y H,KULIK S P,et al.Identifying entanglement using quantum ghost interference and imaging[J].Physical Review Letters,2004,92(23):452-453.
[6] KLYSHKO D N.Photons and nonlinear optics[M].New York:Gordon and Breach,1998.
[7] BURNHAM D C,WEINBERG D L.Observation of simultaneity in parametric production of optical photon pairs[J].Physical Review Letters,1970,25(2):84-87.
[8] TIMOTHY E K,MORTON H R.Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse[J].Physical Review A,1997,56(2):1534-1541.
[9] GRICE W P,WALMSLEY I A.Spectral information and distinguishability in type-II down-conversion with a broadband pump[J].Physical Review A,1997,56(2):1627-1634.
[10] KIM Y H,GRICE W P.Generation of pulsed polarizationentangled two-photon state via temporal and spectral engineering[J].Journal of Modern Optics,2002,49(14):2309-2323.
[11] YUN Juan-juan,YU Kan,FU Jia-qi.Spontaneous parametric down conversion in type-I BBO crystal pumped by femtosecond pulses[J].Acta Photonica Sinica,2011,40(9):1376-1380.尹娟娟,俞侃,包佳祺.飞秒激光泵浦I类BBO晶体中自发参量下转换的研究[J].光子学报,2011,40(9):1376-1380.
[12] BAEK S Y,KIM Y H.Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion[J].Physical Review A,2008,77(4):1912-1917.
[13] BAEK S Y,KIM Y H.Spectral properties of entangled photons generated via type-I frequency-nondegenerate spontaneous parametric down-conversion[J].Physical Review A,2009,80(3):2962-2964.
[14] LU Zong-Gui,LIU Hong-Jun,JING Feng,et al.Theoretical analysis of spectral properties of parametric fluorescence via spontaneous parametric down-conversion[J].Acta Physics Sinica,2009,58(7):4689-4696.卢宗贵,刘红军,景峰,等.基于自发参量下转换产生参量荧光的光谱分布特性理论分析[J].物理学报,2009,58(7):4696.
[15] FEDRIZZI A,HERBST T,POPPE A,et al.A wavelengthtunable fiber-coupled source of narrowband entangled photons[J].Optics Express,2007,15(23):15377-15386.
[16] KIM Y H,KULIK S P,SHIH Y.Quantum teleportation of apolarization state with a complete bell state measurement.[J].Physical Review Letters,2001,86(7):1370-1373.
[17] ARCIKIC I,DE RIDMATTEN H,TITTEL W,et al.Long-distance teleportation of qubits at telecommunication wavelengths[J].Nature,2003,421(6922):509-513.
[18] DE RIEDMATTEN H,MARCIKIC I,SCARANI V,et al.Tailoring photonic entanglement in high-dimensional Hilbert spaces[J].Physical Review A,2004,69(5):050304(R).
[19] BAEK S Y,KIM Y H.Generating entangled states of two ququarts using linear optical elements[J].Physical ReviewA,2007,75(3):723-727.
[20] BAEK S Y,KIM Y H.Scalable scheme for entangling multiple ququarts using linear optical elements[J].Physics Letters A,2007,370(1):28–34.
[21] BAEK S Y,STRAUPE S S,SHURUPOV A P,et al.Preparation and characterization of arbitrary states of fourdimensional qudits based on biphotons[J].Physical Review A,2008,78(4):042321.
[22] BAO X H,QIAN Y,YANG J,et al.Generation of narrowband polarization-entangled photon pairs for atomic quantum memories[J].Physical Review Letters,2008,101(19):6797-6800.
[23] TAKESUE H.Erasing distinguishability using quantum frequency up-conversion.[J].Physical Review Letters,2008,101(17):157-173.
[24] NASR M B,SALEH B E A,TEICH M C,et al.Generation of high-flux ultra-broadband light by bandwidth amplification in spontaneous parametric down conversion[J].Optics Communications,2005,246(4-6):521-528.
[25] GIOVANNETT I,MACCON E,SHAPIR O,et al.Extended phase-matching conditions for improved entanglement generation[J].Physical Review A,2002,66(4):519-531.
[26] LAW C K,WALMSLEY I A,EBERLY J H.Continuous frequency entanglement:effective finite hilbert space and entropy control[J].Physical Review Letters,2000,84(23):5304-5307.
[27] HONG C K,OU Z Y,MANDEL L.Measurement of subpicosecond time intervals between two photons by interference.[J].Physical Review Letters,1987,59(18):2044-2046.
[28] LARCHUK T S,CAMPOS R A,RARITY J G.Interfering entangled photons of different colors.[J].Physical Review Letters,1993,70(11):1603-1606.