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啁啾纠缠光子对具有超宽带的频谱特征，但由于同时产生了二次频率相位因子使其关联时间也被拓宽，限制了其在量子计量、量子光刻等领域的应用.通过类比透镜在空间对光场的相位变换原理，本文提出了一种通过在频域制作类透镜（菲涅耳波带透镜）来等效消除二次频率相位因子，从而压缩啁啾纠缠光子对关联时间的方法.这种类透镜是基于菲涅耳波带片思想，通过将啁啾纠缠光子对光谱划分成菲涅耳频率波带，并进行二元相位（0，）调制来实现.该方法可以在不损耗纠缠光信号的情况下极大地增强光子对的时间关联，同时又避免了相位补偿方法中压缩结果对色散介质长度的依赖和高阶色散影响的缺点.这些结果为产生超宽带、超窄时间关联的纠缠光子对提供了理论依据，在量子计量和量子光刻领域有潜在的应用.Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra. However, the presence of quadratic frequency phase factor restricts their applications in quantum metrology and quantum lithography due to simultaneously lengthening the correlation times of biphotons. The key point to improve the temporal correlation of chirped biphotons is how to compensate for or remove the quadratic frequency phase factor. Phase compensation methods have been demonstrated to solve this problem in earlier reports. But the compressed efficiencies of these methods are strongly dependent on the length of the utilized dispersive medium and decreased by the higher-order dispersion of the dispersive medium. In this paper, based on the phase transform of a lens for a light field in spatial domain, we theoretically propose a method of the equivalent removal of the quadratic phase by realizing a Fresnel-zone lens-like modulation on the biphotons spectrum in frequency domain, thereby compressing the correlation time of chirped biphotons to the Fourier-transform limited width. By analogy to the idea of Fresnel wave zone plate, this lens-like modulation can be realized by dividing the biphoton spectrum into Fresnel frequency zones and applying only binary spectral phase (0, ) sequentially to these zones. The theoretical results show that the correlation time width of chirped biphotons can be reduced, and the correlation signal intensity can be increased compared with the original one, by a factor about 100 and 30, respectively. The physical reason is that these Fresnel frequency zones under binary spectral phase modulation will lead to constructive interference at zero delay and destructive interference elsewhere. This method can significantly enhance biphoton time correlation without biphoton signal loss and avoids the limitations of phase compensation methods. Therefore, we can obtain biphotons with both ultra-broad bandwidth and ultra-short correlation times by using our proposed method. The attainable compression efficiency is constrained by the division resolution of the Fresnel frequency zones and the precision of applied binary phase modulations. It should be noted that a constraint condition about crystal length, chirp parameter and the number of frequency zones is summarized in designing the experimental parameters for the desired compression goal. Since binary spectral phase and 0 are easy to obtain and calibrate in practice, we thus believe that our proposed method is feasible to implement experimentally. Moreover, the proposed method can also be generalized to other fields relating to the quadratic phase factor, such as two-photon absorption, second-harmonic generation and chirped pulse compression.
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Keywords:
- chirped biphotons /
- correlation times /
- compression /
- binary phase modulation
[1] Carrasco S, Torres J P, Torner L, Sergienko A, Saleh B E A, Teich M C 2004 Opt. Lett. 29 2429
[2] Khan I A, Howell J C 2006 Phys. Rev. A 73 031801
[3] Law C K, Walmsley I A, Eberly J H 2000 Phys. Rev. Lett. 84 5304
[4] Dauler E, Jaeger G, Muller A, Migdall A L, Sergienko A V 1999 J. Res. Natl. Inst. Stand. Technol. 104 1
[5] Carrasco S, Nasr M B, Sergienko A V, Saleh B E, Teich M C, Torres J P, Torner L 2006 Opt. Lett. 31 253
[6] O'Donnell K A, U'Ren A B 2007 Opt. Lett. 32 817
[7] Hendrych M, Shi X J, Valencia A, Torres J P 2009 Phys. Rev. A 79 023817
[8] Katamadze K G, Kulik S P 2011 JETP Lett. 112 20
[9] Okano M, Okamoto R, Tanaka A, Subashchandran S, Takeuchi S 2012 Opt. Express 20 13977
[10] Hum D S, Fejer M M 2007 C. R. Phys. 8 180
[11] Nasr M B, Carrasco S, Saleh B E A, Sergienko A V, Teich M C, Torres J P, Torner L, Hum D S, Fejer M M 2008 Phys. Rev. Lett. 100 183601
[12] Nasr M B, Minaeva O, Goltsman G N, Sergienko A V, Saleh B E, Teich M C 2008 Opt. Express 16 15104
[13] Fraine A, Minaeva O, Simon D S, Egorov R, Sergienko A V 2012 Opt. Lett. 37 1910
[14] Antonosyan D A, Tamazyan A R, Kryuchkyan G Y 2012 J. Phys. B:At. Mol. Opt. Phys. 45 215502
[15] Harris S E 2007 Phys. Rev. Lett. 98 063602
[16] Sensarm S, Yin G Y, Harris S E 2010 Phys. Rev. Lett. 104 253602
[17] Tanaka A, Okamoto R, Lim H H, Subashchandran S, Okano M, Zhang L B, Kang L, Chen J, Wu P H, Hirohata T, Kurimura S, Takeuchi S 2012 Opt. Express 20 25228
[18] Brida G, Chekhova M V, Degiovanni I P, Genovese M, Kitaeva G K, Meda A, Shumilkina O A 2009 Phys. Rev. Lett. 103 193602
[19] Brida G, Chekhova M V, Degiovanni I P, Genovese M, Kitaeva G Kh, Meda A, Shumilkina O A 2010 Phys. Rev. A 81 053828
[20] Chekhova M V, Shumilkina O A 2009 JETP Lett. 90 172
[21] Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222
[22] D'Angelo M, Chekhova M V, Shih Y 2001 Phys. Rev. Lett. 87 013602
[23] Gea-Banacloche J 1989 Phys. Rev. Lett. 62 1603
[24] Georgiades N P, Polzik E S, Edamatsu K, Kimble H J, Parkins A S 1995 Phys. Rev. Lett. 75 3426
[25] Valencia A, Scarcelli G, Shih Y 2004 Appl. Phys. Lett. 85 2655
[26] Pe'er A, Dayan B, Friesem A A, Silberberg Y 2005 Phys. Rev. Lett. 94 073601
[27] Weiner A M 2011 Opt. Commun. 284 3669
[28] Zäh F, Halder M, Feurer T 2008 Opt. Express 16 16452
[29] Lukens J M, Dezfooliyan A, Langrock C, Fejer M M, Leaird D E, Weiner A M Opt. Lett. 38 4652
[30] Lukens J M, Dezfooliyan A, Langrock C, Fejer M M, Leaird D E, Weiner A M 2013 Phys. Rev. Lett. 111 193603
[31] Lukens J M, Dezfooliyan A, Langrock C, Fejer M M, Leaird D E, Weiner A M 2014 Phys. Rev. Lett. 112 133602
[32] Lukens J M, Odele O, Langrock C, Fejer M M, Leaird D E, Weiner A M 2014 Opt. Express 22 9585
[33] Hecht E 1989 Optics (2nd Ed.) (Reading, MA:Addison-Wesley) pp434-458
[34] Broers B, Noordam L D, van Linden van den Heuvell H B 1992 Phys. Rev. A 46 2749
[35] Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge:Cambridge University Press)
[36] Chekhova M V 2002 JETP Lett. 75 225
[37] Valencia A, Chekhova M V, Trifonov A, Shih Y 2002 Phys. Rev. Lett. 88 183601
[38] Li B H, Xu Y G, An L, Lin Q L, Zhu H F, Lin F K, Li Y F 2014 Opt. Lett. 39 2443
[39] Li B H, Xu Y G, Zhu H F, Lin Q L, An L, Lin F K, Li Y F 2014 J. Opt. Soc. Am. B 31 2511
-
[1] Carrasco S, Torres J P, Torner L, Sergienko A, Saleh B E A, Teich M C 2004 Opt. Lett. 29 2429
[2] Khan I A, Howell J C 2006 Phys. Rev. A 73 031801
[3] Law C K, Walmsley I A, Eberly J H 2000 Phys. Rev. Lett. 84 5304
[4] Dauler E, Jaeger G, Muller A, Migdall A L, Sergienko A V 1999 J. Res. Natl. Inst. Stand. Technol. 104 1
[5] Carrasco S, Nasr M B, Sergienko A V, Saleh B E, Teich M C, Torres J P, Torner L 2006 Opt. Lett. 31 253
[6] O'Donnell K A, U'Ren A B 2007 Opt. Lett. 32 817
[7] Hendrych M, Shi X J, Valencia A, Torres J P 2009 Phys. Rev. A 79 023817
[8] Katamadze K G, Kulik S P 2011 JETP Lett. 112 20
[9] Okano M, Okamoto R, Tanaka A, Subashchandran S, Takeuchi S 2012 Opt. Express 20 13977
[10] Hum D S, Fejer M M 2007 C. R. Phys. 8 180
[11] Nasr M B, Carrasco S, Saleh B E A, Sergienko A V, Teich M C, Torres J P, Torner L, Hum D S, Fejer M M 2008 Phys. Rev. Lett. 100 183601
[12] Nasr M B, Minaeva O, Goltsman G N, Sergienko A V, Saleh B E, Teich M C 2008 Opt. Express 16 15104
[13] Fraine A, Minaeva O, Simon D S, Egorov R, Sergienko A V 2012 Opt. Lett. 37 1910
[14] Antonosyan D A, Tamazyan A R, Kryuchkyan G Y 2012 J. Phys. B:At. Mol. Opt. Phys. 45 215502
[15] Harris S E 2007 Phys. Rev. Lett. 98 063602
[16] Sensarm S, Yin G Y, Harris S E 2010 Phys. Rev. Lett. 104 253602
[17] Tanaka A, Okamoto R, Lim H H, Subashchandran S, Okano M, Zhang L B, Kang L, Chen J, Wu P H, Hirohata T, Kurimura S, Takeuchi S 2012 Opt. Express 20 25228
[18] Brida G, Chekhova M V, Degiovanni I P, Genovese M, Kitaeva G K, Meda A, Shumilkina O A 2009 Phys. Rev. Lett. 103 193602
[19] Brida G, Chekhova M V, Degiovanni I P, Genovese M, Kitaeva G Kh, Meda A, Shumilkina O A 2010 Phys. Rev. A 81 053828
[20] Chekhova M V, Shumilkina O A 2009 JETP Lett. 90 172
[21] Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222
[22] D'Angelo M, Chekhova M V, Shih Y 2001 Phys. Rev. Lett. 87 013602
[23] Gea-Banacloche J 1989 Phys. Rev. Lett. 62 1603
[24] Georgiades N P, Polzik E S, Edamatsu K, Kimble H J, Parkins A S 1995 Phys. Rev. Lett. 75 3426
[25] Valencia A, Scarcelli G, Shih Y 2004 Appl. Phys. Lett. 85 2655
[26] Pe'er A, Dayan B, Friesem A A, Silberberg Y 2005 Phys. Rev. Lett. 94 073601
[27] Weiner A M 2011 Opt. Commun. 284 3669
[28] Zäh F, Halder M, Feurer T 2008 Opt. Express 16 16452
[29] Lukens J M, Dezfooliyan A, Langrock C, Fejer M M, Leaird D E, Weiner A M Opt. Lett. 38 4652
[30] Lukens J M, Dezfooliyan A, Langrock C, Fejer M M, Leaird D E, Weiner A M 2013 Phys. Rev. Lett. 111 193603
[31] Lukens J M, Dezfooliyan A, Langrock C, Fejer M M, Leaird D E, Weiner A M 2014 Phys. Rev. Lett. 112 133602
[32] Lukens J M, Odele O, Langrock C, Fejer M M, Leaird D E, Weiner A M 2014 Opt. Express 22 9585
[33] Hecht E 1989 Optics (2nd Ed.) (Reading, MA:Addison-Wesley) pp434-458
[34] Broers B, Noordam L D, van Linden van den Heuvell H B 1992 Phys. Rev. A 46 2749
[35] Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge:Cambridge University Press)
[36] Chekhova M V 2002 JETP Lett. 75 225
[37] Valencia A, Chekhova M V, Trifonov A, Shih Y 2002 Phys. Rev. Lett. 88 183601
[38] Li B H, Xu Y G, An L, Lin Q L, Zhu H F, Lin F K, Li Y F 2014 Opt. Lett. 39 2443
[39] Li B H, Xu Y G, Zhu H F, Lin Q L, An L, Lin F K, Li Y F 2014 J. Opt. Soc. Am. B 31 2511
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