## Near-infrared Hong-Ou-Mandel interference on a silicon quantum photonic chip |

Optics Express, Vol. 21, Issue 4, pp. 5014-5024 (2013)

http://dx.doi.org/10.1364/OE.21.005014

Acrobat PDF (1580 KB)

### Abstract

Near-infrared Hong-Ou-Mandel quantum interference is observed in silicon nanophotonic directional couplers with raw visibilities on-chip at 90.5%. Spectrally-bright 1557-nm two-photon states are generated in a periodically-poled KTiOPO_{4} waveguide chip, serving as the entangled photon source and pumped with a self-injection locked laser, for the photon statistical measurements. Efficient four-port coupling in the communications C-band and in the high-index-contrast silicon photonics platform is demonstrated, with matching theoretical predictions of the quantum interference visibility. Constituents for the residual quantum visibility imperfection are examined, supported with theoretical analysis of the sequentially-triggered multipair biphoton, towards scalable high-bitrate quantum information processing and communications. The on-chip HOM interference is useful towards scalable high-bitrate quantum information processing and communications.

© 2013 OSA

## 1. Introduction

1. C. Weedbrook, S. Pirandola, S. Lloyd, and T. C. Ralph, “Quantum cryptography approaching the classical limit,” Phys. Rev. Lett. **105**(11), 110501 (2010). [CrossRef] [PubMed]

5. V. Scarani, A. Acín, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. Rev. Lett. **92**(5), 057901 (2004). [CrossRef] [PubMed]

8. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science **329**(5998), 1500–1503 (2010). [CrossRef] [PubMed]

9. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics **1**(3), 165–171 (2007). [CrossRef]

10. M. A. Albota, F. N. C. Wong, and J. H. Shapiro, “Polarization-independent frequency conversion for quantum optical communication,” J. Opt. Soc. Am. B **23**(5), 918–924 (2006). [CrossRef]

11. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of nonclassical light on a chip via photon-induced tunneling and blockade,” Nat. Phys. **4**(11), 859–863 (2008). [CrossRef]

12. J. Gao, F. W. Sun, and C. W. Wong, “Implementation scheme for quantum controlled phase-flip gate through quantum dot in slow-light photonic crystal waveguide,” Appl. Phys. Lett. **93**(15), 151108 (2008). [CrossRef]

16. Y. F. Xiao, J. Gao, X. Yang, R. Bose, G. C. Guo, and C. W. Wong, “Nanocrystals in silicon photonic crystal standing-wave cavities as spin-photon phase gates for quantum information processing,” Appl. Phys. Lett. **91**(15), 151105 (2007). [CrossRef]

17. F. W. Sun, B. H. Liu, C. W. Wong, and G. C. Guo, “Permutation asymmetry inducing entanglement between degrees of freedom in multiphoton states,” Phys. Rev. A **78**(1), 015804 (2008). [CrossRef]

20. A. Dousse, J. Suffczyński, A. Beveratos, O. Krebs, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, “Ultrabright source of entangled photon pairs,” Nature **466**(7303), 217–220 (2010). [CrossRef] [PubMed]

21. J. D. Franson, “Two-photon interferometry over large distances,” Phys. Rev. A **44**(7), 4552–4555 (1991). [CrossRef] [PubMed]

22. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. **59**(18), 2044–2046 (1987). [CrossRef] [PubMed]

23. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. **75**(24), 4337–4341 (1995). [CrossRef] [PubMed]

24. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics **3**(6), 346–350 (2009). [CrossRef]

29. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science **320**(5876), 646–649 (2008). [CrossRef] [PubMed]

26. A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun **2**, 566 (2011). [CrossRef] [PubMed]

29. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science **320**(5876), 646–649 (2008). [CrossRef] [PubMed]

31. F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, and C. F. RoosJ. Eschner and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature **422**, 408-411(2003). [CrossRef] [PubMed]

29. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science **320**(5876), 646–649 (2008). [CrossRef] [PubMed]

24. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics **3**(6), 346–350 (2009). [CrossRef]

25. D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O'Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. **14**(4), 045003 (2012). [CrossRef]

32. M. D. Birowosuto, H. Sumikura, S. Matsuo, H. Taniyama, P. J. van Veldhoven, R. Nötzel, and M. Notomi, “Fast Purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling,” Sci Rep **2**, 321 (2012). [CrossRef] [PubMed]

34. M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Fiber-based cryogenic and time-resolved spectroscopy of PbS quantum dots,” Opt. Express **19**(3), 1786–1793 (2011). [CrossRef] [PubMed]

_{4}waveguides (PPKTP) as the entangled photon source, we demonstrate raw quantum visibilities up to 90.5% on-chip—one of the highest visibilities observed in the silicon CMOS-compatible platform. Furthermore, we evaluate the various sources of residual visibility degradation including multiphoton pairs, chip-scale excess loss and non-ideal splitting ratios, and polarization effects. The observed interference visibility matches our theoretical predictions, for the different symmetric and asymmetric integrated directional couplers examined.

## 2. Near-infrared Hong-Ou-Mandel experimental setup

_{1}and D

_{2}from Princeton Lightwave, with ~300 ps gate widths and ~20% detection efficiencies. The clock of D

_{1}is set to 15 MHz, and its output signal triggers D

_{2}. This allows the coincidence rate to be read directly from the D

_{2}counting rate, with the optical delay calibrated to compensate the electronic delay.

## 3. Design and fabrication of silicon chip-scale two-photon interference directional coupler

*g*), cross-over coupling lengths (

*l*) and waveguide widths (

_{c}*w*) are illustrated for the optimal coupling length and splitting ratios. The silicon waveguides are designed with a 250-nm thickness and for operation at 1550-nm wavelengths.

37. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express **8**(3), 173–190 (2001). [CrossRef] [PubMed]

*l*of the two waveguides is then represented as

_{c}*π*between the symmetric mode and anti-symmetric mode [38] allows for complete crossover from one waveguide to another [39

39. R. Chatterjee, M. Yu, A. Stein, D. L. Kwong, L. C. Kimerling, and C. W. Wong, “Demonstration of a hitless bypass switch using nanomechanical perturbation for high-bitrate transparent networks,” Opt. Express **18**(3), 3045–3058 (2010). [CrossRef] [PubMed]

*l*is the effective coupler length for the incoming and outgoing bend regions, which can be estimated by an integral of coupling length as a function of gap size along the bending region and computed to be 3-um in our designs (Fig. 1(b)). In addition to the MPB and integral computations, the designs were examined with both rigorous finite-difference time-domain computations and semi-vectorial BeamPROP method from RSoft. With the birefringent character of the directional coupler, we work with the TM mode rather than the TE mode due to its shorter coupling length and greater length control sensitivity. Furthermore, our simulation models and experimental measurements confirm lower loss in the TM mode for straight waveguide as well as the directional coupler regime due to lower electromagnetic field amplitude at the sidewalls (typically rougher than the top and bottom surfaces) [40

_{eff}40. S. Afifi and R. Dusséaux, “Statistical study of radiation loss from planar optical waveguides: the curvilinear coordinate method and the small perturbation method,” J. Opt. Soc. Am. A **27**(5), 1171–1184 (2010). [CrossRef] [PubMed]

_{V=2SR/(1+SR2)}[24

24. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics **3**(6), 346–350 (2009). [CrossRef]

44. J. Liang and T. B. Pittman, “Compensating for beamsplitter asymmetries in quantum interference experiments,” J. Opt. Soc. Am. B **27**(2), 350–353 (2010). [CrossRef]

25. D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O'Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. **14**(4), 045003 (2012). [CrossRef]

26. A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun **2**, 566 (2011). [CrossRef] [PubMed]

30. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature **426**(6964), 264–267 (2003). [CrossRef] [PubMed]

31. F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, and C. F. RoosJ. Eschner and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature **422**, 408-411(2003). [CrossRef] [PubMed]

45. Z. Zhao, A. N. Zhang, X. Q. Zhou, Y. A. Chen, C. Y. Lu, A. Karlsson, and J. W. Pan, “Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation,” Phys. Rev. Lett. **95**(3), 030502 (2005). [CrossRef] [PubMed]

46. L. Bartůšková, M. Dusek, A. Cernoch, J. Soubusta, and J. Fiurásek, “Fiber-optics implementation of an asymmetric phase-covariant quantum cloner,” Phys. Rev. Lett. **99**(12), 120505 (2007). [CrossRef] [PubMed]

47. K. Sanaka, K. J. Resch, and A. Zeilinger, “Filtering out photonic Fock states,” Phys. Rev. Lett. **96**(8), 083601 (2006). [CrossRef] [PubMed]

48. K. J. Resch, J. L. O’Brien, T. J. Weinhold, K. Sanaka, B. P. Lanyon, N. K. Langford, and A. G. White, “Entanglement generation by Fock-state filtration,” Phys. Rev. Lett. **98**(20), 203602 (2007). [CrossRef] [PubMed]

49. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. **28**(15), 1302–1304 (2003). [CrossRef] [PubMed]

## 4. 1557.8-nm Hong-Ou-Mandel visibilities on-chip

50. A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental evaluation of a two-photon wave packet in type-II parametric downconversion,” J. Opt. Soc. Am. B **12**(5), 859–862 (1995). [CrossRef]

51. O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. Wong, and F. X. Kärtner, “Two-photon coincident-frequency entanglement via extended phase matching,” Phys. Rev. Lett. **94**(8), 083601 (2005). [CrossRef] [PubMed]

## 5. Degradation of on-chip HOM interference visibility

35. T. Zhong, F. N. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO^{4} waveguide,” Opt. Express **17**(14), 12019–12030 (2009). [CrossRef] [PubMed]

*n*photon pairs generated in the gate time

*τ*obeys Poisson distribution:

*α*is mean pair number within the gate [52]. To maximize the coincidences, the photon transmitted to the triggered detector is delayed by half the gate time (

*τ/2)*to guarantee it will always appear within the gate whenever the other photon arrives first (Fig. 4(a) ). To calculate the swing coincidences, or the probability of the coincidence event when two photons are relatively delayed and totally distinguishable, we consider only one photon pair per gate to neglect higher order terms (Fig. 4(a)):where

*η*denotes the overall detection efficiency. To calculate the probability of coincidence when two photons are indistinguishable, we consider only one and two photon pairs within the gate. Here we notice that even when there is only one photon pair within the detection gate of triggering detector D

_{1}, there are still some coincidences contributions (Fig. 4(b)):where the possible photon pair within the leak window is considered (Fig. 4(b)) due to gate time mismatch. If there are two photon pairs within the gate window of D

_{1}, there are four possible situations: (a) the first photon pair is in the path to D

_{1}, and second photon pair is in the path to D

_{2}(Fig. 4(c)); (b) the first photon pair is to D

_{2}, and the second photon pair is to D

_{1}; (c) both photon pairs are to D

_{2}; (d) both photon pairs are to D

_{1}. Thus we have

*A*and

_{tt}*A*

_{rr}_{}causing the Hong-Ou-Mandel dip. When the on-chip directional coupler has excess loss

*L*, however, the inherent phase shift will not be 180˚ anymore. Performing a matrix optics calculation, we have the inherent phase shift

_{excess}_{ψ}as

_{cos(ψ)=Lexcess2(1+SR)2/2SR−1,}or

_{2Lexcess2−1}for an ideal symmetric (SR = 0-dB) directional coupler. The visibility reduction caused by the excess loss of the directional coupler can therefore be expressed asHere we estimate that the 0.1-dB excess loss via vertical scattering from the chip even with ideal sidewalls, or a 170˚ internal phase shift, computed by FDTD method as noted in the earlier design section, in the balanced directional coupler will reduce the visibility by 1.5%. This excess loss will be larger when including fabrication disorder-induced losses. For unbalanced directional coupler, the internal phase shift will be further away from 180˚ with corresponding reductions in the visibility. Formally, the output annihilation and creation operators of a lossy directional coupler have to include Langevin noise operators to maintain the commutation relation, while at the same time inducing additional phase shifts [53

53. S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A **57**(3), 2134–2145 (1998). [CrossRef]

## 6. Conclusion

## Acknowledgments

## References and links

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16. | Y. F. Xiao, J. Gao, X. Yang, R. Bose, G. C. Guo, and C. W. Wong, “Nanocrystals in silicon photonic crystal standing-wave cavities as spin-photon phase gates for quantum information processing,” Appl. Phys. Lett. |

17. | F. W. Sun, B. H. Liu, C. W. Wong, and G. C. Guo, “Permutation asymmetry inducing entanglement between degrees of freedom in multiphoton states,” Phys. Rev. A |

18. | T. Yu and J. H. Eberly, “Sudden death of entanglement,” Science |

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46. | L. Bartůšková, M. Dusek, A. Cernoch, J. Soubusta, and J. Fiurásek, “Fiber-optics implementation of an asymmetric phase-covariant quantum cloner,” Phys. Rev. Lett. |

47. | K. Sanaka, K. J. Resch, and A. Zeilinger, “Filtering out photonic Fock states,” Phys. Rev. Lett. |

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49. | V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. |

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51. | O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. Wong, and F. X. Kärtner, “Two-photon coincident-frequency entanglement via extended phase matching,” Phys. Rev. Lett. |

52. | T. Zhong, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO₄ waveguide,” S.M. thesis (Massachusetts Institute of Technology, 2009). |

53. | S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(230.7370) Optical devices : Waveguides

(270.5290) Quantum optics : Photon statistics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: December 3, 2012

Revised Manuscript: January 5, 2013

Manuscript Accepted: January 7, 2013

Published: February 21, 2013

**Citation**

Xinan Xu, Zhenda Xie, Jiangjun Zheng, Junlin Liang, Tian Zhong, Mingbin Yu, Serdar Kocaman, Guo-Qiang Lo, Dim-Lee Kwong, Dirk R. Englund, Franco N. C. Wong, and Chee Wei Wong, "Near-infrared Hong-Ou-Mandel interference on a silicon quantum photonic chip," Opt. Express **21**, 5014-5024 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-5014

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### References

- C. Weedbrook, S. Pirandola, S. Lloyd, and T. C. Ralph, “Quantum cryptography approaching the classical limit,” Phys. Rev. Lett.105(11), 110501 (2010). [CrossRef] [PubMed]
- C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” presented at International Conference on Computers, Systems and Signal Processing, Bangalore, India, Dec 10–12, 1984.
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002). [CrossRef]
- A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991). [CrossRef] [PubMed]
- V. Scarani, A. Acín, G. Ribordy, and N. Gisin, “Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations,” Phys. Rev. Lett.92(5), 057901 (2004). [CrossRef] [PubMed]
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