Abstract

Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components integrated on a single chip, are crucial for efficiently implementing quantum information processing schemes. We present a set of basic transformations that are useful for manipulating modal qubits in Ti:LiNbO3 photonic quantum circuits. These include the mode analyzer, a device that separates the even and odd components of a state into two separate spatial paths; the mode rotator, which rotates the state by an angle in mode space; and modal Pauli spin operators that effect related operations. We also describe the design of a deterministic, two-qubit, single-photon, CNOT gate, a key element in certain sets of universal quantum logic gates. It is implemented as a Ti:LiNbO3 photonic quantum circuit in which the polarization and mode number of a single photon serve as the control and target qubits, respectively. It is shown that the effects of dispersion in the CNOT circuit can be mitigated by augmenting it with an additional path. The performance of all of these components are confirmed by numerical simulations. The implementation of these transformations relies on selective and controllable power coupling among single- and two-mode waveguides, as well as the polarization sensitivity of the Pockels coefficients in LiNbO3.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. F. Saleh, B. E. A. Saleh, and M. C. Teich, “Modal, spectral, and polarization entanglement in guided-wave parametric down-conversion,” Phys. Rev. A 79, 053842 (2009).
    [CrossRef]
  2. M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
    [CrossRef]
  3. M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479–7488 (2007).
    [CrossRef] [PubMed]
  4. M. Avenhaus, M. V. Chekhova, L. A. Krivitsky, G. Leuchs, and C. Silberhorn, “Experimental verification of high spectral entanglement for pulsed waveguided spontaneous parametric down-conversion,” Phys. Rev. A 79, 043836 (2009).
    [CrossRef]
  5. P. J. Mosley, A. Christ, A. Eckstein, and C. Silberhorn, “Direct measurement of the spatial-spectral structure of waveguided parametric down-conversion,” Phys. Rev. Lett. 103, 233901 (2009).
    [CrossRef]
  6. T. Zhong, F. N. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber coupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019–12030 (2009).
  7. J. Chen, A. J. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chip-scale quantum information processing,” Opt. Express 17, 6727–6740 (2009).
    [CrossRef]
  8. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
    [CrossRef] [PubMed]
  9. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
    [CrossRef]
  10. C. H. Bennett, and P. W. Shor, “Quantum information theory,” IEEE Trans. Inf. Theory 44, 2724–2742 (1998).
    [CrossRef]
  11. M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
  12. J. L. O’Brien, A. Furusawa, and J. Vuˇckovi’c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
    [CrossRef]
  13. A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
    [CrossRef]
  14. G. Cincotti, “Prospects on planar quantum computing,” J. Lightwave Technol. 27, 5755–5766 (2009).
    [CrossRef]
  15. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
    [CrossRef] [PubMed]
  16. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw–Hill, 1989).
  17. B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).
  18. A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti:indiffused lithium niobate waveguides,” Appl. Phys. Lett. 84, 4430–4432 (2004).
    [CrossRef]
  19. Y. L. Lee, C. Jung, Y.-C. Noh, M. Park, C. Byeon, D.-K. Ko, and J. Lee, “Channel-selective wavelength conversion and tuning in periodically poled Ti:LiNbO3 waveguides,” Opt. Express 12, 2649–2655 (2004).
    [CrossRef] [PubMed]
  20. S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
    [CrossRef]
  21. H. Guillet de Chatellus, A. V. Sergienko, B. E. A. Saleh, M. C. Teich, and G. Di Giuseppe, “Non-collinear and non-degenerate polarization-entangled photon generation via concurrent type-I parametric downconversion in PPLN,” Opt. Express 14, 10060–10072 (2006).
  22. R. C. Alferness, and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
    [CrossRef]
  23. R. C. Alferness, “Efficient waveguide electro-optic TETM mode converter/wavelength filter,” Appl. Phys. Lett. 36, 513–515 (1980).
    [CrossRef]
  24. J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36, R1–R16 (2003).
    [CrossRef]
  25. D. Runde, S. Brunken, S. Breuer, and D. Kip, “Integrated-optical add/drop multiplexer for DWDM in lithium niobate,” Appl. Phys. B 88, 83–88 (2007).
    [CrossRef]
  26. D. Runde, S. Breuer, and D. Kip, “Mode-selective coupler for wavelength multiplexing using LiNbO3:Ti optical waveguides,” Cent. Eur. J. Phys. 6, 588–592 (2008).
    [CrossRef]
  27. R. V. Schmidt, and H. Kogelnik, “Electro-optically switched coupler with stepped Db reversal using Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 28, 503–506 (1976).
    [CrossRef]
  28. H. Kogelnik, and R. V. Schmidt, “Switched directional couplers with alternating Db,” IEEE J. Quantum Electron. 12, 396–401 (1976).
    [CrossRef]
  29. D. P. DiVincenzo, “Two-bit gates are universal for quantum computation,” Phys. Rev. A 51, 1015–1022 (1995).
    [CrossRef] [PubMed]
  30. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
    [CrossRef] [PubMed]
  31. M. Fiorentino and F. N. C. Wong, “Deterministic controlled-NOT gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93, 070 502 (2004).
    [CrossRef]
  32. N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070 501 (2010).
    [CrossRef]
  33. S. Glancy, H. M. Vasconcelos, and T. C. Ralph, “Transmission of optical coherent-state qubits,” Phys. Rev. A 70, 022 317 (2004).
    [CrossRef]
  34. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [CrossRef]
  35. K. K. Wong, ed., Properties of Lithium Niobate (Institution of Electrical Engineers, 2002).
  36. M. D. Feit, J. A. Fleck, Jr., and L. McCaughan, “Comparison of calculated and measured performance of diffused channel-waveguide couplers,” J. Opt. Soc. Am. 73, 1296–1304 (1983).
    [CrossRef]
  37. S. K. Korotky, and R. C. Alferness, “Ti:LiNbO3 integrated optic technology,” in Integrated Optical Circuits and Components: Design and Applications, L. D. Hutcheson, ed. (Marcel Dekker, 1987).
  38. G. B. Hocker, and W. K. Burns, “Mode dispersion in diffused channel waveguides by the effective index method,” Appl. Opt. 16, 113–118 (1977).
    [CrossRef] [PubMed]
  39. C. H. Bennett, and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the International Conference on Computers, Systems & Signal Processing, pp. 175–179 (Institute of Electrical and Electronics Engineers, 1984).
  40. A. F. Abouraddy, T. Yarnall, B. E. A. Saleh, and M. C. Teich, “Violation of Bell’s inequality with continuous spatial variables,” Phys. Rev. A 75, 052 114 (2007).
    [CrossRef]
  41. T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250 502 (2007).
    [CrossRef]
  42. T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170 408 (2007).
    [CrossRef]
  43. B. E. A. Saleh, and M. C. Teich, “Sub-Poisson light generation by selective deletion from cascaded atomic emissions,” Opt. Commun. 52, 429–432 (1985).
    [CrossRef]
  44. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [CrossRef]
  45. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Degree of entanglement for two qubits,” Phys. Rev. A 64, 050 101 (2001).
    [CrossRef]
  46. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn,, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133 601 (2008).
    [CrossRef]
  47. Z. H. Levine, J. Fan, J. Chen, A. Ling, and A. Migdall, “Heralded, pure-state single-photon source based on a Potassium Titanyl Phosphate waveguide,” Opt. Express 18, 3708–3718 (2010).
    [CrossRef] [PubMed]
  48. W. P. Grice, A. B. U’Ren, and I. A.Walmsley, “Eliminating frequency and space–time correlations in multiphoton states,” Phys. Rev. A 64, 063 815 (2001).
    [CrossRef]
  49. Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion,” Phys. Rev. A 67, 053 810 (2003).
    [CrossRef]
  50. Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70, 052 317 (2004).
    [CrossRef]
  51. S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spatial-to-spectral mapping in spontaneous parametric down-conversion,” Phys. Rev. A 70, 043 817 (2004).
    [CrossRef]
  52. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
    [CrossRef]
  53. L. L. Buhl, and R. C. Alferness, “Ti:LiNbO3 waveguide electro-optic beam combiner,” Opt. Lett. 12, 778–780 (1987).
    [CrossRef] [PubMed]
  54. Y. Mitsumori, J. A. Vaccaro, S. M. Barnett, E. Andersson, A. Hasegawa, M. Takeoka, and M. Sasaki, “Experimental demonstration of quantum source coding,” Phys. Rev. Lett. 91, 217 902 (2003).
    [CrossRef]
  55. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
    [CrossRef]
  56. A. Djupsjobacka, and B. Lagerstrom, “Stabilization of a Ti:LiNbO3 directional coupler,” Appl. Opt. 28, 2205–2206 (1989).
    [CrossRef] [PubMed]
  57. F. Lucchi, D. Janner, M. Belmonte, S. Balsamo, M. Villa, S. Giurgola, P. Vergani, and V. Pruneri, “Very low voltage single drive domain inverted LiNbO3 integrated electro-optic modulator,” Opt. Express 15, 10 739–10 743 (2007).
    [CrossRef]

2010 (3)

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[CrossRef]

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

Z. H. Levine, J. Fan, J. Chen, A. Ling, and A. Migdall, “Heralded, pure-state single-photon source based on a Potassium Titanyl Phosphate waveguide,” Opt. Express 18, 3708–3718 (2010).
[CrossRef] [PubMed]

2009 (4)

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

J. L. O’Brien, A. Furusawa, and J. Vuˇckovi’c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
[CrossRef]

G. Cincotti, “Prospects on planar quantum computing,” J. Lightwave Technol. 27, 5755–5766 (2009).
[CrossRef]

2008 (2)

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

D. Runde, S. Breuer, and D. Kip, “Mode-selective coupler for wavelength multiplexing using LiNbO3:Ti optical waveguides,” Cent. Eur. J. Phys. 6, 588–592 (2008).
[CrossRef]

2007 (2)

2004 (2)

A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti:indiffused lithium niobate waveguides,” Appl. Phys. Lett. 84, 4430–4432 (2004).
[CrossRef]

Y. L. Lee, C. Jung, Y.-C. Noh, M. Park, C. Byeon, D.-K. Ko, and J. Lee, “Channel-selective wavelength conversion and tuning in periodically poled Ti:LiNbO3 waveguides,” Opt. Express 12, 2649–2655 (2004).
[CrossRef] [PubMed]

2003 (1)

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36, R1–R16 (2003).
[CrossRef]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

2001 (2)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

1998 (1)

C. H. Bennett, and P. W. Shor, “Quantum information theory,” IEEE Trans. Inf. Theory 44, 2724–2742 (1998).
[CrossRef]

1997 (1)

1995 (2)

1989 (1)

1987 (1)

1985 (1)

B. E. A. Saleh, and M. C. Teich, “Sub-Poisson light generation by selective deletion from cascaded atomic emissions,” Opt. Commun. 52, 429–432 (1985).
[CrossRef]

1983 (1)

1980 (1)

R. C. Alferness, “Efficient waveguide electro-optic TETM mode converter/wavelength filter,” Appl. Phys. Lett. 36, 513–515 (1980).
[CrossRef]

1978 (1)

R. C. Alferness, and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[CrossRef]

1977 (1)

1976 (2)

R. V. Schmidt, and H. Kogelnik, “Electro-optically switched coupler with stepped Db reversal using Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 28, 503–506 (1976).
[CrossRef]

H. Kogelnik, and R. V. Schmidt, “Switched directional couplers with alternating Db,” IEEE J. Quantum Electron. 12, 396–401 (1976).
[CrossRef]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

Alferness, R. C.

L. L. Buhl, and R. C. Alferness, “Ti:LiNbO3 waveguide electro-optic beam combiner,” Opt. Lett. 12, 778–780 (1987).
[CrossRef] [PubMed]

R. C. Alferness, “Efficient waveguide electro-optic TETM mode converter/wavelength filter,” Appl. Phys. Lett. 36, 513–515 (1980).
[CrossRef]

R. C. Alferness, and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[CrossRef]

Baldi, P.

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

Battle, P.

Beausoleil, R. G.

Bennett, C. H.

C. H. Bennett, and P. W. Shor, “Quantum information theory,” IEEE Trans. Inf. Theory 44, 2724–2742 (1998).
[CrossRef]

Bosenberg, W. R.

Breuer, S.

D. Runde, S. Breuer, and D. Kip, “Mode-selective coupler for wavelength multiplexing using LiNbO3:Ti optical waveguides,” Cent. Eur. J. Phys. 6, 588–592 (2008).
[CrossRef]

D. Runde, S. Brunken, S. Breuer, and D. Kip, “Integrated-optical add/drop multiplexer for DWDM in lithium niobate,” Appl. Phys. B 88, 83–88 (2007).
[CrossRef]

Brunken, S.

D. Runde, S. Brunken, S. Breuer, and D. Kip, “Integrated-optical add/drop multiplexer for DWDM in lithium niobate,” Appl. Phys. B 88, 83–88 (2007).
[CrossRef]

Buhl, L. L.

Burns, W. K.

Busacca, A. C.

A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti:indiffused lithium niobate waveguides,” Appl. Phys. Lett. 84, 4430–4432 (2004).
[CrossRef]

Byeon, C.

Byer, R. L.

Chen, J.

Cincotti, G.

Cryan, M. J.

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

De Micheli, M.

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

De Riedmatten, H.

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

Di Giuseppe, G.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[CrossRef]

DiVincenzo, D. P.

D. P. DiVincenzo, “Two-bit gates are universal for quantum computation,” Phys. Rev. A 51, 1015–1022 (1995).
[CrossRef] [PubMed]

Djupsjobacka, A.

Eason, R. W.

A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti:indiffused lithium niobate waveguides,” Appl. Phys. Lett. 84, 4430–4432 (2004).
[CrossRef]

Eckardt, R. C.

Fan, J.

Feit, M. D.

Fejer, M. M.

Fiorentino, M.

Fleck, J. A.

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vuˇckovi’c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

Hocker, G. B.

Hukriede, J.

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36, R1–R16 (2003).
[CrossRef]

Jelezko, F.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

Jundt, D. H.

Jung, C.

Kip, D.

D. Runde, S. Breuer, and D. Kip, “Mode-selective coupler for wavelength multiplexing using LiNbO3:Ti optical waveguides,” Cent. Eur. J. Phys. 6, 588–592 (2008).
[CrossRef]

D. Runde, S. Brunken, S. Breuer, and D. Kip, “Integrated-optical add/drop multiplexer for DWDM in lithium niobate,” Appl. Phys. B 88, 83–88 (2007).
[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36, R1–R16 (2003).
[CrossRef]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Ko, D.-K.

Kogelnik, H.

R. V. Schmidt, and H. Kogelnik, “Electro-optically switched coupler with stepped Db reversal using Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 28, 503–506 (1976).
[CrossRef]

H. Kogelnik, and R. V. Schmidt, “Switched directional couplers with alternating Db,” IEEE J. Quantum Electron. 12, 396–401 (1976).
[CrossRef]

Ladd, T. D.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

Laflamme, R.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Lagerstrom, B.

Lee, J.

Lee, Y. L.

Levine, Z. H.

Ling, A.

Mailis, S.

A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti:indiffused lithium niobate waveguides,” Appl. Phys. Lett. 84, 4430–4432 (2004).
[CrossRef]

Matthews, J. C. F.

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
[CrossRef]

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

McCaughan, L.

Migdall, A.

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Monroe, C.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

Munro, M. W.

Myers, L. E.

Nakamura, Y.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

Noh, Y.-C.

O’Brien, J. L.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
[CrossRef]

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

J. L. O’Brien, A. Furusawa, and J. Vuˇckovi’c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

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

Ostrowsky, D. B.

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

Park, M.

Pierce, J. W.

Politi, A.

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

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
[CrossRef]

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

Rarity, J. G.

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

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Roberts, T. D.

Runde, D.

D. Runde, S. Breuer, and D. Kip, “Mode-selective coupler for wavelength multiplexing using LiNbO3:Ti optical waveguides,” Cent. Eur. J. Phys. 6, 588–592 (2008).
[CrossRef]

D. Runde, S. Brunken, S. Breuer, and D. Kip, “Integrated-optical add/drop multiplexer for DWDM in lithium niobate,” Appl. Phys. B 88, 83–88 (2007).
[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36, R1–R16 (2003).
[CrossRef]

Saleh, B. E. A.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[CrossRef]

B. E. A. Saleh, and M. C. Teich, “Sub-Poisson light generation by selective deletion from cascaded atomic emissions,” Opt. Commun. 52, 429–432 (1985).
[CrossRef]

Saleh, M. F.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[CrossRef]

Schmidt, R. V.

R. C. Alferness, and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[CrossRef]

R. V. Schmidt, and H. Kogelnik, “Electro-optically switched coupler with stepped Db reversal using Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 28, 503–506 (1976).
[CrossRef]

H. Kogelnik, and R. V. Schmidt, “Switched directional couplers with alternating Db,” IEEE J. Quantum Electron. 12, 396–401 (1976).
[CrossRef]

Shor, P. W.

C. H. Bennett, and P. W. Shor, “Quantum information theory,” IEEE Trans. Inf. Theory 44, 2724–2742 (1998).
[CrossRef]

Sones, C. L.

A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti:indiffused lithium niobate waveguides,” Appl. Phys. Lett. 84, 4430–4432 (2004).
[CrossRef]

Spillane, S. M.

Stefanov, A.

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

Tanzilli, S.

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

Teich, M. C.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[CrossRef]

B. E. A. Saleh, and M. C. Teich, “Sub-Poisson light generation by selective deletion from cascaded atomic emissions,” Opt. Commun. 52, 429–432 (1985).
[CrossRef]

Thompson, M. G.

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

Vu?ckovi’c, J.

J. L. O’Brien, A. Furusawa, and J. Vuˇckovi’c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

Yu, S.

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

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

D. Runde, S. Brunken, S. Breuer, and D. Kip, “Integrated-optical add/drop multiplexer for DWDM in lithium niobate,” Appl. Phys. B 88, 83–88 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

R. V. Schmidt, and H. Kogelnik, “Electro-optically switched coupler with stepped Db reversal using Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 28, 503–506 (1976).
[CrossRef]

R. C. Alferness, and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[CrossRef]

R. C. Alferness, “Efficient waveguide electro-optic TETM mode converter/wavelength filter,” Appl. Phys. Lett. 36, 513–515 (1980).
[CrossRef]

A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti:indiffused lithium niobate waveguides,” Appl. Phys. Lett. 84, 4430–4432 (2004).
[CrossRef]

Cent. Eur. J. Phys. (1)

D. Runde, S. Breuer, and D. Kip, “Mode-selective coupler for wavelength multiplexing using LiNbO3:Ti optical waveguides,” Cent. Eur. J. Phys. 6, 588–592 (2008).
[CrossRef]

Electron. Lett. (1)

S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. 37, 26–28 (2001).
[CrossRef]

IEEE J. Quantum Electron. (2)

H. Kogelnik, and R. V. Schmidt, “Switched directional couplers with alternating Db,” IEEE J. Quantum Electron. 12, 396–401 (1976).
[CrossRef]

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
[CrossRef]

IEEE Photon. J. (1)

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[CrossRef]

IEEE Trans. Inf. Theory (1)

C. H. Bennett, and P. W. Shor, “Quantum information theory,” IEEE Trans. Inf. Theory 44, 2724–2742 (1998).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. Phys. D Appl. Phys. (1)

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D Appl. Phys. 36, R1–R16 (2003).
[CrossRef]

Nat. Photonics (2)

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

J. L. O’Brien, A. Furusawa, and J. Vuˇckovi’c, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

Nature (2)

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

B. E. A. Saleh, and M. C. Teich, “Sub-Poisson light generation by selective deletion from cascaded atomic emissions,” Opt. Commun. 52, 429–432 (1985).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

D. P. DiVincenzo, “Two-bit gates are universal for quantum computation,” Phys. Rev. A 51, 1015–1022 (1995).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Science (1)

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

Other (26)

M. F. Saleh, B. E. A. Saleh, and M. C. Teich, “Modal, spectral, and polarization entanglement in guided-wave parametric down-conversion,” Phys. Rev. A 79, 053842 (2009).
[CrossRef]

M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

M. Avenhaus, M. V. Chekhova, L. A. Krivitsky, G. Leuchs, and C. Silberhorn, “Experimental verification of high spectral entanglement for pulsed waveguided spontaneous parametric down-conversion,” Phys. Rev. A 79, 043836 (2009).
[CrossRef]

P. J. Mosley, A. Christ, A. Eckstein, and C. Silberhorn, “Direct measurement of the spatial-spectral structure of waveguided parametric down-conversion,” Phys. Rev. Lett. 103, 233901 (2009).
[CrossRef]

T. Zhong, F. N. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber coupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019–12030 (2009).

J. Chen, A. J. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chip-scale quantum information processing,” Opt. Express 17, 6727–6740 (2009).
[CrossRef]

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw–Hill, 1989).

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

H. Guillet de Chatellus, A. V. Sergienko, B. E. A. Saleh, M. C. Teich, and G. Di Giuseppe, “Non-collinear and non-degenerate polarization-entangled photon generation via concurrent type-I parametric downconversion in PPLN,” Opt. Express 14, 10060–10072 (2006).

K. K. Wong, ed., Properties of Lithium Niobate (Institution of Electrical Engineers, 2002).

S. K. Korotky, and R. C. Alferness, “Ti:LiNbO3 integrated optic technology,” in Integrated Optical Circuits and Components: Design and Applications, L. D. Hutcheson, ed. (Marcel Dekker, 1987).

M. Fiorentino and F. N. C. Wong, “Deterministic controlled-NOT gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93, 070 502 (2004).
[CrossRef]

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070 501 (2010).
[CrossRef]

S. Glancy, H. M. Vasconcelos, and T. C. Ralph, “Transmission of optical coherent-state qubits,” Phys. Rev. A 70, 022 317 (2004).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Degree of entanglement for two qubits,” Phys. Rev. A 64, 050 101 (2001).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn,, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133 601 (2008).
[CrossRef]

C. H. Bennett, and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of the International Conference on Computers, Systems & Signal Processing, pp. 175–179 (Institute of Electrical and Electronics Engineers, 1984).

A. F. Abouraddy, T. Yarnall, B. E. A. Saleh, and M. C. Teich, “Violation of Bell’s inequality with continuous spatial variables,” Phys. Rev. A 75, 052 114 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250 502 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170 408 (2007).
[CrossRef]

Y. Mitsumori, J. A. Vaccaro, S. M. Barnett, E. Andersson, A. Hasegawa, M. Takeoka, and M. Sasaki, “Experimental demonstration of quantum source coding,” Phys. Rev. Lett. 91, 217 902 (2003).
[CrossRef]

F. Lucchi, D. Janner, M. Belmonte, S. Balsamo, M. Villa, S. Giurgola, P. Vergani, and V. Pruneri, “Very low voltage single drive domain inverted LiNbO3 integrated electro-optic modulator,” Opt. Express 15, 10 739–10 743 (2007).
[CrossRef]

W. P. Grice, A. B. U’Ren, and I. A.Walmsley, “Eliminating frequency and space–time correlations in multiphoton states,” Phys. Rev. A 64, 063 815 (2001).
[CrossRef]

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion,” Phys. Rev. A 67, 053 810 (2003).
[CrossRef]

Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70, 052 317 (2004).
[CrossRef]

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Spatial-to-spectral mapping in spontaneous parametric down-conversion,” Phys. Rev. A 70, 043 817 (2004).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Cross-sectional view of the fabrication of a diffused channel Ti:LiNbO3 waveguide (not to scale). A thin film of titanium of thickness δ ≈ 100 nm and width w is diffused into a z-cut, y-propagating LiNbO3 crystal. The diffusion length D = 3µm.

Fig. 2.
Fig. 2.

(a) Sketch of a photonic circuit that serves as a mode analyzer (not to scale). It is implemented by bringing a single-mode waveguide (SMW) of width w 2 and length L 2 into proximity with a two-mode waveguide (TMW) of width w 1. The two waveguides are separated by a distance b 1. An S-bend waveguide of initial and final width w 2, and bending length Lb , is attached to the end of the SMW. The center-to-center separation between the output of the S-bend and the TMW is denoted S. All S-bends considered in this paper have dimensions Lb = 10 mm and S = 127µm (the standard spatial separation [26]). The odd mode is separated and delivered as an even distribution. (b) Sketch of a mode analyzer (not to scale) that separates the odd mode and delivers it as an odd distribution. It is more complex than the design presented in (a) because it incorporates a second TMW, again of width w 1, that is brought into proximity with a SMW of width w 2 and length L 2 placed at the output of the S-bend. These two waveguides are again separated by a distance b 1. (c) Sketch of a photonic circuit (not to scale) that changes the sign of the odd mode while leaving the even mode intact, thereby implementing the modal Pauli spin operator σz . An electro-optic phase modulator is used to compensate for any unintended differences in the phase delays encountered by the even and odd modes as they transit the circuit.

Fig. 3.
Fig. 3.

(a) Dependencies of the normalized propagation constants β of the fundamental (m = 0) and first-order (m = 1) modes on the widths w of the diffused channel Ti:LiNbO3 waveguides. The input wave has wavelength λ = 0.812µm and TM polarization. The solid curves were obtained using the effective-index method described in [38], whereas the plus signs were computed using the software package RSoft. The dotted vertical lines represent the desired widths w 1 and w 2. (b) Simulated performance of a mode analyzer that takes the form displayed in Fig. 2(a). The blue curve represents the evolution with distance of the normalized amplitude of the odd mode in a TMW of width w 1 = 5.6µm, whereas the green curve shows the evolution of the even mode in a SMW of dimensions w 2 = 3.4µm and L 2 = 6.2 mm. The separation between the TMW and the SMW is b 1 = 4µm and the S-bend has dimensions Lb = 10 mm and S = 127µm. The dip in the curve for the SMW is associated with the tapered nature of the S-bend. The results were obtained with the help of the software package RSoft.

Fig. 4.
Fig. 4.

Sketch of a photonic circuit that serves as a mode rotator (not to scale). It is implemented by sandwiching a directional coupler between a mode analyzer and a mode combiner. The coupling length of the directional coupler is π/2κ. To obtain a specified angle of rotation θ, voltages V 1, V 2, and V 3 are applied to the EO directional coupler, the input EO phase modulator, and the output EO phase modulator, respectively.

Fig. 5.
Fig. 5.

Operating voltages for the mode rotator vs. the angle of rotation θ. Voltages V 1 (solid blue curve), V 2 (dashed green curve), and V 3 (dashed-dotted red curve) are applied to the EO directional coupler, the input EO phase modulator, and the output EO phase modulator, respectively. The input has wavelength λ = 0.812 µm and TM polarization. The directional coupler comprises two identical SMWs separated by d = 5µm; each SMW has width 2.2µm and length 1.73 mm. The input and output EO phase modulators have electrode lengths of 5 mm and electrode separations of 5µm. The curves represent theoretical calculations while the symbols represent simulated data obtained using the RSoft program.

Fig. 6.
Fig. 6.

Sketch of a Ti:LiNbO3 photonic quantum circuit that behaves as a novel deterministic, two-qubit, single-photon, CNOT gate (not to scale). The control qubit is polarization and the target qubit is mode number. The circuit bears some similarity to the mode rotator shown in Fig. 4; both are implemented by sandwiching an EO directional coupler between a mode analyzer and a mode combiner. However, for the CNOT gate, the EO directional coupler comprises a pair of TMWs, whereas the mode rotator uses a conventional EO directional coupler utilizing a pair of SMWs.

Fig. 7.
Fig. 7.

Dependencies of the normalized propagation constants β on the voltage applied to an EO TMW directional coupler comprising two waveguides [WG1 and WG2]. The propagation constants differ for the even and odd modes except at one particular voltage (vertical dashed line) where the even mode in one waveguide can be phase-matched to the odd mode in the other waveguide. The TMWs are identical, each of width 4µm, and they are separated by 4µm. The input has wavelength λ = 0.812µm and TM polarization. The symbols represent simulated data obtained using the RSoft program.

Fig. 8.
Fig. 8.

Sketch of a Ti:LiNbO3 photonic quantum circuit that behaves as a novel dispersionmanaged, deterministic, two-qubit, single-photon, CNOT gate (not to scale). The control qubit is polarization and the target qubit is mode number. The design is more complex than that shown in Fig. 6 because it accommodates dispersion management via path-length adjustments of the upper, middle, and lower paths. An EO TMW directional coupler is sandwiched between polarization-sensitive mode analyzers and polarization-sensitive mode combiners. The lower and upper waveguides of the two-mode directional coupler are denoted WG1 and WG2, respectively. The paths taken by the components of the input state ∣Ψ i 〉 are shown, as is the output state ∣Ψ o 〉.

Fig. 9.
Fig. 9.

Simulation demonstrating the performance of the polarization-dependent mode analyzers and the EO TMW directional coupler associated with the dispersion-managed, deterministic, two-qubit, single-photon, CNOT gate set forth in Fig. 8. The input wavelength is λ = 0.812µm. The TM-mode-analyzer and mode-combiner parameters are w 1 = 5.6µm, w 2 = 3.4µm, b 1 = 4µm, and L 2 = 6.2 mm; the TE-mode-analyzer and mode-combiner parameters are w 2 =3µm, b 1 =4µm, and L 2 =3.7 mm (see Fig. 2 for symbol definitions). The S-bends have dimensions Lb = 10 mm and S = 127µm. The TMW directional-coupler has length L 1 = 2.2 mm, waveguide width w 1 = 5.6µm, electrode separation d = 4µm, and an EO phase-modulator voltage V = 36 V applied to WG2, with WG1 at ground potential. All panels display the spatial evolution of the normalized amplitudes of the interacting modes. (a) The curves display strong coupling between the odd and even modes for TM-polarization inside the TM-mode analyzer. The input odd mode in the TMW is shown in blue and the even mode transferred to the SMW is shown in green [the same color conventions are used in panels (b) and (c)]. The even mode is ultimately coupled to another TMW at the output of the TM-mode analyzer and once again becomes odd. (b) The curves show negligible coupling between the odd and even modes for TE-polarization inside the TM-mode analyzer. (c) The curves display good coupling between the odd and even modes for TE-polarization inside the TE-mode analyzer. At the TE-mode combiner, the even mode in the SMW once again becomes an odd mode in the TMW. Panels (d), (e), and (f) display the performance of the directional coupler for modal inputs that are TM-even, TM-odd, and TE-even, respectively. For a given polarization, the blue and green curves represent the amplitudes of the even [denoted Even(1)] and odd [denoted Odd(1)] modes in WG1, respectively, while the the red and black curves are the amplitudes of the even [denoted Even(2)] and odd [denoted Odd(2)] modes in WG2, respectively. All simulated data in this figure were obtained using the RSoft program.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

T = [ A jB jB * A * ] ,
T = [ cos ( θ 2 ) exp ( j ϕ A ) j sin ( θ 2 ) exp ( j ϕ B ) j sin ( θ 2 ) exp ( j ϕ B ) cos ( θ 2 ) exp ( j ϕ A ) ] ,
T = exp ( j ϕ B ) T 3 T 2 T 1 ,
T 1 = [ 1 0 0 e j Γ 1 ] ; T 2 = [ cos ( θ 2 ) j sin ( θ 2 ) j sin ( θ 2 ) cos ( θ 2 ) ] ; T 3 = [ e j Γ 2 0 0 1 ] ,
T = exp ( j q π 2 ) [ 0 1 1 0 ] ,
T = ( 1 ) p [ exp ( j ϕ A ) 0 0 exp ( j ϕ A ) ] .
Ψ i = α 1 e , TM + α 2 o , TM + α 3 e , TE + α 4 o , TE
= TM [ α 1 e + α 2 o ] + TE [ α 3 e + α 4 o ]
= e [ α 1 TM + α 3 TE ] + o [ α 2 TM + α 4 TE ] ,
Ψ o = α 1 o , TM + α 2 e , TM + α 3 e , TE + α 4 o , TE
= TM [ α 1 o + α 2 e ] + TE [ α 3 e + α 4 o ] ,
φ e , TM = β e , TM 1 + β o , TM 2 + β L D ( 2 q 1 + q 2 ) π 2
φ o , TM = φ e , TM
φ e , TM = 2 β e , TE 1 + β L D
φ o , TE = 2 β o , TE 3 q 3 π + 2 ϕ A ,

Metrics