Modal and polarization qubits in Ti:LiNbO_{3} photonic circuits for a universal quantum logic gate |
Optics Express, Vol. 18, Issue 19, pp. 20475-20490 (2010)
http://dx.doi.org/10.1364/OE.18.020475
Acrobat PDF (1187 KB)
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:LiNbO_{3} 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:LiNbO_{3} 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 LiNbO_{3}.
© 2010 Optical Society of America
1. Introduction
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, 053 842 (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]
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,” Nature Photon. 3, 346–350 (2009). [CrossRef]
10. C. H. Bennett and P. W. Shor, “Quantum information theory,” IEEE Trans. Inform. Theory 44, 2724–2742 (1998). [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]
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]
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:LiNbO_{3} 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]
22. R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978). [CrossRef]
27. R. V. Schmidt and H. Kogelnik, “Electro-optically switched coupler with stepped Δβ reversal using Ti-diffused LiNbO_{3} waveguides,” Appl. Phys. Lett. 28, 503–506 (1976). [CrossRef]
28. H. Kogelnik and R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976). [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]
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]
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]
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]
2. Diffused channel Ti:LiNbO waveguides
3. Modal qubits
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]
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, 053 842 (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]
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]
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]
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]
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]
43. B. E. A. Saleh and M. C. Teich, “Sub-Poisson light generation by selective deletion from cascaded atomic emissions,” Optics 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]
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]
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]
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]
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]
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]
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 LiNbO_{3},” J. Opt. Soc. Am. B 12, 2102–2116 (1995). [CrossRef]
4. Mode coupling between adjacent waveguides
53. L. L. Buhl and R. C. Alferness, “Ti:LiNbO_{3} waveguide electro-optic beam combiner,” Opt. Lett. 12, 778–780 (1987). [CrossRef] [PubMed]
5. Mode analyzer and modal Pauli spin operator
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]
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]
6. Mode rotator and modal Pauli spin operator σx
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]
53. L. L. Buhl and R. C. Alferness, “Ti:LiNbO_{3} waveguide electro-optic beam combiner,” Opt. Lett. 12, 778–780 (1987). [CrossRef] [PubMed]
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]
7. Controlled-NOT (CNOT) gate
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]
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]
23. R. C. Alferness, “Efficient waveguide electro-optic TE⇌TM mode converter/wavelength filter,” Appl. Phys. Lett. 36, 513–515 (1980). [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:LiNbO_{3} 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 LiNbO_{3} integrated electro-optic modulator,” Opt. Express 15, 10 739–10 743 (2007). [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]
8. Conclusion
Acknowledgments
References and links
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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] |
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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 LiNbO_{3},” J. Opt. Soc. Am. B 12, 2102–2116 (1995). [CrossRef] |
53. | L. L. Buhl and R. C. Alferness, “Ti:LiNbO_{3} 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:LiNbO_{3} 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 LiNbO_{3} integrated electro-optic modulator,” Opt. Express 15, 10 739–10 743 (2007). [CrossRef] |
OCIS Codes
(130.3730) Integrated optics : Lithium niobate
(230.7380) Optical devices : Waveguides, channeled
(270.5585) Quantum optics : Quantum information and processing
ToC Category:
Quantum Optics
History
Original Manuscript: July 19, 2010
Revised Manuscript: September 3, 2010
Manuscript Accepted: September 3, 2010
Published: September 10, 2010
Citation
Mohammed F. Saleh, Giovanni Di Giuseppe, Bahaa E. A. Saleh, and Malvin Carl Teich, "Modal and polarization qubits in Ti:LiNbO_{3} photonic circuits for a
universal quantum logic gate," Opt. Express 18, 20475-20490 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20475
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References
- 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. 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]
- 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]
- 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).
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