Abstract

We discuss the feasibility of a quantum nondemolition measurement (QND) of photon number based on cross phase modulation due to the Kerr effect in photonic crystal waveguides (PCW’s). In particular, we derive the equations for two modes propagating in PCW’s and their coupling by a third order nonlinearity. The reduced group velocity and small cross-sectional area of the PCW lead to an enhancement of the interaction relative to bulk materials. We show that in principle, such experiments may be feasible with current photonic technologies, although they are limited by material properties. Our analysis of the propagation equations is sufficiently general to be applicable to the study of soliton formation, all-optical switching and can be extended to processes involving other orders of the nonlinearity.

© 2007 Optical Society of America

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  1. N. Imoto, H. Haus, and Y. Yamamoto, "Quantum nondemolition measurement of the photon number via the optical Kerr effect," Phys. Rev. A 32, 2287 (1985).
    [CrossRef] [PubMed]
  2. M.D. Levenson, R.M. Shelby, M. Reid, and D.F. Walls, "Quantum nondemolition Detection of Optical Quadrature Amplitudes," Phys. Rev. Lett. 57, 2473 (1986).
    [CrossRef] [PubMed]
  3. S.R. Friberg, S. Machida, and Y. Yamamoto, "Quantum-nondemolition measurement of the photon number of an optical soliton," Phys. Rev. Lett. 69, 3165 (1992).
    [CrossRef] [PubMed]
  4. S.R. Friberg, T. Mukai, and S. Machida, "Dual Quantum Nondemolition Measurements via Successive Soliton Collisions," Phys. Rev. Lett. 84, 59 (2000).
    [CrossRef] [PubMed]
  5. F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
    [CrossRef]
  6. J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
    [CrossRef]
  7. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
    [CrossRef]
  8. R. W. Boyd, Nonlinear Optics (Academic Press, 1991).
  9. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
    [CrossRef]
  10. S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
    [CrossRef]
  11. K. Nakatsuhara, T. Mizumoto, E. Takahashi, S. Hossain, Y. Saka, B.-J. Ma, and Y. Nakano, "All-optical switching in a distributed-feedback GaInAsP waveguide," Appl. Opt. 38, 3911 (1999).
    [CrossRef]
  12. Y. Yamamoto and A. Imamoglu, Mesoscopic Quantum Optics (John Wiley and Sons Inc., 1999).
  13. H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111,102 (2005).
    [CrossRef]
  14. Y. Vlasov, M. O’Boyle, H. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 66 (2005).
    [CrossRef]
  15. J. D. Jackson, Classical Electrodynamics (John Wiley and Sons Inc., 1998).
  16. M. Settle, M. Salib, A. Michaeli, and T. F. Krauss, "Low loss silicon on insulator photonic crystal waveguides made by 193nm optical lithography," Opt. Express 14., 2440 (2006).
    [CrossRef] [PubMed]
  17. A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
    [CrossRef]
  18. E. Waks and J. Vuckovic, "Dispersive properties and giant Kerr non-linearities in Dipole Induced Transparency," quant-ph/0511205 (2005).
  19. K. Nemoto and W. J. Munro, "Nearly Deterministic Linear Optical Controlled-NOT Gate," Phys. Rev. Lett. 93, 250,502 (2004).
    [CrossRef]

2006 (1)

2005 (3)

H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111,102 (2005).
[CrossRef]

Y. Vlasov, M. O’Boyle, H. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 66 (2005).
[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

2004 (1)

K. Nemoto and W. J. Munro, "Nearly Deterministic Linear Optical Controlled-NOT Gate," Phys. Rev. Lett. 93, 250,502 (2004).
[CrossRef]

2002 (1)

F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
[CrossRef]

2000 (1)

S.R. Friberg, T. Mukai, and S. Machida, "Dual Quantum Nondemolition Measurements via Successive Soliton Collisions," Phys. Rev. Lett. 84, 59 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
[CrossRef]

1997 (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
[CrossRef]

1993 (1)

A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
[CrossRef]

1992 (1)

S.R. Friberg, S. Machida, and Y. Yamamoto, "Quantum-nondemolition measurement of the photon number of an optical soliton," Phys. Rev. Lett. 69, 3165 (1992).
[CrossRef] [PubMed]

1991 (1)

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

1986 (1)

M.D. Levenson, R.M. Shelby, M. Reid, and D.F. Walls, "Quantum nondemolition Detection of Optical Quadrature Amplitudes," Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

1985 (1)

N. Imoto, H. Haus, and Y. Yamamoto, "Quantum nondemolition measurement of the photon number via the optical Kerr effect," Phys. Rev. A 32, 2287 (1985).
[CrossRef] [PubMed]

Aitchison, J. S.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
[CrossRef]

Altug, H.

H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111,102 (2005).
[CrossRef]

Arakawa, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

Buchler, B.

F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
[CrossRef]

Courty, J.M.

J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
[CrossRef]

Englund, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

Fattal, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

Friberg, S.R.

S.R. Friberg, T. Mukai, and S. Machida, "Dual Quantum Nondemolition Measurements via Successive Soliton Collisions," Phys. Rev. Lett. 84, 59 (2000).
[CrossRef] [PubMed]

S.R. Friberg, S. Machida, and Y. Yamamoto, "Quantum-nondemolition measurement of the photon number of an optical soliton," Phys. Rev. Lett. 69, 3165 (1992).
[CrossRef] [PubMed]

Hamann, H.

Y. Vlasov, M. O’Boyle, H. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 66 (2005).
[CrossRef]

Haus, H.

N. Imoto, H. Haus, and Y. Yamamoto, "Quantum nondemolition measurement of the photon number via the optical Kerr effect," Phys. Rev. A 32, 2287 (1985).
[CrossRef] [PubMed]

Hoa, S.

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

Hobson, W.

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

Hossain, S.

Hutchings, D. C.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
[CrossRef]

Imoto, N.

N. Imoto, H. Haus, and Y. Yamamoto, "Quantum nondemolition measurement of the photon number via the optical Kerr effect," Phys. Rev. A 32, 2287 (1985).
[CrossRef] [PubMed]

Islam, M.

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

Kang, J. U.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
[CrossRef]

Konig, F.

F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
[CrossRef]

J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
[CrossRef]

Krauss, T. F.

Leuchs, G.

F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
[CrossRef]

J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
[CrossRef]

Levenson, M.D.

M.D. Levenson, R.M. Shelby, M. Reid, and D.F. Walls, "Quantum nondemolition Detection of Optical Quadrature Amplitudes," Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

Levi, A.

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

Lin, C.

A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
[CrossRef]

Lin, H.

A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
[CrossRef]

Ma, B.-J.

Machida, S.

S.R. Friberg, T. Mukai, and S. Machida, "Dual Quantum Nondemolition Measurements via Successive Soliton Collisions," Phys. Rev. Lett. 84, 59 (2000).
[CrossRef] [PubMed]

S.R. Friberg, S. Machida, and Y. Yamamoto, "Quantum-nondemolition measurement of the photon number of an optical soliton," Phys. Rev. Lett. 69, 3165 (1992).
[CrossRef] [PubMed]

McNab, S. J.

Y. Vlasov, M. O’Boyle, H. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 66 (2005).
[CrossRef]

Michaeli, A.

Mizumoto, T.

Mukai, T.

S.R. Friberg, T. Mukai, and S. Machida, "Dual Quantum Nondemolition Measurements via Successive Soliton Collisions," Phys. Rev. Lett. 84, 59 (2000).
[CrossRef] [PubMed]

Munro, W. J.

K. Nemoto and W. J. Munro, "Nearly Deterministic Linear Optical Controlled-NOT Gate," Phys. Rev. Lett. 93, 250,502 (2004).
[CrossRef]

Nakano, Y.

Nakaoka, T.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

Nakatsuhara, K.

Nemoto, K.

K. Nemoto and W. J. Munro, "Nearly Deterministic Linear Optical Controlled-NOT Gate," Phys. Rev. Lett. 93, 250,502 (2004).
[CrossRef]

O’Boyle, M.

Y. Vlasov, M. O’Boyle, H. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 66 (2005).
[CrossRef]

Rechtenwald, T.

F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
[CrossRef]

Reid, M.

M.D. Levenson, R.M. Shelby, M. Reid, and D.F. Walls, "Quantum nondemolition Detection of Optical Quadrature Amplitudes," Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

Saka, Y.

Salib, M.

Settle, M.

Shelby, R.M.

M.D. Levenson, R.M. Shelby, M. Reid, and D.F. Walls, "Quantum nondemolition Detection of Optical Quadrature Amplitudes," Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

Sitzmann, A.

F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
[CrossRef]

Sizmann, A.

J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
[CrossRef]

Slusher, R.

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

Soccolich, C.

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

Solomon, G.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

Spa, S.

J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
[CrossRef]

Stegeman, G.

A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
[CrossRef]

Stegeman, G. I.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
[CrossRef]

Takahashi, E.

Villeneuve, A.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
[CrossRef]

A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
[CrossRef]

Vlasov, Y.

Y. Vlasov, M. O’Boyle, H. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 66 (2005).
[CrossRef]

Vuckovic, J.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111,102 (2005).
[CrossRef]

Waks, E.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

Walls, D.F.

M.D. Levenson, R.M. Shelby, M. Reid, and D.F. Walls, "Quantum nondemolition Detection of Optical Quadrature Amplitudes," Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

Yamamoto, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

S.R. Friberg, S. Machida, and Y. Yamamoto, "Quantum-nondemolition measurement of the photon number of an optical soliton," Phys. Rev. Lett. 69, 3165 (1992).
[CrossRef] [PubMed]

N. Imoto, H. Haus, and Y. Yamamoto, "Quantum nondemolition measurement of the photon number via the optical Kerr effect," Phys. Rev. A 32, 2287 (1985).
[CrossRef] [PubMed]

Yang, C.

A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
[CrossRef]

Zhang, B.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

S. Hoa, C. Soccolich, M. Islam, W. Hobson, A. Levi, and R. Slusher, "Large nonlinear phase shifts in low-loss AIGaAs waveguides near half-gap," Appl. Phys. Lett. 59, 2558 (1991).
[CrossRef]

H. Altug and J. Vuckovic, "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111,102 (2005).
[CrossRef]

A. Villeneuve, C. Yang, G. Stegeman, C. Lin, and H. Lin, "Nonlinear refractive-index and two photon-absorption near half the band gap in AlGaAs," Appl. Phys. Lett. 62, 2465 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The Nonlinear Optical Properties of AlGaAs at the Half Band Gap," IEEE J. Quantum Electron. 33(3), 341 (1997).
[CrossRef]

Nature (1)

Y. Vlasov, M. O’Boyle, H. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 66 (2005).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (3)

N. Imoto, H. Haus, and Y. Yamamoto, "Quantum nondemolition measurement of the photon number via the optical Kerr effect," Phys. Rev. A 32, 2287 (1985).
[CrossRef] [PubMed]

F. Konig, B. Buchler, T. Rechtenwald, G. Leuchs, and A. Sitzmann, "Soliton backaction-evading measurement using spectral filtering," Phys. Rev. A 66, 043810 (2002).
[CrossRef]

J.M. Courty, S. Spa, F. Konig, A. Sizmann, and G. Leuchs, "Noise-free quantum-nondemolition measurement using optical solitons," Phys. Rev. A 58, 1501 (1998).
[CrossRef]

Phys. Rev. Lett. (5)

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal," Phys. Rev. Lett. 95, 013,904 (2005).
[CrossRef]

M.D. Levenson, R.M. Shelby, M. Reid, and D.F. Walls, "Quantum nondemolition Detection of Optical Quadrature Amplitudes," Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

S.R. Friberg, S. Machida, and Y. Yamamoto, "Quantum-nondemolition measurement of the photon number of an optical soliton," Phys. Rev. Lett. 69, 3165 (1992).
[CrossRef] [PubMed]

S.R. Friberg, T. Mukai, and S. Machida, "Dual Quantum Nondemolition Measurements via Successive Soliton Collisions," Phys. Rev. Lett. 84, 59 (2000).
[CrossRef] [PubMed]

K. Nemoto and W. J. Munro, "Nearly Deterministic Linear Optical Controlled-NOT Gate," Phys. Rev. Lett. 93, 250,502 (2004).
[CrossRef]

Other (4)

E. Waks and J. Vuckovic, "Dispersive properties and giant Kerr non-linearities in Dipole Induced Transparency," quant-ph/0511205 (2005).

J. D. Jackson, Classical Electrodynamics (John Wiley and Sons Inc., 1998).

Y. Yamamoto and A. Imamoglu, Mesoscopic Quantum Optics (John Wiley and Sons Inc., 1999).

R. W. Boyd, Nonlinear Optics (Academic Press, 1991).

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Figures (3)

Fig. 1.
Fig. 1.

Top left: waveguide mode dispersions calculated by the 3D Finite Difference Time Domain (FDTD) method. The solid (black) line is the light line in the photonic crystal, above which modes are not confined by total internal reflection.Top right: group velocities of the two modes derived from the disperion curves by numerical differentiation ( v g = d ω d k ). Bottom left: modes of the PhC lattice at the k = π a point. The mode with even vertical symmetry relative to the waveguide axis corresponds to the red dispersion curve and the odd symmetry mode is that of the blue dispersion curve. Bottom right: A scanning electron micrograph of a fabricated PCW in AlGaAs.

Fig. 2.
Fig. 2.

Amplitude of E field for k = 2 3 π a , 5 6 π a and π a

Fig. 3.
Fig. 3.

Phase shift due to a single signal photon with a lifetime of 200 ps, after propagation through a 100 μm AlGaAs waveguide with a narrow probe and no group velocity mismatch (A), and the energy required for an external pulse to obtain a SNR of 1 (B). In (A) and (B) it is assumed that the signal and probe are at 1500 nm and two-photon absorption is not present. In (C) we plot the phase for the case of the signal photon in waveguide 1 at 1550 nm and probe at 1620 nm in waveguide 0. The required probe energy for this scheme is shown in (D). In all plots, the blue and red curves correspond to both the signal and the probe in waveguide modes 0 or 1. The black curve corresponds to the probe and signal in different waveguide modes

Tables (1)

Tables Icon

Table 1. values for coupling γ for different modes of the waveguide in units of a -2, and mode volumes for each unit cell of the waveguide (in units of a -3. 1 and 2 refer to the first and second modes of the waveguide.

Equations (60)

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× × E = 1 c 2 2 ( ε ( r ) E ) t 2
× × ( u k ( r ) e ikz ) = ω ( k ) 2 c 2 ε ( r ) u k ( r ) e ikz
Ω d 3 ( r ) u k m u k n e i ( k k ) z = δ mn δ kk
O ̂ = 1 ε × × 1 ε
E = dkA ( k , t ) u k ( r ) e i ( kz ω ( k ) t ) u k 0 ( r ) e i ( k 0 z ω 0 t ) dkA ( k , t ) e i [ ( k k 0 ) z ( ω ( k ) ω 0 ) t ]
E u k 0 ( r ) e i ( k 0 z ω 0 t ) dqA ( q + k 0 , t ) e i [ q ( z ν g t ) 1 2 q 2 ν g k k ]
= u k 0 ( r ) e i ( k 0 z ω 0 t ) × F ( z , t ) = 1 ε u , k 0 × F ( z , t )
S ˙ = i 1 2 k ω s ( γ s , s S 2 + 2 γ s , p P 2 ) S ν s S + i 1 2 ν s k S
P ˙ = i 1 2 k ω p ( γ p , p P 2 + 2 γ p , s S 2 ) P ν p P + i 1 2 ν p k P
γ s , p = 1 a Λ d 3 r ε ˜ ( r ) u s 2 u p 2
P ( z ) = Exp [ i κ ω p 0 t ( γ p , p P ( z ) 2 + 2 γ s , p S ( z + Δ νt ) 2 ) dt ] P ( 0 ) = P ( 0 ) e i ( ϕ P + ϕ S )
ϕ P = 1 2 κ ω p 0 t γ p , p P ( z ) 2 dt 1 2 κ ω p γ p , p L ν P ( z ) 2
ϕ S = κ ω p 0 t γ s , p S ( z + Δ νt ) 2 dt κ ω p γ s , p L ν S ( z ) 2
ϕ s , ideal = c n 2 γ s , p h ¯ ω s ω p L v p 1 v s τ s
1 Δ n ̂ s , observed 2 = 1 N s + 4 ϕ s 2 N p
Δ n ̂ s , observed 2 = 1 4 ϕ s 2 N p
P t = t dkA k t e i [ ( k k 0 ) z ( ω ( k ) ω 0 ) t ]
t dqA ( q + k 0 , t ) e i [ q ( z v g t ) 1 2 q 2 v g k t ]
= d q ( A ( q + k 0 , t ) t i ( v g q + 1 2 v g k q 2 ) A ( q + k 0 , t ) ) e i [ q ( z v g t ) 1 2 q 2 v g k t ]
= d q ( A ( q + k 0 , t ) t e i [ q ( z v g t ) 1 2 q 2 v g k t ] ( v g z i 1 2 v g k 2 z 2 ) dqA ( q + k 0 , t ) ) e i [ q ( z v g t ) 1 2 q 2 v g k t ]
= d q A ( q + k 0 , t ) t e i [ q ( z v g t ) 1 2 q 2 v g k t ] v g z P + i 1 2 v g k 2 z 2 P
× × E = 1 c 2 2 ( ε ( r ) E ) t 2 + μ 0 2 P t 2
1 ε × × 1 ε ε E = O ̂ ε E = 1 c 2 2 ( ε E ) t 2 + μ 0 2 t 2 1 ε P
O ̂ + Δ O ̂ = 1 ε × × 1 ε 1 2 [ δ ε 1 ε × × 1 ε + 1 ε × × 1 ε δ ε ] + o [ ( δ ε ) 2 ]
O ̂ + Δ O ̂ O ̂ 1 2 [ δ ε O ̂ + O ̂ δ ε ] = O ̂ 1 2 { δ ε , O ̂ }
u ( O ̂ + Δ O ̂ ) dkA u = u 1 c 2 2 t 2 dkA u
dkA ( u O ̂ u + u Δ O ̂ ) u = u 1 c 2 dk ( Ä ω 2 A 2 A ˙ ) u
dkA u′ Δ O ̂ u = 2 i ω c 2 d k A ˙ u′ u
1 2 dkA u′ δ ε O ̂ + O ̂ δ ε u = 2 i ω c 2 A ˙ ( k′ )
1 2 dkA u′ δ ε u ( ω′ 2 c 2 + ω 2 c 2 ) = 2 i ω c 2 A ˙ ( k′ )
ω 2 c 2 dkA ( k ) u′ δ ε u = 2 i ω c 2 A ˙ ( k′ )
δ s , p = i α 1 + 3 ε 0 ( χ r ( 3 ) + i χ i ( 3 ) ) ( E ( ω s , p ) 2 + 2 E ( ω p , s ) 2 )
A ˙ ( k′ ) = i ω p dk d 3 r A ( k ′′ ) κ ε ˜ u p 2 u s 2 S ( z ) 2 e i [ ( k ′′ k ) z ( ω ( k ′′ ) ω ( k ) ) t ]
i ω p κ d k A ( k ′′ ) d z S ( z ) 2 e i [ ( k ′′ k ) z ( ω ( k ′′ ) ω ( k ) ) t ] 1 a Λ d 3 r ε ˜ u s 2 u p 2
i ω p κ γ s , p d k ′′ A ( k ′′ ) d z S ( z ) 2 e i [ ( k ′′ k ) z ( ω ( k ′′ ) ω ( k ) ) t ]
d k A ˙ k t e i ( k k 0 ) z ( ω ( k ) ω 0 ) t ) =
= i ω p κ γ s , p d k d k ′′ A ( k ′′ ) d z S ( z ) 2 e i [ ( k ′′ k ) z ( ω ( k ′′ ) ω ( k ) ) t ] e i [ ( k k 0 ) z ( ω ( k ) ω 0 ) t ]
= i ω p κ γ s , p d z d k ′′ A ( k ′′ ) S ( z ) 2 e i [ ( k ′′z k 0 z ) ( ω ( k ′′ ) ω 0 ) t ] ) d k e i k ( z z )
= i ω p κ γ s , p d z S ( z ) 2 e i k 0 ( z z ) δ ( z z ) d k A ( k ′′ ) e i [ ( k ′′ k 0 ) z ( ω ( k ′′ ) ω 0 ) t ] )
= i ω p κ γ s , p d z S ( z ) 2 e i k 0 ( z z ) δ ( z z ) P ( z )
= i ω p κ γ s , p S ( z ) 2 P ( z )
N s h ¯ ω s = d 3 r ε 0 ε ( r ) S 2 u s 2
d z ε 0 S 2 1 a Λ d 3 r ε ( r ) u s 2
N s h ¯ ω s = d z ε 0 S 2
1 = 1 a Λ d 3 r ε ( r ) u s 2
S ˙ = i 1 2 κ ω s ( γ s , s S 2 + 2 γ s , p P 2 ) S v s S + i 1 2 v s k S ′′
P ˙ = i 1 2 κ ω p ( γ p , p P 2 + 2 γ p , s S 2 ) P v p P′ + i 1 2 v p k P ′′
ρ ˙ + ( v p + v p k ϕ′ ) ρ = v p k 2 ϕ ρ
ϕ ρ ˙ + v p ϕ′ ρ = 1 2 κ ω p ( γ p , p ρ 2 + 2 γ s , p η 2 ) ρ + v p k 2 ( ρ ′′ ( ϕ′ ) 2 ρ )
ϕ ˙ + v p ϕ′ + v p k 2 ( ϕ′ ) 2 = 1 2 κ ω p ( γ p , p ρ 2 + 2 γ s , p η 2 )
d p ( z ) d t i 2 κ ω p ( γ p , p P ( z ) 2 + 2 γ s , p S ( z + Δ v t ) 2 ) P ( z )
P ( z ) = P ( 0 ) Exp [ i 2 κ ω p 0 t ( γ p , p P ( z ) 2 + 2 γ s , p S ( z + Δ v t ) 2 ) d t ] = P ( 0 ) e i ( ϕ P + ϕ S )
ϕ P = 1 2 κ ω p 0 t γ p , p P ( z ) 2 d t 1 2 κ ω p γ p , p L v p P ( z ) 2
ϕ S = κ ω p 0 t γ s , p S ( z + Δ v t ) 2 d t κ ω p γ s , p L v p S ( z ) 2
I det d 3 r ε 0 P ( z ) 2 ϕ S ( z ) ε u n 2
d z ε 0 P ( z ) 2 ϕ S ( z ) 1 a Λ d 3 u p 2
= d z ε 0 P ( z ) 2 ϕ S ( z )
κ ω p γ s , p L v p N s h ¯ ω s ε 0 L eff , s N p h ¯ ω p L eff , p d z p ( z ) s ( z )
I det κ ω p γ p , s L v p N s h ¯ ω s ε 0 τ s v s N p h ¯ ω p
= c n 2 h ¯ 2 ω p 2 ω s γ p , s L v p N s N p τ s v s

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