Abstract

The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in three dimensional photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated for structures made in Al0.3Ga0.7As, using finite-difference time-domain simulations. Squeezing up to ~30% below the shot noise level is predicted for 10 mW average power, 80 MHz repetition, 500 ps excitation pulses using in a [111] oriented wafer.

© 2008 Optical Society of America

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    [Crossref]

2007 (6)

A. J. Shields, “Semiconductor quantum light sources,” Nature Photon.  1, 215–223 (2007).
[Crossref]

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

J. A. Gaj, et al., “Semiconductor heterostructures for spintronics and quantum information,” C. R. Physique 8, 243–252 (2007).
[Crossref]

L. Xiao, Y. Wang, W. Zhang, Y. Huang, and J. Peng, “A 2-D photonic crystal based source of polarization entangled photon pairs with high nonlinear conversion efficiency and without walk-off compensation,” Opt. Commun. 272, 525–528 (2007).
[Crossref]

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and Jeff F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 193106 (2007).
[Crossref]

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
[Crossref]

2006 (4)

G. Weihs, “Parametric down-conversion in photonic crystal waveguides,” Int. J. Mod. Phys. B 20, 1543–1550 (2006).
[Crossref]

G. Burkard, “Spin qubits: Connect the dots,” Nature Phys. 2, 807–808 (2006).
[Crossref]

M. Shapiro and P. Brumer, “Quantum control of bound and continuum state dynamics,” Phys. Rep. 425, 195–264 (2006).
[Crossref]

T. Asano, Bong-Shik Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

2005 (2)

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77513–577 (2005).
[Crossref]

2004 (2)

J. P. Karr, A. Bass, R. Houdre, and E. Giacobino, “Squeezing in semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A 69, 031802(R) (2004).

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Theory of spontaneous parametric down-conversion from photonic crystals,” Phys. Rev. A 70, 043810 (2004).
[Crossref]

2003 (3)

C. Viviescas and G. Hackenbroich, “Field quantization for open optical cavities,” Phys. Rev. A 67, 013805 (2003).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donortype cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341–1343 (2003).
[Crossref]

2002 (1)

2001 (1)

E. Knill, L. Laflamme, and G. J. Milburn, “Efficient linear optics quantum computation,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

1998 (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

1997 (1)

M. Hillery and L. Mlodinow, “Quantized fields in a nonlinear dielectric medium: a microscopic approach,” Phys. Rev. A 55, 678–689 (1997).
[Crossref]

1992 (1)

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[Crossref]

1990 (2)

M. D. Reid and P.D. Drummond, “Correlations in nondegenerate parametric oscillation II, below threshold results,” Phys. Rev. A 41, 3930–3949 (1990).
[Crossref] [PubMed]

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

1988 (1)

M. D. Reid and P.D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett,  60, 2731–2733 (1988).
[Crossref] [PubMed]

1987 (1)

S. Reynaud, C. Fabre, and E. Giacobino, “Quantum fluctuations in a 2-mode parametric oscillator,” J. Opt. Soc. Am. B 4, 152–1524 (1987).
[Crossref]

1975 (1)

S. Nordholm and S. A. Rice, “A quantum ergodic theory approach to unimolecular fragmentation,” J. Chem. Phys. 62, 157–168 (1975).
[Crossref]

1962 (1)

H. Feshbach, “A unified theory of nuclear reactions. II,” Ann. Phys. 19, 287–313 (1962).
[Crossref]

Abram, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Adachi, S.

S. Adachi, GaAs and Related Materials: Bulk Semiconducting and Superlattice Properties (World Scientific Publishing Company, 1994).
[Crossref]

Aers, G. C.

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Akahane, Y.

T. Asano, Bong-Shik Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donortype cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341–1343 (2003).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Asano, T.

T. Asano, Bong-Shik Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donortype cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341–1343 (2003).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Banaee, M. G.

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and Jeff F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 193106 (2007).
[Crossref]

Bass, A.

J. P. Karr, A. Bass, R. Houdre, and E. Giacobino, “Squeezing in semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A 69, 031802(R) (2004).

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77513–577 (2005).
[Crossref]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

S. L. Braunstein and A. K. Pati, Quantum information with continuous variables (Kluwer Academic Publishers, 2003).

Brumer, P.

M. Shapiro and P. Brumer, “Quantum control of bound and continuum state dynamics,” Phys. Rep. 425, 195–264 (2006).
[Crossref]

Burkard, G.

G. Burkard, “Spin qubits: Connect the dots,” Nature Phys. 2, 807–808 (2006).
[Crossref]

Carmichael, H.

H. Carmichael, An open systems approach to quantum optics (Springer-Verlag, 1993).

Cheung, I. W.

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Dalacu, D.

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Drummond, P.D.

M. D. Reid and P.D. Drummond, “Correlations in nondegenerate parametric oscillation II, below threshold results,” Phys. Rev. A 41, 3930–3949 (1990).
[Crossref] [PubMed]

M. D. Reid and P.D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett,  60, 2731–2733 (1988).
[Crossref] [PubMed]

Dumeige, Y.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Dusek, M.

M. Dusek, N. Lutkenhaus, and M. Hendrych, “Quantum Cryptography,” Progress in Optics, E. Wolf, ed., (Elsevier, 2006), Vol. 49.

Englund, D.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
[Crossref]

Fabre, C.

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

S. Reynaud, C. Fabre, and E. Giacobino, “Quantum fluctuations in a 2-mode parametric oscillator,” J. Opt. Soc. Am. B 4, 152–1524 (1987).
[Crossref]

Faraon, A.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
[Crossref]

Feshbach, H.

H. Feshbach, “A unified theory of nuclear reactions. II,” Ann. Phys. 19, 287–313 (1962).
[Crossref]

Frederick, S.

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Fuchs, C. A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Furusawa, A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Fushman, I.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
[Crossref]

Gaj, J. A.

J. A. Gaj, et al., “Semiconductor heterostructures for spintronics and quantum information,” C. R. Physique 8, 243–252 (2007).
[Crossref]

Giacobino, E.

J. P. Karr, A. Bass, R. Houdre, and E. Giacobino, “Squeezing in semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A 69, 031802(R) (2004).

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

S. Reynaud, C. Fabre, and E. Giacobino, “Quantum fluctuations in a 2-mode parametric oscillator,” J. Opt. Soc. Am. B 4, 152–1524 (1987).
[Crossref]

Hackenbroich, G.

C. Viviescas and G. Hackenbroich, “Field quantization for open optical cavities,” Phys. Rev. A 67, 013805 (2003).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

Heidmann, A.

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

Hendrych, M.

M. Dusek, N. Lutkenhaus, and M. Hendrych, “Quantum Cryptography,” Progress in Optics, E. Wolf, ed., (Elsevier, 2006), Vol. 49.

Hijlkema, M.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

Hillery, M.

M. Hillery and L. Mlodinow, “Quantized fields in a nonlinear dielectric medium: a microscopic approach,” Phys. Rev. A 55, 678–689 (1997).
[Crossref]

M. Hillery, Quantum Squeezing (Springer-Verlag, 2004), edited by P. D. Drummond and Z. Ficek, chap. 2.

Houdre, R.

J. P. Karr, A. Bass, R. Houdre, and E. Giacobino, “Squeezing in semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A 69, 031802(R) (2004).

Huang, Y.

L. Xiao, Y. Wang, W. Zhang, Y. Huang, and J. Peng, “A 2-D photonic crystal based source of polarization entangled photon pairs with high nonlinear conversion efficiency and without walk-off compensation,” Opt. Commun. 272, 525–528 (2007).
[Crossref]

Kaige, Wang

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

Karr, J. P.

J. P. Karr, A. Bass, R. Houdre, and E. Giacobino, “Squeezing in semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A 69, 031802(R) (2004).

Kimble, H. J.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[Crossref]

H. J. Kimble, Fundamental Systems in Quantum Optics (Elsevier Science Publishing, 1992) Chap. 10.

Knill, E.

E. Knill, L. Laflamme, and G. J. Milburn, “Efficient linear optics quantum computation,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Kuhn, A.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

Laflamme, L.

E. Knill, L. Laflamme, and G. J. Milburn, “Efficient linear optics quantum computation,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Levenson, A.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Lugiato, L.

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

Lutkenhaus, N.

M. Dusek, N. Lutkenhaus, and M. Hendrych, “Quantum Cryptography,” Progress in Optics, E. Wolf, ed., (Elsevier, 2006), Vol. 49.

Mandel, L.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

McCutcheon, M. W.

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and Jeff F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 193106 (2007).
[Crossref]

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Meriadec, C.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Milburn, G. J.

E. Knill, L. Laflamme, and G. J. Milburn, “Efficient linear optics quantum computation,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Mlodinow, L.

M. Hillery and L. Mlodinow, “Quantized fields in a nonlinear dielectric medium: a microscopic approach,” Phys. Rev. A 55, 678–689 (1997).
[Crossref]

Mochizuki, M.

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donortype cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341–1343 (2003).
[Crossref]

Monnier, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Noda, S.

T. Asano, Bong-Shik Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donortype cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341–1343 (2003).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Nordholm, S.

S. Nordholm and S. A. Rice, “A quantum ergodic theory approach to unimolecular fragmentation,” J. Chem. Phys. 62, 157–168 (1975).
[Crossref]

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[Crossref]

Painter, O.

Pati, A. K.

S. L. Braunstein and A. K. Pati, Quantum information with continuous variables (Kluwer Academic Publishers, 2003).

Pattantyus-Abraham, A. G.

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and Jeff F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 193106 (2007).
[Crossref]

Peng, J.

L. Xiao, Y. Wang, W. Zhang, Y. Huang, and J. Peng, “A 2-D photonic crystal based source of polarization entangled photon pairs with high nonlinear conversion efficiency and without walk-off compensation,” Opt. Commun. 272, 525–528 (2007).
[Crossref]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[Crossref]

Polzik, E. S.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Poole, P. J.

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Reid, M. D.

M. D. Reid and P.D. Drummond, “Correlations in nondegenerate parametric oscillation II, below threshold results,” Phys. Rev. A 41, 3930–3949 (1990).
[Crossref] [PubMed]

M. D. Reid and P.D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett,  60, 2731–2733 (1988).
[Crossref] [PubMed]

Rempe, G.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

Reynaud, S.

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

S. Reynaud, C. Fabre, and E. Giacobino, “Quantum fluctuations in a 2-mode parametric oscillator,” J. Opt. Soc. Am. B 4, 152–1524 (1987).
[Crossref]

Rice, S. A.

S. Nordholm and S. A. Rice, “A quantum ergodic theory approach to unimolecular fragmentation,” J. Chem. Phys. 62, 157–168 (1975).
[Crossref]

Rieger, G. W.

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and Jeff F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 193106 (2007).
[Crossref]

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Sagnes, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Saleh, B. E. A.

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Theory of spontaneous parametric down-conversion from photonic crystals,” Phys. Rev. A 70, 043810 (2004).
[Crossref]

Sergienko, A. V.

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Theory of spontaneous parametric down-conversion from photonic crystals,” Phys. Rev. A 70, 043810 (2004).
[Crossref]

Shapiro, M.

M. Shapiro and P. Brumer, “Quantum control of bound and continuum state dynamics,” Phys. Rep. 425, 195–264 (2006).
[Crossref]

Shields, A. J.

A. J. Shields, “Semiconductor quantum light sources,” Nature Photon.  1, 215–223 (2007).
[Crossref]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Song, Bong-Shik

T. Asano, Bong-Shik Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Sorensen, J. L.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Specht, H. P.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

Srinivasan, K.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

Tanaka, Y.

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donortype cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341–1343 (2003).
[Crossref]

Teich, M. C.

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Theory of spontaneous parametric down-conversion from photonic crystals,” Phys. Rev. A 70, 043810 (2004).
[Crossref]

Vadacchino, M.

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

Vamivakas, A. N.

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Theory of spontaneous parametric down-conversion from photonic crystals,” Phys. Rev. A 70, 043810 (2004).
[Crossref]

van Loock, P.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77513–577 (2005).
[Crossref]

Vidakovic, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Viviescas, C.

C. Viviescas and G. Hackenbroich, “Field quantization for open optical cavities,” Phys. Rev. A 67, 013805 (2003).
[Crossref]

Vuckovic, J.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
[Crossref]

Waks, E.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
[Crossref]

Wang, Y.

L. Xiao, Y. Wang, W. Zhang, Y. Huang, and J. Peng, “A 2-D photonic crystal based source of polarization entangled photon pairs with high nonlinear conversion efficiency and without walk-off compensation,” Opt. Commun. 272, 525–528 (2007).
[Crossref]

Weber, B.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

Webster, S. C.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

Weihs, G.

G. Weihs, “Parametric down-conversion in photonic crystal waveguides,” Int. J. Mod. Phys. B 20, 1543–1550 (2006).
[Crossref]

Williams, R. L.

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Wolf, E.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

Xiao, L.

L. Xiao, Y. Wang, W. Zhang, Y. Huang, and J. Peng, “A 2-D photonic crystal based source of polarization entangled photon pairs with high nonlinear conversion efficiency and without walk-off compensation,” Opt. Commun. 272, 525–528 (2007).
[Crossref]

Young, J. F.

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Young, Jeff F.

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and Jeff F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 193106 (2007).
[Crossref]

Zhang, W.

L. Xiao, Y. Wang, W. Zhang, Y. Huang, and J. Peng, “A 2-D photonic crystal based source of polarization entangled photon pairs with high nonlinear conversion efficiency and without walk-off compensation,” Opt. Commun. 272, 525–528 (2007).
[Crossref]

Ann. Phys. (1)

H. Feshbach, “A unified theory of nuclear reactions. II,” Ann. Phys. 19, 287–313 (1962).
[Crossref]

Appl. Phys. B (1)

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[Crossref]

Appl. Phys. Lett. (3)

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
[Crossref]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, “Design of a channel drop filter by using a donortype cavity with high-quality factor in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 82, 1341–1343 (2003).
[Crossref]

M. G. Banaee, A. G. Pattantyus-Abraham, M. W. McCutcheon, G. W. Rieger, and Jeff F. Young, “Efficient coupling of photonic crystal microcavity modes to a ridge waveguide,” Appl. Phys. Lett. 90, 193106 (2007).
[Crossref]

C. R. Physique (1)

J. A. Gaj, et al., “Semiconductor heterostructures for spintronics and quantum information,” C. R. Physique 8, 243–252 (2007).
[Crossref]

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

T. Asano, Bong-Shik Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Int. J. Mod. Phys. B (1)

G. Weihs, “Parametric down-conversion in photonic crystal waveguides,” Int. J. Mod. Phys. B 20, 1543–1550 (2006).
[Crossref]

J. Chem. Phys. (1)

S. Nordholm and S. A. Rice, “A quantum ergodic theory approach to unimolecular fragmentation,” J. Chem. Phys. 62, 157–168 (1975).
[Crossref]

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

S. Reynaud, C. Fabre, and E. Giacobino, “Quantum fluctuations in a 2-mode parametric oscillator,” J. Opt. Soc. Am. B 4, 152–1524 (1987).
[Crossref]

Nature (2)

E. Knill, L. Laflamme, and G. J. Milburn, “Efficient linear optics quantum computation,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Nature Photon (1)

A. J. Shields, “Semiconductor quantum light sources,” Nature Photon.  1, 215–223 (2007).
[Crossref]

Nature Phys. (2)

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nature Phys. 3, 253–255 (2007).
[Crossref]

G. Burkard, “Spin qubits: Connect the dots,” Nature Phys. 2, 807–808 (2006).
[Crossref]

Opt. Commun. (1)

L. Xiao, Y. Wang, W. Zhang, Y. Huang, and J. Peng, “A 2-D photonic crystal based source of polarization entangled photon pairs with high nonlinear conversion efficiency and without walk-off compensation,” Opt. Commun. 272, 525–528 (2007).
[Crossref]

Opt. Express (1)

photonic crystal microcavities Appl. Phys. Lett. (1)

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar,” photonic crystal microcavities Appl. Phys. Lett. 87, 221110 (2005).

Phys. Rep. (1)

M. Shapiro and P. Brumer, “Quantum control of bound and continuum state dynamics,” Phys. Rep. 425, 195–264 (2006).
[Crossref]

Phys. Rev. A (5)

M. Hillery and L. Mlodinow, “Quantized fields in a nonlinear dielectric medium: a microscopic approach,” Phys. Rev. A 55, 678–689 (1997).
[Crossref]

M. D. Reid and P.D. Drummond, “Correlations in nondegenerate parametric oscillation II, below threshold results,” Phys. Rev. A 41, 3930–3949 (1990).
[Crossref] [PubMed]

J. P. Karr, A. Bass, R. Houdre, and E. Giacobino, “Squeezing in semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A 69, 031802(R) (2004).

A. N. Vamivakas, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Theory of spontaneous parametric down-conversion from photonic crystals,” Phys. Rev. A 70, 043810 (2004).
[Crossref]

C. Viviescas and G. Hackenbroich, “Field quantization for open optical cavities,” Phys. Rev. A 67, 013805 (2003).
[Crossref]

Phys. Rev. Lett (1)

M. D. Reid and P.D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett,  60, 2731–2733 (1988).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, “Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length,” Phys. Rev. Lett. 89, 043901 (2002).
[PubMed]

Quantum Opt. (1)

C. Fabre, E. Giacobino, A. Heidmann, L. Lugiato, S. Reynaud, M. Vadacchino, and Wang Kaige, “Squeezing in detuned degenerate optical parametric oscillators,” Quantum Opt. 2, 159–187 (1990).
[Crossref]

Rev. Mod. Phys. (1)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77513–577 (2005).
[Crossref]

Science (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Other (8)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

H. J. Kimble, Fundamental Systems in Quantum Optics (Elsevier Science Publishing, 1992) Chap. 10.

H. Carmichael, An open systems approach to quantum optics (Springer-Verlag, 1993).

M. Dusek, N. Lutkenhaus, and M. Hendrych, “Quantum Cryptography,” Progress in Optics, E. Wolf, ed., (Elsevier, 2006), Vol. 49.

S. L. Braunstein and A. K. Pati, Quantum information with continuous variables (Kluwer Academic Publishers, 2003).

S. Adachi, GaAs and Related Materials: Bulk Semiconducting and Superlattice Properties (World Scientific Publishing Company, 1994).
[Crossref]

M. Hillery, Quantum Squeezing (Springer-Verlag, 2004), edited by P. D. Drummond and Z. Ficek, chap. 2.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, 1995).

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Figures (6)

Fig. 1.
Fig. 1.

2D photonic crystal microcavities, a) an isolated cavity and b) adding a 1D waveguide channel to the cavity structure.

Fig. 2.
Fig. 2.

The model cavity that communicates with several output channels.

Fig. 3.
Fig. 3.

a) Spectrum at threshold of squeezing for the Y quadrature in a degenerate down-conversion process. b) Squeezing versus g factor at Ω=0. The solid lines are for the case when the cavity couples to a single channel (γx =0) and the dashed lines are when γx =γ 1.

Fig. 4.
Fig. 4.

a) Shift of the holes next to the cavity in order to increase its Q and also its coupling efficiency to the waveguide, b) the cavity is tilted with respect to the waveguide to boost their coupling efficiencies.

Fig. 5.
Fig. 5.

Intensity profile of a) X component and b) Y component of the electric field associated with the cavity in Fig.(4), and c) total intensity of the pump beam in the vicinity of the cavity. Center of the cavity is located at (x=0,y=0).

Fig. 6.
Fig. 6.

The spectrum of squeezing for the Y quadrature of the sample in Fig. (4) for a crystal oriented along the [111] direction pumped with 500 ps pulses of 80 MHz repetition rate and 10 mW average power.

Equations (30)

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

f m ( r , ω ) = λ α λ m ( ω ) U λ ( r ) + n d ω β n m ( ω , ω ) V n ( r , ω ) .
H ̂ = λ h ̅ ω λ a ̂ λ a ̂ λ + m d ω h ̅ ω r ̂ m ( ω ) r ̂ m ( ω )
+ h ̅ λ m d ω [ W λ m ( ω ) a ̂ λ r ̂ m ( ω ) + W λ m * ( ω ) a ̂ λ r ̂ m ( ω )
+ T λ m ( ω ) a ̂ λ r ̂ m ( ω ) + T λ m * ( ω ) a ̂ λ r ̂ m ( ω ) ] ,
H ̂ I = 2 ε 0 3 d 3 r E ̂ ( r , t ) . χ ( 2 ) ( r ) : E ̂ ( r , t ) E ̂ ( r , t ) ,
E ̂ c ( r , t ) = i h ̅ ω 1 2 ε 0 [ a ̂ 1 ( t ) U 1 ( r ) a ̂ 1 ( t ) U 1 * ( r ) ] .
E p ( r , t ) = i A p ( t ) [ U p ( r ) e 2 i ω 0 t U p * ( r ) e + 2 i ω 0 t ] ,
H ̂ I = i h ̅ [ g a ̂ 1 ( t ) a ̂ 1 ( t ) e 2 i ω 0 t g * a ̂ 1 ( t ) a ̂ 1 ( t ) e 2 i ω 0 t ] ,
g = ω 1 3 A p ( t ) d 3 r [ U 1 . χ ( 2 ) : U 1 U p + U 1 . χ ( 2 ) : U p U 1 + U p . χ ( 2 ) : U 1 U 1 ] .
a ˜ 1 ( Ω ) = 2 g 2 γ 1 r ˜ 1 in ( Ω ) + 2 g m = 2 2 γ m r ˜ m in ( Ω ) [ Γ i ( Δ + Ω ) ] [ Γ + i ( Δ Ω ) ] 4 g 2
+ [ Γ + i ( Δ Ω ) ] [ 2 γ 1 r ˜ 1 in ( Ω ) + m = 2 2 γ m r ˜ m in ( Ω ) ] [ Γ i ( Δ + Ω ) ] [ Γ + i ( Δ Ω ) ] 4 g 2 ,
S X ( Ω ) = < X out ( Ω ) , X out ( Ω ) > 1 ,
S Y ( Ω ) = < Y out ( Ω ) , Y out ( Ω ) > 1 ,
X out ( Ω ) = r ˜ 1 out ( Ω ) + r ˜ 1 out ( Ω ) ,
Y out ( Ω ) = i [ r ˜ 1 out ( Ω ) r ˜ 1 out ( Ω ) ] .
r ˜ 1 out ( Ω ) r ˜ 1 in ( Ω ) = 2 γ 1 a ˜ 1 ( Ω ) ,
S X ( Ω ) = 8 g γ 1 ( γ 1 2 g ) 2 + Ω 2 ,
S Y ( Ω ) = 8 g γ 1 ( γ 1 + 2 g ) 2 + Ω 2 .
r ˜ m out ( Ω ) r ˜ m in ( Ω ) = 2 γ 1 a ˜ 1 ( Ω ) ,
S X ( Ω ) = 8 g γ 1 [ ( γ 1 + γ x ) 2 g ] 2 + Ω 2 ,
S Y ( Ω ) = 8 g γ 1 [ ( γ 1 + γ x ) + 2 g ] 2 + Ω 2 ,
γ x = m = 2 γ m ,
S Y ( Ω = 0 ) = γ 1 γ 1 + γ x ,
χ [ 001 ] ( 2 ) ( ω 1 ; 2 ω 0 , ω 1 ) = ( χ xxx ( 2 ) χ xxy ( 2 ) χ xxz ( 2 ) χ xyx ( 2 ) χ xyy ( 2 ) χ xyz ( 2 ) χ xzx ( 2 ) χ xzy ( 2 ) χ xzz ( 2 ) χ yxx ( 2 ) χ yxy ( 2 ) χ yxz ( 2 ) χ yyx ( 2 ) χ yyy ( 2 ) χ yyz ( 2 ) χ yzx ( 2 ) χ yzy ( 2 ) χ yzz ( 2 ) χ zxx ( 2 ) χ zxy ( 2 ) χ zxz ( 2 ) χ zyx ( 2 ) χ zyy ( 2 ) χ zyz ( 2 ) χ zzx ( 2 ) χ zzy ( 2 ) χ zzz ( 2 ) )
= β ( 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 ) ,
χ [ 111 ] ( 2 ) ( ω 1 ; 2 ω 0 , ω 1 ) = β ( 3 3 0 2 2 3 0 1 3 0 2 2 3 0 1 2 2 3 0 1 3 0 1 3 0 2 3 0 2 3 0 2 2 3 0 1 2 2 3 0 2 3 0 1 2 2 3 0 3 2 3 )
1 Q T = 1 Q i + 1 Q wg ,
γ 1 = ω 1 Q wg = 46 GHz , γ x = ω 1 Q i = 16 GHz .
g [ 111 ] = 0.839 GHz .
g [ 111 ] = 4.199 GHz .

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