Abstract

We demonstrate the design of an integrated conditional quantum teleportation circuit and a readout circuit using a two-dimensional photonic crystal single chip. Fabrication and testing of the proposed quantum circuit can be accomplished with current or near future semiconductor process technology and experimental techniques. The readout part of our device can also be used on its own or integrated with other compatible optical circuits to achieve atomic state detection. Further improvement of the device in terms of compactness and robustness could be achieved by integrating it with sources and detectors in the optical regime.

© 2007 Optical Society of America

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2007 (1)

2005 (3)

E. Waks and J. Vuckovic, "Coupled mode theory for photonic crystal cavity-waveguide interaction," Opt. Express 13, 5064-5073 (2005).
[CrossRef] [PubMed]

A. Sugitatsu, T. Asano, and S. Noda, "Line-defect-waveguide laser integrated with a point defect in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 86, 171106 (2005).
[CrossRef]

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

2004 (2)

S.-B. Zheng, "Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement," Phys. Rev. A 69, 064302 (2004).
[CrossRef]

Y. A. Vlasov, N. Moll, and S. J. McNab, "Observation of surface states in a truncated photonic crystal slab," Opt. Lett. 29, 2175-2177 (2004).
[CrossRef] [PubMed]

2003 (3)

A. Martinez, A. Garcia, P. Sanchis, and J. Marti, "Group velocity dispersion model of coupled-cavity waveguides in photonic crystals," J. Opt. Soc. Am. A 20, 147-150 (2003).
[CrossRef]

S. Zippilli, D. Vitali, P. Tombesi, and J.-M. Raimond, "Scheme for decoherence control in microwave cavities," Phys. Rev. 67, 052101 (2003).
[CrossRef]

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

2002 (3)

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electro-magnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedelikovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).
[CrossRef]

2001 (5)

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 075313 (2001).
[CrossRef]

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

T. Ochiai and J. Sanchez-Dehesa, "Superprism effect in opal-based photonic crystals," Phys. Rev. B 64, 245113 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane," Phys. Rev. B 59, 15112-15120 (1999).
[CrossRef]

1997 (2)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

1993 (2)

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche, "Quantum switches and nonlocal microwave fields," Phys. Rev. Lett. 71, 2360-2363 (1993).
[CrossRef] [PubMed]

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Asano, T.

A. Sugitatsu, T. Asano, and S. Noda, "Line-defect-waveguide laser integrated with a point defect in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 86, 171106 (2005).
[CrossRef]

Auffeves, A.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

Bandyopadhyay, S.

S. Bandyopadhyay, "Prospects for a quantum dynamic random access memory (Q-DRAM)," http://arxiv.org/abs/quant-ph/0101058.

Barclay, P.

B. Lev, K. Srinivasan, P. Barclay, O. Painter, and H. Mabuchi, "Feasibility of detecting single atoms using photonic bandgap cavities," http://arxiv.org/abs/quant-ph/0402093.

Benisty, H.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Bertet, P.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

Bonnefont, S.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Boscolo, S.

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electro-magnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

Boucaud, P.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Brune, M.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche, "Quantum switches and nonlocal microwave fields," Phys. Rev. Lett. 71, 2360-2363 (1993).
[CrossRef] [PubMed]

Checoury, X.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Chuang, I. L.

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

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Cuisin, C.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Davidovich, L.

L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche, "Quantum switches and nonlocal microwave fields," Phys. Rev. Lett. 71, 2360-2363 (1993).
[CrossRef] [PubMed]

De La Rue, R. M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Derouin, E.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Doll, T.

Domokos, P.

P. Domokos, P. Horak, and H. Ritsch, "Quantum description of light pulse scattering on a single atom in waveguides," http://arxiv/abs/quant-ph/0202005.

Dressela, M.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Drisse, O.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Duan, G. H.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

Fan, S.

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 075313 (2001).
[CrossRef]

Garcia, A.

Gatteschif, D.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Gauthier-Lafaye, O.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Golyatin, V. Y.

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedelikovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).
[CrossRef]

Gorshunovab, B.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Goy, P.

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

Guerra, E. S.

E. S. Guerra, "Teleportation of atomic states via cavity quantum electrodynamics," http://arxiv.org/abs/quant-ph/0409194.

Güney, D. Ö.

Hagley, E.

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane," Phys. Rev. B 59, 15112-15120 (1999).
[CrossRef]

Haroche, S.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche, "Quantum switches and nonlocal microwave fields," Phys. Rev. Lett. 71, 2360-2363 (1993).
[CrossRef] [PubMed]

Horak, P.

P. Domokos, P. Horak, and H. Ritsch, "Quantum description of light pulse scattering on a single atom in waveguides," http://arxiv/abs/quant-ph/0202005.

Houdre, R.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

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S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 075313 (2001).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

John, S.

N. Vats, T. Rudolph, and S. John, "Quantum information processing in localized modes of light within a photonic band-gap material," http://arxiv.org/abs/quant-ph/9910046.

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 075313 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Karla, N.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

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T. Koponen, Tunnelling of light in photonic crystal waveguides (Thesis, University of Jyvskyl, Finland, 2003).

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C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Krzystekc, J.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Kuchinsky, S.

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedelikovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).
[CrossRef]

Kutikov, A. Y.

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedelikovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).
[CrossRef]

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P. Kwiat and G. Milburn, "Optical approaches to quantum information processing and quantum computing," in A Quantum Information Science and Technology Roadmap, 2004, http://qist.lanl.gov.

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X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Lelarge, F.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Lev, B.

B. Lev, K. Srinivasan, P. Barclay, O. Painter, and H. Mabuchi, "Feasibility of detecting single atoms using photonic bandgap cavities," http://arxiv.org/abs/quant-ph/0402093.

Loncar, M.

Lourtioz, J.-M.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Lozes-Dupuy, F.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Maali, A.

L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche, "Quantum switches and nonlocal microwave fields," Phys. Rev. Lett. 71, 2360-2363 (1993).
[CrossRef] [PubMed]

Mabuchi, H.

B. Lev, K. Srinivasan, P. Barclay, O. Painter, and H. Mabuchi, "Feasibility of detecting single atoms using photonic bandgap cavities," http://arxiv.org/abs/quant-ph/0402093.

Maioli, P.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

Maitre, X.

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

Marti, J.

Martinez, A.

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

McNab, S. J.

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Meyer, D. A.

Midrio, M.

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electro-magnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

Milburn, G.

P. Kwiat and G. Milburn, "Optical approaches to quantum information processing and quantum computing," in A Quantum Information Science and Technology Roadmap, 2004, http://qist.lanl.gov.

Mllere, A.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Moll, N.

Mukhinb, A. A.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Mulin, D.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Nedelikovic, D.

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedelikovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).
[CrossRef]

Nielsen, M. A.

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

Noda, S.

A. Sugitatsu, T. Asano, and S. Noda, "Line-defect-waveguide laser integrated with a point defect in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 86, 171106 (2005).
[CrossRef]

Nogues, G.

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

Ochiai, T.

T. Ochiai and J. Sanchez-Dehesa, "Superprism effect in opal-based photonic crystals," Phys. Rev. B 64, 245113 (2001).
[CrossRef]

Oesterle, U.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Olivier, S.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Osnaghi, S.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

Painter, O.

B. Lev, K. Srinivasan, P. Barclay, O. Painter, and H. Mabuchi, "Feasibility of detecting single atoms using photonic bandgap cavities," http://arxiv.org/abs/quant-ph/0402093.

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

Pearsall, T. R.

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedelikovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).
[CrossRef]

Peres, A.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Poingt, F.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Pommereau, F.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 075313 (2001).
[CrossRef]

Raimond, J. M.

S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, "Coherent control of an atomic collision in a cavity," Phys. Rev. Lett. 87, 037902 (2001).
[CrossRef] [PubMed]

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

L. Davidovich, A. Maali, M. Brune, J. M. Raimond, and S. Haroche, "Quantum switches and nonlocal microwave fields," Phys. Rev. Lett. 71, 2360-2363 (1993).
[CrossRef] [PubMed]

Raimond, J.-M.

S. Zippilli, D. Vitali, P. Tombesi, and J.-M. Raimond, "Scheme for decoherence control in microwave cavities," Phys. Rev. 67, 052101 (2003).
[CrossRef]

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F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane," Phys. Rev. B 59, 15112-15120 (1999).
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N. Ramsey, Molecular Beams (Clarendon, 1956).

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

Rattier, M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Ritsch, H.

P. Domokos, P. Horak, and H. Ritsch, "Quantum description of light pulse scattering on a single atom in waveguides," http://arxiv/abs/quant-ph/0202005.

Rudolph, T.

N. Vats, T. Rudolph, and S. John, "Quantum information processing in localized modes of light within a photonic band-gap material," http://arxiv.org/abs/quant-ph/9910046.

Sanchez-Dehesa, J.

T. Ochiai and J. Sanchez-Dehesa, "Superprism effect in opal-based photonic crystals," Phys. Rev. B 64, 245113 (2001).
[CrossRef]

Sanchis, P.

Sangregoriof, C.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Scherer, A.

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Smith, C. J. M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Someda, C. G.

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electro-magnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

Srinivasan, K.

B. Lev, K. Srinivasan, P. Barclay, O. Painter, and H. Mabuchi, "Feasibility of detecting single atoms using photonic bandgap cavities," http://arxiv.org/abs/quant-ph/0402093.

Sugitatsu, A.

A. Sugitatsu, T. Asano, and S. Noda, "Line-defect-waveguide laser integrated with a point defect in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 86, 171106 (2005).
[CrossRef]

Telserd, J.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Tombesi, P.

S. Zippilli, D. Vitali, P. Tombesi, and J.-M. Raimond, "Scheme for decoherence control in microwave cavities," Phys. Rev. 67, 052101 (2003).
[CrossRef]

Valentin, J.

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

van Slageren, J.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Vats, N.

N. Vats, T. Rudolph, and S. John, "Quantum information processing in localized modes of light within a photonic band-gap material," http://arxiv.org/abs/quant-ph/9910046.

Vitali, D.

S. Zippilli, D. Vitali, P. Tombesi, and J.-M. Raimond, "Scheme for decoherence control in microwave cavities," Phys. Rev. 67, 052101 (2003).
[CrossRef]

Vlasov, Y. A.

Vongtragoola, S.

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Vuckovic, J.

Waks, E.

Weinfurter, H.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

Weisbuch, C.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Wunderlich, C.

X. Maitre, E. Hagley, G. Nogues, C. Wunderlich, P. Goy, M. Brune, J. M. Raimond, and S. Haroche, "Quantum memory with a single photon in a cavity," Phys. Rev. Lett. 79, 769-772 (1997).
[CrossRef]

Zeilinger, A.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

Zheng, S.-B.

S.-B. Zheng, "Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement," Phys. Rev. A 69, 064302 (2004).
[CrossRef]

Zheng, Shi-Biao

Shi-Biao Zheng, Department of Electronic Science and Applied Physics, Fuzhou University, Fuzhou, 350002, China (personal communication, 2005).

Zippilli, S.

S. Zippilli, D. Vitali, P. Tombesi, and J.-M. Raimond, "Scheme for decoherence control in microwave cavities," Phys. Rev. 67, 052101 (2003).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Appl. Phys. Lett. (4)

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, "Coupled guide and cavity in a two-dimensional photonic crystal," Appl. Phys. Lett. 78, 1487-1489 (2001).
[CrossRef]

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

A. Sugitatsu, T. Asano, and S. Noda, "Line-defect-waveguide laser integrated with a point defect in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 86, 171106 (2005).
[CrossRef]

X. Checoury, P. Boucaud, J.-M. Lourtioz, O. Gauthier-Lafaye, S. Bonnefont, D. Mulin, J. Valentin, F. Lozes-Dupuy, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, and G. H. Duan, "1.5μm room-temperature emission of square-lattice photonic-crystal waveguide lasers with a single line defect," Appl. Phys. Lett. 86, 151111 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electro-magnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. R. Pearsall, and D. Nedelikovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum Electron. 38, 1349-1352 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

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

Nature (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (1)

J. van Slageren, S. Vongtragoola, B. Gorshunovab, A. A. Mukhinb, N. Karla, J. Krzystekc, J. Telserd, A. Mllere, C. Sangregoriof, D. Gatteschif, and M. Dressela, "Frequency-domain magnetic resonance spectroscopy of molecular magnetic materials," Phys. Chem. Chem. Phys. 5, 3837-3843 (2003).
[CrossRef]

Phys. Rev. (1)

S. Zippilli, D. Vitali, P. Tombesi, and J.-M. Raimond, "Scheme for decoherence control in microwave cavities," Phys. Rev. 67, 052101 (2003).
[CrossRef]

Phys. Rev. A (1)

S.-B. Zheng, "Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement," Phys. Rev. A 69, 064302 (2004).
[CrossRef]

Phys. Rev. B (4)

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 075313 (2001).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961-10964 (1991).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Illustration of the proposed photonic crystal quantum circuit. This illustration is not to scale.

Fig. 2
Fig. 2

(a) The time-dependent atom–cavity coupling parameter and (b) the evolution of the probability amplitudes of states 1 B 0 (initially at 1; black curve) and i 0 B 1 (initially at 0; gray curve) in Eq. (3), as atom B travels across the cavity.

Fig. 3
Fig. 3

(a) Time-dependent coupling parameter for atom A and (b) the evolution of the probability amplitudes of states c 0 0 B 0 (initially at 0; gray curve), c 1 1 B 0 (dark curve initially at 1; black curve), and i c 1 0 B 1 (light curve initially at 1; white curve) for the unnormalized state (i.e., numerator) in Eq. (8).

Fig. 4
Fig. 4

The steady-state cross section of the electric field magnitude, for Δ = 0 , along the path of atom B (see text).

Fig. 5
Fig. 5

Calculated values of c 01 2 (solid curve), c 11 2 (× curve), 2 ( c 01 c 11 ) ( r ) (dotted curve), 2 ( c 01 c 11 ) ( i ) (o curve), and to be measured value of P 1 (+ curve) (see text).

Equations (23)

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H a t o m c a v i t y = ω 2 j σ z j + ω α α + j g ( r j ) ( α σ j + α σ + j ) ,
g ( r j ) = g 0 E ( r j ) E ( r m ) .
Ψ ( t ) = cos G B ( t ) 1 B 0 i sin G B ( t ) 0 B 1 ,
G j ( t ) t 0 t g ( r j ) d τ .
ϕ A = c 0 0 A + c 1 1 A .
φ ( t 1 ) 1 2 ( c 0 0 A + c 1 1 A ) ( 1 B 0 i 0 B 1 ) .
φ ( t 1 + t 2 ) 1 2 { c 0 0 A 1 B 0 i c 0 0 B
× [ cos G A ( t 2 ) 0 A 1 i sin G A ( t 2 ) 1 A 0 ] + c 1 1 B
× [ cos G A ( t 2 ) 1 A 0 i sin G A ( t 2 ) 0 A 1 ] i c 1 0 B
× [ cos 2 G A ( t 2 ) 1 A 1 i sin 2 G A ( t 2 ) 0 A 2 ] } ,
ψ ( t 1 + t 2 ) c 0 sin G A ( t 2 ) 0 B 0 + c 1 cos G A ( t 2 ) 1 B 0 i c 1 cos 2 G A ( t 2 ) 0 B 1 [ c 0 2 sin 2 G A ( t 2 ) + c 1 2 cos 2 G A ( t 2 ) + c 1 2 cos 2 2 G A ( t 2 ) ] 1 2 .
ϕ B c 0 0 B + c 1 1 B .
H a t o m m a s e r = ω 2 σ z + Ω ( r ) 2 ( e i ω m t σ + e i ω m t σ + ) ,
Ω ( r ) = 2 μ 10 E ( r )
c 0 ( t + t 4 ) = { [ i cos Θ sin ( Λ t 4 2 ) + cos ( Λ t 4 2 ) ] c 0 + i sin Θ sin ( Λ t 4 2 ) e i ω m t c 1 } e i ω m t 4 2 ,
c 1 ( t + t 4 ) = { i sin Θ sin ( Λ t 4 2 ) e i ω m t c 0 + [ i cos Θ sin ( Λ t 4 2 ) + cos ( Λ t 4 2 ) ] c 1 } e i ω m t 4 2 ,
Λ ( ω ω m ) 2 + Ω 0 2 ,
cos Θ ( ω ω m ) Λ ,
sin Θ Ω 0 Λ .
ϕ ( t + 2 t 4 ) B ( c 0 c 00 + c 1 c 10 ) 0 B + ( c 0 c 01 + c 1 c 11 ) 1 B ,
P 1 = c 0 2 c 01 2 + c 1 2 c 11 2 + [ c 0 ( r ) c 1 ( r ) + c 0 ( i ) c 1 ( i ) ] 2 ( c 01 c 11 ) ( r ) + [ c 0 ( r ) c 1 ( i ) + c 0 ( i ) c 1 ( r ) ] 2 ( c 01 c 11 ) ( i ) .
ϕ B cos ( θ 2 ) 0 B + sin ( θ 2 ) e i φ 1 B ,
ϕ B = cos ( π 8 ) 0 B + sin ( π 8 ) e i π 6 1 B .

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