Abstract

In this paper, the non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals is studied based on a semi-finite tight binding model. Using the exact master equation, we solve analytically and numerically the general and exact solution of the non-Markovain dynamics for the cavity coupled to the waveguide in different coupling regime. A critical transition is revealed when the coupling increases between the cavity and the waveguide. In particular, the cavity field becomes dissipationless when the coupling strength goes beyond a critical value, as a manifestation of strong non-Markovian memory effect. The result also indicates that the cavity can maintain in a coherent state with arbitrary small number of photons when it strongly couples to the waveguide at very low temperature. These properties can be measured experimentally through the photon current flowing over the waveguide in photonic crystals.

© 2010 OSA

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  4. P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
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  33. J. S. Jin, M. W. Y. Tu, W. M. Zhang, and Y. J. Yan, “A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach,” arXiv:0910.1675 (to appear in N. J. Phys., 2010).
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  36. A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vuckovic, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90, 073102 (2007).
    [CrossRef]
  37. S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
    [CrossRef]
  38. D. Mogilevtsev, S. Kilin, F. Moreira, and S. B. Cavalcanti, “Markovian and non-Markovian decay in pseudo-gaps,” Photon Nanostruct.: Fundam Appl. 5, 1 (2007).
    [CrossRef]

2010 (2)

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot V nanocavity system,” Nat. Phys. 6, 279 (2010).
[CrossRef]

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99 (2010).
[CrossRef]

2009 (5)

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[CrossRef]

S. Longhi, “Spectral singularities in a non-Hermitian Friedrichs-Fano-Anderson model,” Phys. Rev. B 80, 165125 (2009).
[CrossRef]

M. W. Y. Tu, M. T. Lee, and W. M. Zhang, “Exact master equation and non-markovian decoherence for quantum dot quantum computing,” Quantum Inf. Process 8, 631 (2009).
[CrossRef]

J. H. Au, M. Feng, and W. M. Zhang, “Non-Markovian decoherence dynamics of entangled coherent states,” Quant. Info. Comput. 9, 0317 (2009).

F. Bordas, C. Seassal, E. Dupuy, P. Regreny, M. Gendry, P. Viktorovich, M. J. Steel, and A. Rahmani, “Room temperature low-threshold InAs/InP quantum dot single mode photonic crystal microlasers at 1.5 gm using cavity-confined slow light,” Opt. Express 17, 5439 (2009).
[CrossRef] [PubMed]

2008 (4)

A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express,  16, 12084 (2008).
[CrossRef] [PubMed]

M. W. Y. Tu and W. M. Zhang, “Non-Markovian decoherence theory for a double-dot charge qubit,” Phys. Rev. B 78, 235311 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2, 465 (2008).
[CrossRef]

H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
[CrossRef]

2007 (5)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449 (2007).
[CrossRef]

D. Mogilevtsev, F. Moreira, S. B. Cavalcanti, and S. Kilin, “Field-emitter bound states in structured thermal reservoirs,” Phys. Rev. A 75, 043802 (2007).
[CrossRef]

J. H. Au and W. M. Zhang, “Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels,” Phys. Rev. A,  76, 042127 (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]

D. Mogilevtsev, S. Kilin, F. Moreira, and S. B. Cavalcanti, “Markovian and non-Markovian decay in pseudo-gaps,” Photon Nanostruct.: Fundam Appl. 5, 1 (2007).
[CrossRef]

2006 (2)

S. Longhi, “Non-Markovian decay and lasing condition in an optical microcavity coupled to a structured reservoir,” Phys. Rev. A 74, 063826 (2006).
[CrossRef]

M. Skorobogatiy and A. V. Kabashin, “Photon crystal waveguide-based surface plasmon resonance biosensor,” Appl. Phys. Lett. 89, 143518 (2006).
[CrossRef]

2005 (1)

2004 (2)

J. K. Poon, J. Scheuer, Y. Xu, and A. Yariv, “Designing coupled-resonator optical waveguide delay lines,” J. Opt. Soc. Am. B 21, 1665 (2004).
[CrossRef]

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[CrossRef]

2003 (2)

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

M. Loncar and A. Scherer, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

2000 (2)

P. Lambropoulos, G. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-Binding Description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

1999 (1)

1994 (2)

A. G. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and Induced Atomic Decay in Photonic Band Structures,” J. Mod. Opt. 41, 353 (1994).
[CrossRef]

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

1992 (1)

S. Kilin and D. Mogilevtsev, ““Freezing” of decay of a quantum system with a dip in a spectrum of the heat bath-coupling constants,” Laser Phys. 2, 153 (1992).

1990 (2)

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: Photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418 (1990).
[CrossRef] [PubMed]

W. M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states: theory and some applications,” Rev. Mod. Phys. 62, 867 (1990).
[CrossRef]

1987 (1)

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

1963 (1)

R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118 (1963).
[CrossRef]

1961 (1)

U. Fano, “Effects of Configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961).
[CrossRef]

Akahane, Y.

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

Arakawa, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot V nanocavity system,” Nat. Phys. 6, 279 (2010).
[CrossRef]

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449 (2007).
[CrossRef]

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

Au, J. H.

J. H. Au, M. Feng, and W. M. Zhang, “Non-Markovian decoherence dynamics of entangled coherent states,” Quant. Info. Comput. 9, 0317 (2009).

J. H. Au and W. M. Zhang, “Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels,” Phys. Rev. A,  76, 042127 (2007).
[CrossRef]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2, 465 (2008).
[CrossRef]

Barrelet, C. J.

H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
[CrossRef]

Bay, S.

P. Lambropoulos, G. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455 (2000).
[CrossRef]

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-Binding Description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

Baym, G.

L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, (Benjamin, New York, 1962).

Bordas, F.

Cavalcanti, S. B.

D. Mogilevtsev, S. Kilin, F. Moreira, and S. B. Cavalcanti, “Markovian and non-Markovian decay in pseudo-gaps,” Photon Nanostruct.: Fundam Appl. 5, 1 (2007).
[CrossRef]

D. Mogilevtsev, F. Moreira, S. B. Cavalcanti, and S. Kilin, “Field-emitter bound states in structured thermal reservoirs,” Phys. Rev. A 75, 043802 (2007).
[CrossRef]

Chakravarty, S.

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

De La Rue, R. M.

Dorsey, A. T.

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

Dupuy, E.

Dutton, R.

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]

Erickson, D.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99 (2010).
[CrossRef]

Fan, S.

Fano, U.

U. Fano, “Effects of Configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961).
[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]

Feng, D. H.

W. M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states: theory and some applications,” Rev. Mod. Phys. 62, 867 (1990).
[CrossRef]

Feng, M.

J. H. Au, M. Feng, and W. M. Zhang, “Non-Markovian decoherence dynamics of entangled coherent states,” Quant. Info. Comput. 9, 0317 (2009).

Feynman, R. P.

R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118 (1963).
[CrossRef]

Fisher, M.P.

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449 (2007).
[CrossRef]

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]

Garg, A.

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

Gendry, M.

Gilmore, R.

W. M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states: theory and some applications,” Rev. Mod. Phys. 62, 867 (1990).
[CrossRef]

Han, M.

Hughes, S.

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[CrossRef]

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[CrossRef]

Iwamoto, S.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot V nanocavity system,” Nat. Phys. 6, 279 (2010).
[CrossRef]

Jin, J. S.

J. S. Jin, M. W. Y. Tu, W. M. Zhang, and Y. J. Yan, “A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach,” arXiv:0910.1675 (to appear in N. J. Phys., 2010).

John, S.

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: Photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418 (1990).
[CrossRef] [PubMed]

Johnson, N. P.

Kabashin, A. V.

M. Skorobogatiy and A. V. Kabashin, “Photon crystal waveguide-based surface plasmon resonance biosensor,” Appl. Phys. Lett. 89, 143518 (2006).
[CrossRef]

Kadanoff, L. P.

L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, (Benjamin, New York, 1962).

Kamada, H.

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[CrossRef]

Kilin, S.

D. Mogilevtsev, S. Kilin, F. Moreira, and S. B. Cavalcanti, “Markovian and non-Markovian decay in pseudo-gaps,” Photon Nanostruct.: Fundam Appl. 5, 1 (2007).
[CrossRef]

D. Mogilevtsev, F. Moreira, S. B. Cavalcanti, and S. Kilin, “Field-emitter bound states in structured thermal reservoirs,” Phys. Rev. A 75, 043802 (2007).
[CrossRef]

S. Kilin and D. Mogilevtsev, ““Freezing” of decay of a quantum system with a dip in a spectrum of the heat bath-coupling constants,” Laser Phys. 2, 153 (1992).

Kofman, A. G.

A. G. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and Induced Atomic Decay in Photonic Band Structures,” J. Mod. Opt. 41, 353 (1994).
[CrossRef]

Kumagai, N.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot V nanocavity system,” Nat. Phys. 6, 279 (2010).
[CrossRef]

Kurizki, G.

A. G. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and Induced Atomic Decay in Photonic Band Structures,” J. Mod. Opt. 41, 353 (1994).
[CrossRef]

Lambropoulos, P.

P. Lambropoulos, G. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455 (2000).
[CrossRef]

Lee, M. T.

M. W. Y. Tu, M. T. Lee, and W. M. Zhang, “Exact master equation and non-markovian decoherence for quantum dot quantum computing,” Quantum Inf. Process 8, 631 (2009).
[CrossRef]

Lee, R. K.

Leggett, A. J.

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

Lieber, C. M.

H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
[CrossRef]

Liu, Y.

Loncar, M.

M. Loncar and A. Scherer, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

Longhi, S.

S. Longhi, “Spectral singularities in a non-Hermitian Friedrichs-Fano-Anderson model,” Phys. Rev. B 80, 165125 (2009).
[CrossRef]

S. Longhi, “Non-Markovian decay and lasing condition in an optical microcavity coupled to a structured reservoir,” Phys. Rev. A 74, 063826 (2006).
[CrossRef]

Mandal, S.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99 (2010).
[CrossRef]

Mogilevtsev, D.

D. Mogilevtsev, F. Moreira, S. B. Cavalcanti, and S. Kilin, “Field-emitter bound states in structured thermal reservoirs,” Phys. Rev. A 75, 043802 (2007).
[CrossRef]

D. Mogilevtsev, S. Kilin, F. Moreira, and S. B. Cavalcanti, “Markovian and non-Markovian decay in pseudo-gaps,” Photon Nanostruct.: Fundam Appl. 5, 1 (2007).
[CrossRef]

S. Kilin and D. Mogilevtsev, ““Freezing” of decay of a quantum system with a dip in a spectrum of the heat bath-coupling constants,” Laser Phys. 2, 153 (1992).

Moreira, F.

D. Mogilevtsev, S. Kilin, F. Moreira, and S. B. Cavalcanti, “Markovian and non-Markovian decay in pseudo-gaps,” Photon Nanostruct.: Fundam Appl. 5, 1 (2007).
[CrossRef]

D. Mogilevtsev, F. Moreira, S. B. Cavalcanti, and S. Kilin, “Field-emitter bound states in structured thermal reservoirs,” Phys. Rev. A 75, 043802 (2007).
[CrossRef]

Nielsen, T. R.

P. Lambropoulos, G. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455 (2000).
[CrossRef]

Nikolopoulos, G.

P. Lambropoulos, G. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455 (2000).
[CrossRef]

Noda, S.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449 (2007).
[CrossRef]

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

Nomura, M.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot V nanocavity system,” Nat. Phys. 6, 279 (2010).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Ota, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot V nanocavity system,” Nat. Phys. 6, 279 (2010).
[CrossRef]

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M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-Binding Description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

Park, H. G.

H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
[CrossRef]

Poon, J. K.

Qian, F.

H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
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M. Loncar and A. Scherer, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648 (2003).
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Serey, X.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99 (2010).
[CrossRef]

Sherman, B.

A. G. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and Induced Atomic Decay in Photonic Band Structures,” J. Mod. Opt. 41, 353 (1994).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
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M. Skorobogatiy and A. V. Kabashin, “Photon crystal waveguide-based surface plasmon resonance biosensor,” Appl. Phys. Lett. 89, 143518 (2006).
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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 (2003).
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Sorel, M.

Steel, M. J.

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

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M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-Binding Description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

Tian, B.

H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
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M. W. Y. Tu, M. T. Lee, and W. M. Zhang, “Exact master equation and non-markovian decoherence for quantum dot quantum computing,” Quantum Inf. Process 8, 631 (2009).
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M. W. Y. Tu and W. M. Zhang, “Non-Markovian decoherence theory for a double-dot charge qubit,” Phys. Rev. B 78, 235311 (2008).
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J. S. Jin, M. W. Y. Tu, W. M. Zhang, and Y. J. Yan, “A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach,” arXiv:0910.1675 (to appear in N. J. Phys., 2010).

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H. N. Xiong, W. M. Zhang, X. G. Wang, and M. H. Wu, “Exact non-Markovian cavity dynamics strongly coupled to a reservoir,” arXiv:1005.0904 (to appear in Phys. Rev. A, 2010).

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Wu, M. H.

H. N. Xiong, W. M. Zhang, X. G. Wang, and M. H. Wu, “Exact non-Markovian cavity dynamics strongly coupled to a reservoir,” arXiv:1005.0904 (to appear in Phys. Rev. A, 2010).

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H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
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H. N. Xiong, W. M. Zhang, X. G. Wang, and M. H. Wu, “Exact non-Markovian cavity dynamics strongly coupled to a reservoir,” arXiv:1005.0904 (to appear in Phys. Rev. A, 2010).

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M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

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J. S. Jin, M. W. Y. Tu, W. M. Zhang, and Y. J. Yan, “A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach,” arXiv:0910.1675 (to appear in N. J. Phys., 2010).

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P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[CrossRef]

Yariv, A.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

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Zhang, W. M.

M. W. Y. Tu, M. T. Lee, and W. M. Zhang, “Exact master equation and non-markovian decoherence for quantum dot quantum computing,” Quantum Inf. Process 8, 631 (2009).
[CrossRef]

J. H. Au, M. Feng, and W. M. Zhang, “Non-Markovian decoherence dynamics of entangled coherent states,” Quant. Info. Comput. 9, 0317 (2009).

M. W. Y. Tu and W. M. Zhang, “Non-Markovian decoherence theory for a double-dot charge qubit,” Phys. Rev. B 78, 235311 (2008).
[CrossRef]

J. H. Au and W. M. Zhang, “Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels,” Phys. Rev. A,  76, 042127 (2007).
[CrossRef]

W. M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states: theory and some applications,” Rev. Mod. Phys. 62, 867 (1990).
[CrossRef]

H. N. Xiong, W. M. Zhang, X. G. Wang, and M. H. Wu, “Exact non-Markovian cavity dynamics strongly coupled to a reservoir,” arXiv:1005.0904 (to appear in Phys. Rev. A, 2010).

J. S. Jin, M. W. Y. Tu, W. M. Zhang, and Y. J. Yan, “A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach,” arXiv:0910.1675 (to appear in N. J. Phys., 2010).

Zwerger, W.

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

Ann. Phys. (1)

R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys. 24, 118 (1963).
[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]

M. Loncar and A. Scherer, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648 (2003).
[CrossRef]

M. Skorobogatiy and A. V. Kabashin, “Photon crystal waveguide-based surface plasmon resonance biosensor,” Appl. Phys. Lett. 89, 143518 (2006).
[CrossRef]

J. Mod. Opt. (1)

A. G. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and Induced Atomic Decay in Photonic Band Structures,” J. Mod. Opt. 41, 353 (1994).
[CrossRef]

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

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S. Kilin and D. Mogilevtsev, ““Freezing” of decay of a quantum system with a dip in a spectrum of the heat bath-coupling constants,” Laser Phys. 2, 153 (1992).

Nano Lett. (1)

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10, 99 (2010).
[CrossRef]

Nat. Photon. (3)

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2, 465 (2008).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449 (2007).
[CrossRef]

H. G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622 (2008).
[CrossRef]

Nat. Phys. (1)

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot V nanocavity system,” Nat. Phys. 6, 279 (2010).
[CrossRef]

Nature (1)

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

Opt. Express (3)

Opt. Lett. (1)

Photon Nanostruct.: Fundam Appl. (1)

D. Mogilevtsev, S. Kilin, F. Moreira, and S. B. Cavalcanti, “Markovian and non-Markovian decay in pseudo-gaps,” Photon Nanostruct.: Fundam Appl. 5, 1 (2007).
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Phys. Rev. A (4)

D. Mogilevtsev, F. Moreira, S. B. Cavalcanti, and S. Kilin, “Field-emitter bound states in structured thermal reservoirs,” Phys. Rev. A 75, 043802 (2007).
[CrossRef]

S. Longhi, “Non-Markovian decay and lasing condition in an optical microcavity coupled to a structured reservoir,” Phys. Rev. A 74, 063826 (2006).
[CrossRef]

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

J. H. Au and W. M. Zhang, “Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels,” Phys. Rev. A,  76, 042127 (2007).
[CrossRef]

Phys. Rev. B (4)

M. W. Y. Tu and W. M. Zhang, “Non-Markovian decoherence theory for a double-dot charge qubit,” Phys. Rev. B 78, 235311 (2008).
[CrossRef]

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[CrossRef]

S. Longhi, “Spectral singularities in a non-Hermitian Friedrichs-Fano-Anderson model,” Phys. Rev. B 80, 165125 (2009).
[CrossRef]

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80, 165128 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: Photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418 (1990).
[CrossRef] [PubMed]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-Binding Description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140 (2000).
[CrossRef] [PubMed]

Quant. Info. Comput. (1)

J. H. Au, M. Feng, and W. M. Zhang, “Non-Markovian decoherence dynamics of entangled coherent states,” Quant. Info. Comput. 9, 0317 (2009).

Quantum Inf. Process (1)

M. W. Y. Tu, M. T. Lee, and W. M. Zhang, “Exact master equation and non-markovian decoherence for quantum dot quantum computing,” Quantum Inf. Process 8, 631 (2009).
[CrossRef]

Rep. Prog. Phys. (1)

P. Lambropoulos, G. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455 (2000).
[CrossRef]

Rev. Mod. Phys. (2)

A. J. Leggett, S. Chakravarty, A. T. Dorsey, M.P. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1 (1987).
[CrossRef]

W. M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states: theory and some applications,” Rev. Mod. Phys. 62, 867 (1990).
[CrossRef]

Other (3)

L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, (Benjamin, New York, 1962).

J. S. Jin, M. W. Y. Tu, W. M. Zhang, and Y. J. Yan, “A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach,” arXiv:0910.1675 (to appear in N. J. Phys., 2010).

H. N. Xiong, W. M. Zhang, X. G. Wang, and M. H. Wu, “Exact non-Markovian cavity dynamics strongly coupled to a reservoir,” arXiv:1005.0904 (to appear in Phys. Rev. A, 2010).

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Figures (5)

Fig. 1.
Fig. 1.

(Color online) A schematic plot of a microcavity coupled to a waveguide in photonic crystals.

Fig. 2.
Fig. 2.

(Color online) The exact solution of the scaled field amplitude |u(t)| of the microcavity in photonic crystals, coupled to the waveguide with (a) ωc = 0.5ω 0 (apart from the waveguide band), (b) ωc = 1.025ω 0 (near the upper band edge of the waveguide) and (c) ωc = ω 0 (at the band center of the waveguide) from the weak coupling (η < 0.7) to the strong coupling (η > 1.0) regime.

Fig. 3.
Fig. 3.

(Color online) (a) A contour plot of the scaled cavity field amplitude |u(t)| by varying the time t and the coupling rate η = ξ/ξ 0, combined with other two plots for the decay coefficient in the master equation, κ(t), in (b) strong coupling η = 1.5 and (c) weak coupling η = 0.5. The cavity frequency is set to be the same as the resonator frequency of the waveguide, ωc = ω 0.

Fig. 4.
Fig. 4.

(Color online) The temporal evolution of the thermal-fluctuation-induced photon correlation function v(t) in the cavity coupled to the waveguide from weak coupling to strong coupling regime with the initial temperature of the waveguide at (a) T = 5 mK, and (b) T = 5 K. The curves of different colors with different couplings are the same as in Fig. 2, here ωc = ω 0.

Fig. 5.
Fig. 5.

(Color online) The temporal evolution of the photon number n(t) in the cavity and the photon current flowing in the waveguide, by varying the coupling from weak (η < 0.7) to strong (η > 1.0) coupling regime with the initial temperature of the waveguide at (a) T = 5 mK, and (b) T = 5 K. The curves of different colors with different couplings are the same as in Fig. 2, here ωc = ω 0.

Equations (23)

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

H = ω c a a + n ω 0 a n a n n = 1 N ξ 0 ( a n a n + 1 + H . c . ) + ξ ( a a 1 + H . c . ) .
H = ω c a a + k ω k a k a k + k [ V k a a k + H . c . ] ,
ω k = ω 0 2 ξ 0 cos ( k ) , V k = 2 π ξ sin ( k ) ,
a k = 2 π n = 1 sin ( nk ) a n .
d dt ρ ( t ) = i ω c ( t ) [ a a , ρ ( t ) ] + κ ( t ) { 2 a ρ ( t ) a a a ρ ( t ) ρ ( t ) a a }
+ κ ˜ ( t ) { a ρ ( t ) a + a ρ ( t ) a a a ρ ( t ) ρ ( t ) a a } ,
ω c ( t ) = Im [ u ˙ ( t ) u 1 ( t ) ] ,
κ ( t ) = Re [ u ˙ ( t ) u 1 ( t ) ] ,
κ ˜ ( t ) = v ˙ ( t ) 2 v ( t ) Re [ u ˙ ( t ) u 1 ( t ) ] ,
u ˙ ( τ ) + i ω c u ( τ ) + t 0 τ d τ g ( τ τ ) u ( τ ) = 0 ,
v ( t ) = t 0 t d τ 1 t 0 t d τ 2 u ¯ ( τ 1 ) g ˜ ( τ 1 τ 2 ) u ¯ * ( τ 2 ) ,
g ( τ τ ) = 0 d ω 2 π J ( ω ) e i ω ( τ τ ) ,
g ˜ ( τ τ ) = 0 d ω 2 π J ( ω ) n ¯ ( ω , T ) e i ω ( τ τ ) ,
g ( ω ) = dk d ω = 1 4 ξ 0 2 ( ω ω 0 ) 2 , V ( ω ) = 1 2 π ( ξ ξ 0 ) 4 ξ 0 2 ( ω ω 0 ) 2 ,
J ( ω ) = ( ξ ξ 0 ) 2 4 ξ 0 2 ( ω ω 0 ) 2 .
a ˙ ( t ) = [ i ω 0 ( t ) + κ ( t ) ] a ( t ) = u ˙ ( t ) u ( t ) a ( t ) .
a ( t ) = u ( t ) a ( t 0 ) .
n ˙ ( t ) = 2 κ ( t ) n ( t ) + κ ˜ ( t ) .
v ˙ ( t ) = 2 κ ( t ) v ( t ) + κ ˜ ( t ) ,
n ( t ) = u ( t ) n ( t 0 ) u * ( t ) + v ( t ) .
ρ ( t 0 ) = e α 0 2 α 0 α 0 ,
ρ ( t ) = exp { α ( t ) 2 1 + v ( t ) } n = 0 [ v ( t ) ] n [ 1 + v ( t ) ] n + 1 α ( t ) 1 + v ( t ) , n n , α ( t ) 1 + v ( t ) ,
ρ ( t ) T = 0 = e α ( t ) 2 α ( t ) α ( t ) .

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