Abstract

Modification of the spontaneous emission of a multilevel quantum emitter driven by an elliptically polarized control field in the vicinity of the photonic crystal (PC) is investigated in detail. It is shown that one can control the spectral response by altering several key parameters: (i) the rotation polarization angle, (ii) the position-dependent angle parameter, and (iii) the emitter’s location around the PC, respectively. These parameters affect the polarization of the control field and the coupling strength between the emitter and the PC, which leads to modification of the emission spectra of the emitter. A few interesting phenomena such as multipeak structure, enhanced ultranarrow spectral line, as well as the splitting and merging of spectral lines can be observed by adjusting these parameters. Moreover, control over the emission spectra by varying these angle parameters can provide more degrees of freedom and may offer an emitter with any desired spectral behavior.

© 2013 Optical Society of America

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2013 (3)

W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Spontaneous emission in the presence of a spherical plasmonic metamaterial,” Phys. Rev. A 87, 023837 (2013).
[CrossRef]

S. Yang, M. Al-Amri, S. Y. Zhu, and M. S. Zubairy, “Effect of counter-rotating terms on the spontaneous emission in an anisotropic photonic crystal,” Phys. Rev. A 87, 033818 (2013).
[CrossRef]

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[CrossRef]

2012 (8)

Y. Li, J. Evers, H. Zheng, and S. Y. Zhu, “Collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 85, 053830 (2012).
[CrossRef]

X. S. Huang and H. L. Liu, “The coherent control of the spontaneous emission spectrum of a driven atom in photonic crystals with two atomic position-dependent bands,” J. Opt. Soc. Am. B 29, 1413–1417 (2012).
[CrossRef]

U. Hoeppe, C. Wolff, J. Küchenmeister, J. Niegemann, M. Drescher, H. Benner, and K. Busch, “Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals,” Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef]

S. R. Entezar, “Position dependent spontaneous emission spectra of a Λ-type atomic system embedded in a defective photonic crystal,” Commun. Theor. Phys. 57, 115–122 (2012).
[CrossRef]

J. T. Sheng, U. Khadka, and M. Xiao, “Realization of all-optical multistate switching in an atomic coherent medium,” Phys. Rev. Lett. 109, 223906 (2012).
[CrossRef]

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J. M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[CrossRef]

A. N. Poddubny, P. Ginzburg, P. A. Belov, A. V. Zayats, and Y. S. Kivshar, “Tailoring and enhancing spontaneous two-photon emission using resonant plasmonic nanostructures,” Phys. Rev. A 86, 033826 (2012).
[CrossRef]

S. C. Tian, C. L. Wang, C. Z. Tong, L. J. Wang, H. H. Wang, X. B. Yang, Z. H. Kang, and J. Y. Gao, “Observation of the fluorescence spectrum for a driven cascade model system in atomic beam,” Opt. Express 20, 23559–23569 (2012).
[CrossRef]

2011 (4)

S. Evangelou, V. Yannopapas, and E. Paspalakis, “Modifying free-space spontaneous emission near a plasmonic nanostructure,” Phys. Rev. A 83, 023819 (2011).
[CrossRef]

J. T. Sheng, X. H. Yang, U. Khadka, and M. Xiao, “All-optical switching in an N-type foul-level atom-cavity system,” Opt. Express 19, 17059–17064 (2011).
[CrossRef]

J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
[CrossRef]

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef]

2010 (3)

2009 (5)

G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
[CrossRef]

M. R. Singh, “Two-photon absorption in photonic nanowires made from photonic crystals,” J. Opt. Soc. Am. B 26, 1801–1807 (2009).
[CrossRef]

M. R. Singh, “Photon transparency in metallic photonic crystals doped with an ensemble of nanoparticles,” Phys. Rev. A 79, 013826 (2009).
[CrossRef]

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).
[CrossRef]

M. R. Singh, “Controlling photon absorption in photonic nanowires via dipole-dipole interaction,” Opt. Lett. 34, 2909–2911 (2009).
[CrossRef]

2008 (4)

M. R. Singh and R. H. Lipson, “Optical switching in nonlinear photonic crystals lightly doped with nanostructures,” J. Phys. B 41, 015401 (2008).
[CrossRef]

M. R. Singh, “Study of nonlinear effects in photonic crystals doped with nanoparticles,” J. Phys. B 41, 135401 (2008).
[CrossRef]

M. R. Singh, “Inhibition of two-photon absorption due to dipole-dipole interaction in nanoparticles,” Phys. Lett. A 372, 5083–5088 (2008).
[CrossRef]

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77, 053806 (2008).
[CrossRef]

2007 (3)

J. H. Li, “Control of spontaneous emission spectra via an external coherent magnetic field in a cycle-configuration atomic medium,” Eur. Phys. J. D 42, 467–473 (2007).
[CrossRef]

M. R. Singh, “Controlling spontaneous emission in photonic-band-gap materials doped with nanoparticles,” Phys. Rev. A 75, 033810 (2007).
[CrossRef]

M. R. Singh, “Switching mechanism due to the spontaneous emission cancellation in photonic band gap materials doped with nano-particles,” Phys. Lett. A 363, 177–181 (2007).
[CrossRef]

2006 (2)

C. Ottaviani, S. Rebić, D. Vitali, and P. Tombesi, “Cross phase modulation in a five-level atomic medium: semiclassical theory,” Eur. Phys. J. D 40, 281–296 (2006).
[CrossRef]

M. R. Singh, “Transparency and spontaneous emission in a densely doped photonic band gap material,” J. Phys. B 39, 5131–5141 (2006).
[CrossRef]

2005 (4)

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296–1298 (2005).
[CrossRef]

H. Gotoh, H. Kamada, T. Saitoh, H. Ando, and J. Temmyo, “Exciton absorption properties of coherently coupled exciton–biexciton systems in quantum dots,” Phys. Rev. B 71, 195334 (2005).
[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[CrossRef]

2004 (3)

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef]

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1-x As quantum dots by annealing,” Phys. Rev. B 69, 161301(R) (2004).
[CrossRef]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

2003 (4)

M. Macovei and C. H. Keitel, “Laser control of collective spontaneous emission,” Phys. Rev. Lett. 91, 123601 (2003).
[CrossRef]

H. Z. Zhang, J. B. Yang, and S. H. Tang, “Spontaneous emission from a double V-type four-level atom in a double-band photonic crystal,” J. Mod. Opt. 50, 1649–1662 (2003).

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Y. P. Yang, M. Fleischhauer, and S. Y. Zhu, “Spontaneous emission from a two-level atom in two-band anisotropic photonic crystals,” Phys. Rev. A 68, 043805 (2003).
[CrossRef]

2002 (2)

H. Z. Zhang, S. H. Tang, P. Dong, and J. He, “Quantum interference in spontaneous emission of an atom embedded in a double-band photonic crystal,” Phys. Rev. A 65, 063802 (2002).
[CrossRef]

W. U. Huynh, J. J. Dittmer, and A. P. Alivisatos, “Hybrid nanorod-polymer solar cells,” Science 295, 2425–2427 (2002).
[CrossRef]

2001 (3)

G. X. Li, F. L. Li, and S. Y. Zhu, “Quantum interference between decay channels of a three-level atom in a multilayer dielectric medium,” Phys. Rev. A 64, 013819 (2001).
[CrossRef]

M. Bayer, F. Weidner, A. Larionov, A. McDonald, A. Forchel, and T. L. Reinecke, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett. 86, 3168–3171 (2001).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef]

2000 (2)

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and Lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2136–2139 (2000).
[CrossRef]

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

1999 (4)

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
[CrossRef]

C. H. Keitel, “Narrowing spontaneous emission without intensity reduction,” Phys. Rev. Lett. 83, 1307–1310 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24, 345–347 (1999).
[CrossRef]

1998 (2)

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

H. D. Summers, G. M. Berry, G. W. Lewis, and P. Blood, “Spontaneous emission control in quantum well laser diodes,” Opt. Express 2, 151–156 (1998).
[CrossRef]

1997 (1)

S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205–208 (1997).
[CrossRef]

1996 (3)

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1034 (1996).
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S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
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P. Zhou and S. Swain, “Ultranarrow spectral lines via quantum interference,” Phys. Rev. Lett. 77, 3995–3998 (1996).
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1995 (1)

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791–4802 (1995).
[CrossRef]

1994 (1)

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
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E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
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Abstreiter, G.

K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
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W. U. Huynh, J. J. Dittmer, and A. P. Alivisatos, “Hybrid nanorod-polymer solar cells,” Science 295, 2425–2427 (2002).
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H. Gotoh, H. Kamada, T. Saitoh, H. Ando, and J. Temmyo, “Exciton absorption properties of coherently coupled exciton–biexciton systems in quantum dots,” Phys. Rev. B 71, 195334 (2005).
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Arakawa, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
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Asano, T.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296–1298 (2005).
[CrossRef]

Bayer, M.

M. Bayer, F. Weidner, A. Larionov, A. McDonald, A. Forchel, and T. L. Reinecke, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett. 86, 3168–3171 (2001).
[CrossRef]

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Belov, P. A.

A. N. Poddubny, P. Ginzburg, P. A. Belov, A. V. Zayats, and Y. S. Kivshar, “Tailoring and enhancing spontaneous two-photon emission using resonant plasmonic nanostructures,” Phys. Rev. A 86, 033826 (2012).
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Benner, H.

U. Hoeppe, C. Wolff, J. Küchenmeister, J. Niegemann, M. Drescher, H. Benner, and K. Busch, “Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals,” Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef]

Benson, O.

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
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Berry, G. M.

Bimberg, D.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401 (2001).
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Bleuse, J.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J. M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
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J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
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K. Brunner, G. Abstreiter, G. Böhm, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
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W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1-x As quantum dots by annealing,” Phys. Rev. B 69, 161301(R) (2004).
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P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401 (2001).
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U. Hoeppe, C. Wolff, J. Küchenmeister, J. Niegemann, M. Drescher, H. Benner, and K. Busch, “Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals,” Phys. Rev. Lett. 108, 043603 (2012).
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K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
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S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205–208 (1997).
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M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J. M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
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S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).
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M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J. M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
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J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
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J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
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O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
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Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
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J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
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W. U. Huynh, J. J. Dittmer, and A. P. Alivisatos, “Hybrid nanorod-polymer solar cells,” Science 295, 2425–2427 (2002).
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Dong, P.

H. Z. Zhang, S. H. Tang, P. Dong, and J. He, “Quantum interference in spontaneous emission of an atom embedded in a double-band photonic crystal,” Phys. Rev. A 65, 063802 (2002).
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Drescher, M.

U. Hoeppe, C. Wolff, J. Küchenmeister, J. Niegemann, M. Drescher, H. Benner, and K. Busch, “Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals,” Phys. Rev. Lett. 108, 043603 (2012).
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Dupuy, E.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J. M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
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Englund, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
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S. R. Entezar, “Position dependent spontaneous emission spectra of a Λ-type atomic system embedded in a defective photonic crystal,” Commun. Theor. Phys. 57, 115–122 (2012).
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S. Evangelou, V. Yannopapas, and E. Paspalakis, “Modifying free-space spontaneous emission near a plasmonic nanostructure,” Phys. Rev. A 83, 023819 (2011).
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Evers, J.

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
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Y. Li, J. Evers, H. Zheng, and S. Y. Zhu, “Collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 85, 053830 (2012).
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G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
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M. Kiffner, M. Macovei, J. Evers, and C. H. Keitel, in Vacuum-Induced Processes in Multi-level Atoms, E. Wolf, ed., Vol. 55 of Progress in Optics (Elsevier, 2010).

Farina, C.

W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Spontaneous emission in the presence of a spherical plasmonic metamaterial,” Phys. Rev. A 87, 023837 (2013).
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Fattal, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
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Feng, W.

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
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Fleischhauer, M.

Y. P. Yang, M. Fleischhauer, and S. Y. Zhu, “Spontaneous emission from a two-level atom in two-band anisotropic photonic crystals,” Phys. Rev. A 68, 043805 (2003).
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Forchel, A.

M. Bayer, F. Weidner, A. Larionov, A. McDonald, A. Forchel, and T. L. Reinecke, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett. 86, 3168–3171 (2001).
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Fujita, M.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296–1298 (2005).
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Gammon, D.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
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Gao, J. Y.

S. C. Tian, C. L. Wang, C. Z. Tong, L. J. Wang, H. H. Wang, X. B. Yang, Z. H. Kang, and J. Y. Gao, “Observation of the fluorescence spectrum for a driven cascade model system in atomic beam,” Opt. Express 20, 23559–23569 (2012).
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A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77, 053806 (2008).
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J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
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Gérard, J. M.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J. M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
[CrossRef]

J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
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Ginzburg, P.

A. N. Poddubny, P. Ginzburg, P. A. Belov, A. V. Zayats, and Y. S. Kivshar, “Tailoring and enhancing spontaneous two-photon emission using resonant plasmonic nanostructures,” Phys. Rev. A 86, 033826 (2012).
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H. Gotoh, H. Kamada, T. Saitoh, H. Ando, and J. Temmyo, “Exciton absorption properties of coherently coupled exciton–biexciton systems in quantum dots,” Phys. Rev. B 71, 195334 (2005).
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Gregersen, N.

M. Munsch, J. Claudon, J. Bleuse, N. S. Malik, E. Dupuy, J. M. Gérard, Y. Chen, N. Gregersen, and J. Mørk, “Linearly polarized, single-mode spontaneous emission in a photonic nanowire,” Phys. Rev. Lett. 108, 077405 (2012).
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Hagley, E. W.

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
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A. Hatef and M. R. Singh, “Plasmonic effect on quantum coherence and interference in metallic photonic crystals doped with quantum dots,” Phys. Rev. A 81, 063816 (2010).
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H. Z. Zhang, S. H. Tang, P. Dong, and J. He, “Quantum interference in spontaneous emission of an atom embedded in a double-band photonic crystal,” Phys. Rev. A 65, 063802 (2002).
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K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
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U. Hoeppe, C. Wolff, J. Küchenmeister, J. Niegemann, M. Drescher, H. Benner, and K. Busch, “Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals,” Phys. Rev. Lett. 108, 043603 (2012).
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Hsieh, W. F.

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).
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P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
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S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205–208 (1997).
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Huang, X. S.

Hugonin, J. P.

J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
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M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
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Huynh, W. U.

W. U. Huynh, J. J. Dittmer, and A. P. Alivisatos, “Hybrid nanorod-polymer solar cells,” Science 295, 2425–2427 (2002).
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Imamoglu, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
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P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
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S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
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H. Gotoh, H. Kamada, T. Saitoh, H. Ando, and J. Temmyo, “Exciton absorption properties of coherently coupled exciton–biexciton systems in quantum dots,” Phys. Rev. B 71, 195334 (2005).
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Kan, H.

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
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Kang, Z. H.

Katzer, D. S.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
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Keitel, C. H.

G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
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M. Macovei and C. H. Keitel, “Laser control of collective spontaneous emission,” Phys. Rev. Lett. 91, 123601 (2003).
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C. H. Keitel, “Narrowing spontaneous emission without intensity reduction,” Phys. Rev. Lett. 83, 1307–1310 (1999).
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M. Kiffner, M. Macovei, J. Evers, and C. H. Keitel, in Vacuum-Induced Processes in Multi-level Atoms, E. Wolf, ed., Vol. 55 of Progress in Optics (Elsevier, 2010).

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M. Kiffner, M. Macovei, J. Evers, and C. H. Keitel, in Vacuum-Induced Processes in Multi-level Atoms, E. Wolf, ed., Vol. 55 of Progress in Optics (Elsevier, 2010).

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
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Kim, J.

J. Kim, O. Benson, H. Kan, and Y. Yamamoto, “A single-photon turnstile device,” Nature 397, 500–503 (1999).
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P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
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A. N. Poddubny, P. Ginzburg, P. A. Belov, A. V. Zayats, and Y. S. Kivshar, “Tailoring and enhancing spontaneous two-photon emission using resonant plasmonic nanostructures,” Phys. Rev. A 86, 033826 (2012).
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W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Spontaneous emission in the presence of a spherical plasmonic metamaterial,” Phys. Rev. A 87, 023837 (2013).
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U. Hoeppe, C. Wolff, J. Küchenmeister, J. Niegemann, M. Drescher, H. Benner, and K. Busch, “Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals,” Phys. Rev. Lett. 108, 043603 (2012).
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M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
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J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
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W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1-x As quantum dots by annealing,” Phys. Rev. B 69, 161301(R) (2004).
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M. Bayer, F. Weidner, A. Larionov, A. McDonald, A. Forchel, and T. L. Reinecke, “Inhibition and enhancement of the spontaneous emission of quantum dots in structured microresonators,” Phys. Rev. Lett. 86, 3168–3171 (2001).
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O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
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M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
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A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77, 053806 (2008).
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S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).
[CrossRef]

Yang, X.

Yang, X. B.

Yang, X. H.

Yang, Y. P.

Y. P. Yang, M. Fleischhauer, and S. Y. Zhu, “Spontaneous emission from a two-level atom in two-band anisotropic photonic crystals,” Phys. Rev. A 68, 043805 (2003).
[CrossRef]

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and Lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2136–2139 (2000).
[CrossRef]

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S. Evangelou, V. Yannopapas, and E. Paspalakis, “Modifying free-space spontaneous emission near a plasmonic nanostructure,” Phys. Rev. A 83, 023819 (2011).
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O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Ye, C. Y.

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1034 (1996).
[CrossRef]

Yeganegi, E.

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
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A. N. Poddubny, P. Ginzburg, P. A. Belov, A. V. Zayats, and Y. S. Kivshar, “Tailoring and enhancing spontaneous two-photon emission using resonant plasmonic nanostructures,” Phys. Rev. A 86, 033826 (2012).
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H. Z. Zhang, J. B. Yang, and S. H. Tang, “Spontaneous emission from a double V-type four-level atom in a double-band photonic crystal,” J. Mod. Opt. 50, 1649–1662 (2003).

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[CrossRef]

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P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
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Y. Li, J. Evers, H. Zheng, and S. Y. Zhu, “Collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 85, 053830 (2012).
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S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and Lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2136–2139 (2000).
[CrossRef]

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P. Zhou and S. Swain, “Ultranarrow spectral lines via quantum interference,” Phys. Rev. Lett. 77, 3995–3998 (1996).
[CrossRef]

Zhu, J. P.

Zhu, S. Y.

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
[CrossRef]

S. Yang, M. Al-Amri, S. Y. Zhu, and M. S. Zubairy, “Effect of counter-rotating terms on the spontaneous emission in an anisotropic photonic crystal,” Phys. Rev. A 87, 033818 (2013).
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Y. Li, J. Evers, H. Zheng, and S. Y. Zhu, “Collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 85, 053830 (2012).
[CrossRef]

Y. P. Yang, M. Fleischhauer, and S. Y. Zhu, “Spontaneous emission from a two-level atom in two-band anisotropic photonic crystals,” Phys. Rev. A 68, 043805 (2003).
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G. X. Li, F. L. Li, and S. Y. Zhu, “Quantum interference between decay channels of a three-level atom in a multilayer dielectric medium,” Phys. Rev. A 64, 013819 (2001).
[CrossRef]

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and Lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2136–2139 (2000).
[CrossRef]

S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205–208 (1997).
[CrossRef]

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef]

H. R. Xia, C. Y. Ye, and S. Y. Zhu, “Experimental observation of spontaneous emission cancellation,” Phys. Rev. Lett. 77, 1032–1034 (1996).
[CrossRef]

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791–4802 (1995).
[CrossRef]

Zubairy, M. S.

S. Yang, M. Al-Amri, S. Y. Zhu, and M. S. Zubairy, “Effect of counter-rotating terms on the spontaneous emission in an anisotropic photonic crystal,” Phys. Rev. A 87, 033818 (2013).
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S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and Lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2136–2139 (2000).
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J. Mod. Opt. (1)

H. Z. Zhang, J. B. Yang, and S. H. Tang, “Spontaneous emission from a double V-type four-level atom in a double-band photonic crystal,” J. Mod. Opt. 50, 1649–1662 (2003).

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Opt. Express (3)

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Phys. Rev. A (17)

Y. Li, J. Evers, W. Feng, and S. Y. Zhu, “Spectrum of collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 87, 053837 (2013).
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Y. Li, J. Evers, H. Zheng, and S. Y. Zhu, “Collective spontaneous emission beyond the rotating-wave approximation,” Phys. Rev. A 85, 053830 (2012).
[CrossRef]

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).
[CrossRef]

Y. P. Yang, M. Fleischhauer, and S. Y. Zhu, “Spontaneous emission from a two-level atom in two-band anisotropic photonic crystals,” Phys. Rev. A 68, 043805 (2003).
[CrossRef]

S. Yang, M. Al-Amri, S. Y. Zhu, and M. S. Zubairy, “Effect of counter-rotating terms on the spontaneous emission in an anisotropic photonic crystal,” Phys. Rev. A 87, 033818 (2013).
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M. R. Singh, “Photon transparency in metallic photonic crystals doped with an ensemble of nanoparticles,” Phys. Rev. A 79, 013826 (2009).
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A. N. Poddubny, P. Ginzburg, P. A. Belov, A. V. Zayats, and Y. S. Kivshar, “Tailoring and enhancing spontaneous two-photon emission using resonant plasmonic nanostructures,” Phys. Rev. A 86, 033826 (2012).
[CrossRef]

S. Evangelou, V. Yannopapas, and E. Paspalakis, “Modifying free-space spontaneous emission near a plasmonic nanostructure,” Phys. Rev. A 83, 023819 (2011).
[CrossRef]

M. R. Singh, “Controlling spontaneous emission in photonic-band-gap materials doped with nanoparticles,” Phys. Rev. A 75, 033810 (2007).
[CrossRef]

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

G. X. Li, F. L. Li, and S. Y. Zhu, “Quantum interference between decay channels of a three-level atom in a multilayer dielectric medium,” Phys. Rev. A 64, 013819 (2001).
[CrossRef]

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791–4802 (1995).
[CrossRef]

H. Z. Zhang, S. H. Tang, P. Dong, and J. He, “Quantum interference in spontaneous emission of an atom embedded in a double-band photonic crystal,” Phys. Rev. A 65, 063802 (2002).
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A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77, 053806 (2008).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
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U. Hoeppe, C. Wolff, J. Küchenmeister, J. Niegemann, M. Drescher, H. Benner, and K. Busch, “Direct observation of non-Markovian radiation dynamics in 3D bulk photonic crystals,” Phys. Rev. Lett. 108, 043603 (2012).
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M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef]

S. Y. Zhu, H. Chen, and H. Huang, “Quantum interference effects in spontaneous emission from an atom embedded in a photonic band gap structure,” Phys. Rev. Lett. 79, 205–208 (1997).
[CrossRef]

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, “Spontaneous radiation and Lamb shift in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2136–2139 (2000).
[CrossRef]

J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J. M. Gérard, I. Maksymov, J. P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011).
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P. Zhou and S. Swain, “Ultranarrow spectral lines via quantum interference,” Phys. Rev. Lett. 77, 3995–3998 (1996).
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C. H. Keitel, “Narrowing spontaneous emission without intensity reduction,” Phys. Rev. Lett. 83, 1307–1310 (1999).
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Science (5)

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of an emitter embedded in a double-band PBG structure with anisotropic dispersion relations. ρ(ωk) is the DOSs of the PBG modes. ωg1 and ωg2 denote the lower-band and upper-band edge frequencies, respectively. The transition from the intermediate state |3 (|2) to the lower state |1 is coupled by the upper (lower) band of the PBG reservoir. It is assumed that the transitions from the two intermediate states |2 and |3 to the ground state |0 are far away from the PBG edges and are coupled by the free-space reservoir. In addition, the two components of an elliptically polarized laser field are used to couple the transitions from the excited state |4 to the intermediate states |2 and |3. Also, the degeneracy among the two intermediate states is removed by a static magnetic field, and an amount ΔB is the Zeeman shift.

Fig. 2.
Fig. 2.

Emission spectra S(δλ) (in arbitrary units) as a function of the detuning δλ. (a)–(a′) φ=0, π/2; (b)–(b′) φ=π/12; and (c)–(c′) φ=π/4. The other system parameters are chosen as Ωc=5, ΔB=0.5, δ31g2=δ21g1=0.4, ω32=0.5, α21=α31=1.0, γ20=γ30=0.1, η=1, and θ(r⃗0)=π/3, respectively. The microparticle is initially prepared in an equal superposition of two intermediate states |2 and |3, i.e., a2(0)=a3(0)=1/2. The curves (a)–(c) correspond to Δc=0.4; The curves (a′)–(c′) correspond to the resonant case, i.e., Δc=0.

Fig. 3.
Fig. 3.

Emission spectra S(δγ) (in arbitrary units) as a function of the detuning δγ. (a) φ=π/12, (b) φ=π/6, (c) φ=2π/9; and (a′) φ=π/12, (b′) φ=π/6, (c′) φ=2π/9. The other system parameters used are the same as Fig. 2 except that δ31g2=δ21g1=0.2, θ(r⃗0)=π/4, and Δc=0.4.

Fig. 4.
Fig. 4.

Emission spectra S(δγ) (in arbitrary units) as a function of the detuning δγ. (a) φ=π/9, θ(r⃗0)=π/3; (b) φ=π/9, θ(r⃗0)=π/6; (c) φ=π/5, θ(r⃗0)=π/3; and (d) φ=π/5, θ(r⃗0)=π/6. The other system parameters used are the same as Fig. 2 except that δ31g2=δ21g1=0.2 and Δc=0.

Equations (23)

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HI/=Ωc+ei(ΔcΔB)tσ42++Ωcei(Δc+ΔB)tσ43++κgκ(r⃗0)eiμκtb^κσ21++γgγ(r⃗0)eiμγtb^γσ31++λgλ2eiμλ2tb^λσ20++λgλ3eiμλ3tb^λσ30++H.c.,
gκ(r⃗0)=ω21(2ε0ωκV)1/2d⃗21·E⃗ksinθ(r⃗0)=gκsinθ(r⃗0),gγ(r⃗0)=ω31(2ε0ωγV)1/2d⃗31·E⃗kcosθ(r⃗0)=gγcosθ(r⃗0),
|Ψ(t)=[a4(t)|4+a3(t)ei(Δc+ΔB)t|3+a2(t)ei(ΔcΔB)t|2]|{0}+κaκ(t)|1|1κ+γaγ(t)|1|1γ+λaλ(t)|0|1λ,
a4(t)t=iΩca3(t)iΩc+a2(t),
a3(t)t=i(Δc+ΔB)a3(t)i(Ωc)*a4(t)iγgγ(r⃗0)eiμγtei(Δc+ΔB)taγ(t)iλgλ3eiμλ3tei(Δc+ΔB)taλ(t),
a2(t)t=i(ΔcΔB)a2(t)i(Ωc+)*a4(t)iκgκ(r⃗0)eiμκtei(ΔcΔB)taκ(t)iλgλ2eiμλ2tei(ΔcΔB)taλ(t),
aγ(t)t=igγ*(r⃗0)eiμγtei(Δc+ΔB)ta3(t),
aκ(t)t=igκ*(r⃗0)eiμκtei(ΔcΔB)ta2(t),
aλ(t)t=igλ3*eiμλ3tei(Δc+ΔB)ta3(t)igλ2*eiμλ2tei(ΔcΔB)ta2(t).
a3(t)t=i(Δc+ΔB)a3(t)i(Ωc)*a4(t)cos2θ(r⃗0)0tei(Δc+ΔB)(tt)Gγ(tt)a3(t)dt0tei(Δc+ΔB)(tt)K33(tt)a3(t)dt0tei(ΔcΔB)(tt)K32(tt)a2(t)dt,
a2(t)t=i(ΔcΔB)a2(t)i(Ωc+)*a4(t)sin2θ(r⃗0)0tei(ΔcΔB)(tt)Gκ(tt)a2(t)dt0tei(Δc+ΔB)(tt)K23(tt)a3(t)dt0tei(ΔcΔB)(tt)K22(tt)a2(t)dt.
Kjl(tt)=λgλjgλl*eiμλl(tt)=ηjlγj0γl02δ(tt),
Gγ(κ)(tt)=γ(κ)|gγ(κ)|2eiμγ(κ)(tt),
Gγ(tt)=α312·exp{i[δ31g2(tt)+π/4]}4π(tt)3,
Gκ(tt)=α212·exp{i[δ21g1(tt)π/4]}4π(tt)3,
E(t+τ)E+(t)t=Ψ(t)|λ,λbλbλeiωλ(t+τ)eiωλt|Ψ(t)t.
E(t+τ)E+(t)t=λeaλe*()aλe()eiωλτ=+eiωλτdωλρ(ωλ)e=12[aλe*()aλe()]dΩ,
S(ωλ)γ30|a˜3[siμλ3i(Δc+ΔB)]|2+γ20|a˜2[siμλ2i(ΔcΔB)]|2+ηγ20γ30{a˜3*[siμλ3i(Δc+ΔB)]a˜2[siμλ2i(ΔcΔB)]+a˜2*[siμλ2i(ΔcΔB)]a˜3[siμλ3i(Δc+ΔB)]},
a˜2(s)=Da3(0)Ba2(0)ADBC,
a˜3(s)=Aa2(0)Ca3(0)ADBC,
A=(Ωc)*Ωc+s+ηγ20γ302,B=s+i(Δc+ΔB)+|Ωc|2s+cos2θ(r⃗0)G˜γ[s+i(Δc+ΔB)]+γ302,C=s+i(ΔcΔB)+|Ωc+|2s+sin2θ(r⃗0)G˜κ[s+i(ΔcΔB)]+γ202,D=(Ωc+)*Ωcs+ηγ20γ302.
G˜γ(s)=α312is+δ31g2,
G˜κ(s)=α212(iis+δ21g1).

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