I theoretically demonstrate the population inversion of collective two-level atoms using photonic crystals in three-dimensional (3D) systems by self-consistent solution of the semiclassical Maxwell-Bloch equations. In the semiclassical theory, while electrons are quantized to ground and excited states, electromagnetic fields are treated classically. For control of spontaneous emission and steady-state population inversion of two-level atoms driven by an external laser which is generally considered impossible, large contrasts of electromagnetic local densities of states (EM LDOS’s) are necessary. When a large number of two-level atoms are coherently excited (Dicke model), the above properties can be recaptured by the Maxwell-Bloch equations based on the first-principle calculation. In this paper, I focus on the realistic 1D PC’s with finite structures perpendicular to periodic directions in 3D systems. In such structures, there appear pseudo photonic band gaps (PBG’s) in which light leaks into air regions, unlike complete PBG’s. Nevertheless, these pseudo PBG’s provide large contrasts of EM LDOS’s in the vicinity of the upper photonic band edges. I show that the realistic 1D PC’s in 3D systems enable the control of spontaneous emission and population inversion of collective two-level atoms driven by an external laser. This finding facilitates experimental fabrication and realization.

© 2012 OSA

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Appl. Phys. Lett.

• S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett.94061108 (2009). [CrossRef]
• M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett.96161108 (2010). [CrossRef]

J. Non-Crystalline Solids

• P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids3523633–3635 (2006). [CrossRef]

J. Opt. A: Pure Appl. Opt.

• S. John and M. Florescu, “Photonic bandgap materials: towards an all-optical micro-transistor,” J. Opt. A: Pure Appl. Opt.3S103–S120 (2001). [CrossRef]

J. Opt. Soc. Am. B

• I. Kang and F. W. Wise, “Electronic structure and optical properties of PbS and PbSe quantum dots,” J. Opt. Soc. Am. B141632–1646 (1997). [CrossRef]

Laser Photonics Rev.

• P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev.4499–516 (2010). [CrossRef]

Laser Phys.

• A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys.13161–167 (2003).

Nature

• T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432, 200–203 (2004). [CrossRef] [PubMed]
• K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445, 896–899 (2007). [CrossRef] [PubMed]
• J. P. Reithmaier, G. Se.k, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity,” Nature432, 197–200 (2004). [CrossRef] [PubMed]

Opt. Lett.

• I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett.35, 1094–1096 (2010). [CrossRef] [PubMed]

Phys. Rev.

• R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.9399–110 (1954). [CrossRef]
• E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69681 (1946).
• B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev.1881969–1975 (1969). [CrossRef]

Phys. Rev. A

• M. Florescu and S. John, “Single-atom switching in photonic crystals,” Phys. Rev. A64033801 (2001). [CrossRef]
• M. Florescu and S. John, “Resonance fluorescence in photonic band gap waveguide architectures: Engineering the vacuum for all-optical switching,” Phys. Rev. A69053810 (2004). [CrossRef]
• M. Lindberg and C. M. Savage, “Steady-state two-level atomic population inversion via a quantized cavity field,” Phys. Rev. A385182–5192 (1988). [CrossRef] [PubMed]
• F. T. Arecchi and E. Courtens, “Cooperative phenomena in resonant electromagnetic propagation,” Phys. Rev. A21730–1737 (1970). [CrossRef]
• R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A4302–313 (1971). [CrossRef]
• R. Bonifacio and L. A. Lugiato, “Cooperative radiation processes in two-level systems: Superfluorescence,” Phys. Rev. A111507–1521 (1975). [CrossRef]
• H. Takeda and S. John, “Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals,” Phys. Rev. A83053811 (2011). [CrossRef]
• H. Takeda, “Collective population evolution of two-level atoms based on mean-field theory,” Phys. Rev. A85, 023837 (2012). [CrossRef]

Phys. Rev. E

• K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E583896–3908 (1998). [CrossRef]

Phys. Rev. Lett.

• M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett.108, 057402 (2012). [CrossRef] [PubMed]
• 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] [PubMed]
• U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett.108, 043603 (2012). [CrossRef] [PubMed]
• S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic systems,” Phys. Rev. Lett.781888–1891 (1997). [CrossRef]
• T. M. Stace, A. C. Doherty, and S. D. Barrett, “Population inversion of a driven two-level system in a structureless bath,” Phys. Rev. Lett.95106801 (2005). [CrossRef] [PubMed]
• S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett.107, 193601 (2011). [CrossRef] [PubMed]
• S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.582486–2489 (1987). [CrossRef] [PubMed]
• E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.582059–2062 (1987). [CrossRef] [PubMed]

Other

• P. W. Milloni and J. H. Eberly, Laser Physics (Wiley, 2009).
• L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover Publications, Inc., New York, 1987).
• A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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