Abstract

We demonstrate the possibility of room-temperature, thermal equilibrium Bose-Einstein condensation (BEC) of exciton-polaritons in a multiple quantum well (QW) system composed of InGaAs quantum wells surrounded by InP barriers, allowing for the emission of light near telecommunication wavelengths. The QWs are embedded in a cavity consisting of double slanted pore (SP2) photonic crystals composed of InP. We consider exciton-polaritons that result from the strong coupling between the multiple quantum well excitons and photons in the lowest planar guided mode within the photonic band gap (PBG) of the photonic crystal cavity. The collective coupling of three QWs results in a vacuum Rabi splitting of 3% of the bare exciton recombination energy. Due to the full three-dimensional PBG exhibited by the SP2 photonic crystal (16% gap to mid-gap frequency ratio), the radiative decay of polaritons is eliminated in all directions. Due to the short exciton-phonon scattering time in InGaAs quantum wells of 0.5 ps and the exciton non-radiative decay time of 200 ps at room temperature, polaritons can achieve thermal equilibrium with the host lattice to form an equilibrium BEC. Using a SP2 photonic crystal with a lattice constant of a = 516 nm, a unit cell height of 2a=730nm and a pore radius of 0.305a = 157 nm, light in the lowest planar guided mode is strongly localized in the central slab layer. The central slab layer consists of 3 nm InGaAs quantum wells with 7 nm InP barriers, in which excitons have a recombination energy of 0.944 eV, a binding energy of 7 meV and a Bohr radius of aB = 10 nm. We take the exciton recombination energy to be detuned 35 meV above the lowest guided photonic mode so that an exciton-polariton has a photonic fraction of approximately 97% per QW. This increases the energy range of small-effective-mass photonlike states and increases the critical temperature for the onset of a Bose-Einstein condensate. With three quantum wells in the central slab layer, the strong light confinement results in light-matter coupling strength of ℏΩ = 13.7 meV. Assuming an exciton density per QW of (15aB)−2, well below the saturation density, in a 2-D box-trap with a side length of 10 to 500 µm, we predict thermal equilibrium Bose-Einstein condensation well above room temperature.

© 2016 Optical Society of America

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2015 (1)

2014 (5)

J. Schmitt, T. Damm, D. Dung, F. Vewinger, J. Klaers, and M. Weitz, “Observation of grand-canonical number statistics in a photon Bose-Einstein condensate,” Phys. Rev. Lett. 112(3), 030401 (2014).
[Crossref] [PubMed]

J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature BoseEinstein condensation of cavity excitonpolaritons in a polymer,” Nat. Mat. 13(3), 247–252 (2014).
[Crossref]

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(11), 803–813 (2014).
[Crossref]

J.-H. Jiang and S. John, “Photonic crystal architecture for room-temperature equilibrium Bose-Einstein condensation of exciton polaritons,” Phys. Rev. X 4(03), 031025 (2014).

J.-H. Jiang and S. John, “Photonic architectures for equilibrium high-temperature Bose-Einstein condensation in dichalcogenide monolayers,” Nat. Sci. Rep. 4(7432), 1–6 (2014).

2013 (3)

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85(1), 299–366 (2013).
[Crossref]

B. Nelsen, G. Liu, M. Steger, D. W. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3(4), 041015 (2013).

F. Li, L. Orosz, O. Kamoun, S. Bouchoule, C. Brimont, P. Disseix, T. Guillet, X. Lafosse, M. Leroux, J. Leymarie, M. Mexis, M. Mihailovic, G. Patriarche, F. Réveret, D. Solnyshkov, J. Zuniga-Perez, and G. Malpuech, “From excitonic to photonic polariton condensate in a ZnO-Based microcavity,” Phys. Rev. Lett. 110(19), 196406 (2013).
[Crossref] [PubMed]

2012 (3)

A. Das, J. Heo, A. Bayraktaroglu, W. Guo, T.-K. Ng, J. Phillips, B. S. Ooi, and P. Bhattacharya, “Room temperature strong coupling effects from single ZnO nanowire microcavity,” Opt. Express 20(11), 11830–11837 (2012).
[Crossref] [PubMed]

L. Orosz, F. Réveret, F. Médard, P. Disseix, J. Leymarie, M. Mihailovic, D. Solnyshkov, G. Malpuech, J. Zuniga-Pérez, and G. Malpuech, “LO-phonon assisted polariton lasing in a ZnO based microcavity,” Phys. Rev. B 85(12), 121201 (2012).
[Crossref]

J. Klaers, J. Schmitt, T. Damm, F. Vewinger, and M. Weitz, “Statistical physics of Bose-Einstein-condensed light in a dye microcavity,” Phys. Rev. Lett. 108(16), 160403 (2012).
[Crossref] [PubMed]

2011 (2)

D. M. Coles, P. Michetti, C. Clark, W. C. Tsoi, A. M. Adawi, J.-S. Kim, and D. G. Lidzey, “Vibrationally assisted polariton-relaxation processes in strongly coupled organic-semiconductor microcavities,” Adv. Functional Mater. 21(19), 3691–3696 (2011).
[Crossref]

S. Juodkazis, L. Rosa, S. Bauerdick, L. Peto, R. E.-Ganainy, and S. John, “Sculpturing of photonic crystals by ion beam lithography: towards complete photonic bandgap at visible wavelengths,” Opt. Express 19(7), 5802–5810 (2011).
[Crossref] [PubMed]

2010 (4)

J. Klaers, F. Vewinger, and M. Weitz, “Thermalisation of a two-dimensional photonic gas in a ’white-wall’ photon box,” Nat. Phys. 6(7), 512–515 (2010).
[Crossref]

S. Kéna-Cohen and S. R. Forrest, “Room Temperature Polariton Lasing in an Organic Single Crystal Microcavity,” Nat. Photonics 4(6), 371–375 (2010).
[Crossref]

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “BoseEinstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
[Crossref] [PubMed]

H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82(2), 1489–1537 (2010).
[Crossref]

2009 (1)

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mat. 8(9), 721–725 (2009).
[Crossref]

2008 (3)

J. Kasprzak, D. D. Solnyshkov, R. André, L. S. Dang, and G. Malpuech, “Formation of an exciton polariton condensate: thermodynamic versus kinetic regimes,” Phys. Rev. Lett. 82(14) 146404 (2008).
[Crossref]

R. Johne, D. Solnyshkov, and G. Malpuech, “Theory of exciton-polariton lasing at room temperature in ZnO microcavities,” Appl. Phys. Lett. 93(21), 211105 (2008).
[Crossref]

R. Schmidt-Grund, B. Rheinländer, C. Czkalla, G. Benndorf, H. Hochmuth, M. Lorenz, and M. Grundmann, “Excitonpolariton formation at room temperature in a planar ZnO resonator structure,” Appl. Phys. B 93(2), 331–337 (2008).
[Crossref]

2007 (5)

Y. Takahashi, H. Hagino, Y. Tanaka, B.-S. Song, T. Asano, and S. Noda, “High-Q photonic nanocavity with a 2-ns photon lifetime,” Opt. Express 15(25), 17206–17213 (2007).
[Crossref] [PubMed]

S. Christopoulos, G. Baldassari Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref] [PubMed]

S. Yang and S. John, “Exciton dressing and capture by a photonic band edge,” Phys. Rev. B 75(23), 235332 (2007).
[Crossref]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

2006 (4)

N. Ttreault, G. Freymann, M. Deubel, M. Hermatschweiler, F. Prez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
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V. V. Kocharovsky, V. V. Kocharovsky, M. Holthaus, C. H. RaymondOoi, A. Svidzinsky, W. Ketterle, and M. O. Scully, “Fluctuations in Ideal and Interacting Bose-Einstein Condensates: From the Laser Phase Transition Analogy to Squeezed States and Bogoliubov Quasiparticles,” Adv. Atomic, Molecular Opt. Phys. 53(6), 291–411 (2006).
[Crossref]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “BoseEinstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
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H. Deng, D. Press, S. Götzinger, R. Hey, K. H. Ploog, and Y. Yamamoto, “Quantum degenerate exciton-polaritons in thermal equilibrium,” Phys. Rev. Lett. 97(14), 146402 (2006).
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2005 (2)

O. Toader and S. John, “Slanted-pore photonic band-gap materials,” Phys. Rev. E 71(3), 036605 (2005)
[Crossref]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mat. 4(3), 207–210 (2005).
[Crossref]

2004 (4)

D. S. Petrov, D. M. Gangardt, and G. V. Shlyapnikov, “Low-dimensional trapped gases,” J. Phys. IV France 116, 5–44 (2004).
[Crossref]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305(5681), 227–229 (2004).
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M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of “slanted pore” photonic crystals,” Appl. Phys. Lett. 85(11) 1895–1897 (2004).
[Crossref]

M. Litinskaya, P. Reineker, and V. M. Agranovich, “Fast polariton relaxation in strongly coupled organic microcavities,” J. Luminescence 110(4), 364–372 (2004).
[Crossref]

2003 (2)

N. Antoine-Vincent, F. Natali, D. Byrne, A. Vasson, P. Disseix, J. Leymarie, M. Leroux, F. Semond, and J. Massies, “Observation of Rabi splitting in a bulk GaN microcavity grown on silicon,” Phys. Rev. B 68(15), 153313 (2003).
[Crossref]

H. Deng, G. Weihs, D. Snoke, J. Bloch, and Y. Yamamoto, “Polariton lasing vs. photon lasing in a semiconductor microcavity,” Proc. Nat. Acad. Sci. 100(26), 15318–15323 (2003).
[Crossref] [PubMed]

2002 (1)

M. Zamfirescu, A. Kavokin, B. Gil, G. Malpuech, and M. Kaliteevski, “ZnO as a material mostly adapted for realization of room-temperature polariton lasers,” Phys. Rev. B 65(16), 161205 (2002).
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2001 (2)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
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I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for IIIV compound semiconductors and their alloys,” J. Appl. Phys. 89(11), 5815–5875 (2001).
[Crossref]

1999 (1)

F. Tassone and Y. Yamamoto, “Exciton-exciton scattering dynamics in a semiconductor microcavity and stimulated scattering into polaritons,” Phys. Rev. B 59(16), 10830–10842 (1999).
[Crossref]

1998 (1)

M. Leroux, N. Grandjean, M. Laügt, J. Massies, B. Gil, P. Lefebvre, and P. Bigenwald, “Quantum confined Stark effect due to built-in internal polarization fields in (Al,Ga)N/GaN quantum wells,” Phys. Rev. B 58(20), R13371 (1998).
[Crossref]

1996 (2)

G. S. Buller, S. J. Fancey, J. S. Massa, A. C. Walker, S. Cova, and A. Lacaita, “Time-resolved photoluminescence measurements of InGaAs/InP multiple-quantum-well structures at 1.3-µ m wavelengths by use of germanium single-photon avalanche photodiodes,” Appl. Opt. 25(6), 916–921 (1996).
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W. Ketterle and N. J. van Druten, “Bose-Einstein condensation of a finite number of particles trapped in any-dimensional space,” Phys. Rev. A 54(1), 656–660 (1996).
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1995 (2)

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semiconductor microcavities: Unified treatment of weak and strong coupling regimes,” Solid State Commun. 93(9), 733–739 (1995).
[Crossref]

K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. Van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75(22), 3969–3973 (1995).
[Crossref] [PubMed]

1994 (1)

T. Ishikawa and J. E. Bowers, “Band lineup and in-plane effective mass of InGaAsP or InGaAlAs on InP strained-layer quantum well,” IEEE J. Quantum Electron. 30(2), 562–570 (1994).
[Crossref]

1989 (3)

S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, “Linear and nonlinear optical properties of semiconductor quantum wells,” Adv. Phys. 38(2), 89–188 (1989).
[Crossref]

D. W. Snoke and J. P. Wolfe, “Population dynamics of a Bose gas near saturation,” Phys. Rev. B 39(7), 4030–4037 (1989).
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A. Honold, L. Schultheis, J. Kuhl, and C. W. Tu, “Collision broadening of two-dimensional excitons in a GaAs single quantum well,” Phys. Rev. B 40(9), 6442–6445 (1989).
[Crossref]

1988 (2)

S.-K. Chang, A. V. Nurmikko, J.-W. Wu, L. A. Kolodziejski, and R. L. Gunshor, “Band offsets and excitons in CdTe/(Cd, Mn) Te quantum wells,” Phys. Rev. B 37(3), 1191–1198 (1988).
[Crossref]

G. Livescu, D. A. B. Miller, D. S. Chemla, M. Ramaswamy, T. Y. Chang, N. Sauer, A. C. Goassard, and J. H. English, “Free carrier and many-body effects in absorption spectra of modulation-doped quantum wells,” IEEE J. Quantum Electron. 24(8), 1677–1689 (1988).
[Crossref]

1987 (6)

M. S. Skolnick, K. J. Nash, M. K. Saker, S. J. Bass, P.A. Claxton, and J. S. Roberts, “Free-carrier effects on luminescence linewidths in quantum wells,” Appl. Phys. Lett. 50(26), 1885–1887 (1987).
[Crossref]

Y. Kawaguchi and H. Asahi, “High-temperature observation of heavy-hole and light-hole excitons in InGaAs/InP multiple quantum well structures grown by metalorganic molecular beam epitaxy,” Appl. Phys. Lett. 50(18), 1243–1245 (1987).
[Crossref]

K. Tai, J. Hegarty, and W. T. Tsang, “Observation of optical Stark effect in InGaAs/InP multiple quantum wells,” Appl. Phys. Lett. 51(3), 152–154 (1987).
[Crossref]

D. J. Westland, A. M. Fox, A. C. Maciel, J. F. Ryan, M. D. Scott, J. I. Davies, and J. R. Riffat, “Optical studies of excitons in Ga0.47In0.53As/InP multiple quantum wells,” Appl. Phys. Lett. 50(13), 839–841 (1987).
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S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
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E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
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1986 (2)

M. S. Skolnick, P. R. Tapster, S. J. Bass, A. D. Pitt, N. Apsley, and S. P. Aldred, “Investigation of InGaAs-InP quantum wells by optical spectroscopy,” Semicond. Sci. Techn. 1(1), 29–40 (1986).
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E. Zielinski, H. Schweizer, K. Streubel, H. Eisele, and G. Weimann, “Excitonic transitions and exciton damping processes in InGaAs/InP,” J. Appl. Phys. 59(6), 2196–2204 (1986).
[Crossref]

1985 (1)

S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B 32(10), 6601–6609 (1985).
[Crossref]

1981 (1)

R. C. Miller, D. A. Kleinman, W. T. Tsang, and A. C. Gossard, “Observation of the excited level of excitons in GaAs quantum wells,” Phys. Rev. B 24(2), 1134–1136 (1981).
[Crossref]

1977 (1)

E. Hanamura and H. Haug, “Condensation effects of excitons,” Phys. Lett. 33(4), 209–284 (1977).

1969 (1)

É. B. Sonin, “Quantization of the magnetic flux of superconducting rings and Bose condensation,” Sov. Phys. JETP 29(3), 520–525 (1969).

1967 (1)

P. Hohenberg, “Existence of long-range order in one and two dimensions,” Phys. Rev. 158(2), 383–386 (1967).
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1966 (1)

N. D. Mermin and H. Wagner, “Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models,” Phys. Rev. Lett. 17(22), 1133–1136 (1966).
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1956 (1)

O. Penrose and L. Onsager, “Bose-Einstein condensation and liquid helium,” Phys. Rev. 104(3), 576–584 (1956).
[Crossref]

Adawi, A. M.

D. M. Coles, P. Michetti, C. Clark, W. C. Tsoi, A. M. Adawi, J.-S. Kim, and D. G. Lidzey, “Vibrationally assisted polariton-relaxation processes in strongly coupled organic-semiconductor microcavities,” Adv. Functional Mater. 21(19), 3691–3696 (2011).
[Crossref]

Agranovich, V. M.

M. Litinskaya, P. Reineker, and V. M. Agranovich, “Fast polariton relaxation in strongly coupled organic microcavities,” J. Luminescence 110(4), 364–372 (2004).
[Crossref]

Akahane, Y.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mat. 4(3), 207–210 (2005).
[Crossref]

Aldred, S. P.

M. S. Skolnick, P. R. Tapster, S. J. Bass, A. D. Pitt, N. Apsley, and S. P. Aldred, “Investigation of InGaAs-InP quantum wells by optical spectroscopy,” Semicond. Sci. Techn. 1(1), 29–40 (1986).
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André, R.

J. Kasprzak, D. D. Solnyshkov, R. André, L. S. Dang, and G. Malpuech, “Formation of an exciton polariton condensate: thermodynamic versus kinetic regimes,” Phys. Rev. Lett. 82(14) 146404 (2008).
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J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “BoseEinstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref] [PubMed]

Andreani, L. C.

V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semiconductor microcavities: Unified treatment of weak and strong coupling regimes,” Solid State Commun. 93(9), 733–739 (1995).
[Crossref]

Andrews, M. R.

K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. Van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75(22), 3969–3973 (1995).
[Crossref] [PubMed]

Antoine-Vincent, N.

N. Antoine-Vincent, F. Natali, D. Byrne, A. Vasson, P. Disseix, J. Leymarie, M. Leroux, F. Semond, and J. Massies, “Observation of Rabi splitting in a bulk GaN microcavity grown on silicon,” Phys. Rev. B 68(15), 153313 (2003).
[Crossref]

Apsley, N.

M. S. Skolnick, P. R. Tapster, S. J. Bass, A. D. Pitt, N. Apsley, and S. P. Aldred, “Investigation of InGaAs-InP quantum wells by optical spectroscopy,” Semicond. Sci. Techn. 1(1), 29–40 (1986).
[Crossref]

Asahi, H.

Y. Kawaguchi and H. Asahi, “High-temperature observation of heavy-hole and light-hole excitons in InGaAs/InP multiple quantum well structures grown by metalorganic molecular beam epitaxy,” Appl. Phys. Lett. 50(18), 1243–1245 (1987).
[Crossref]

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

Y. Takahashi, H. Hagino, Y. Tanaka, B.-S. Song, T. Asano, and S. Noda, “High-Q photonic nanocavity with a 2-ns photon lifetime,” Opt. Express 15(25), 17206–17213 (2007).
[Crossref] [PubMed]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mat. 4(3), 207–210 (2005).
[Crossref]

Baas, A.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “BoseEinstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref] [PubMed]

Baldassari Höger von Högersthal, G.

S. Christopoulos, G. Baldassari Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

Balili, R.

B. Nelsen, G. Liu, M. Steger, D. W. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3(4), 041015 (2013).

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref] [PubMed]

Bass, S. J.

M. S. Skolnick, K. J. Nash, M. K. Saker, S. J. Bass, P.A. Claxton, and J. S. Roberts, “Free-carrier effects on luminescence linewidths in quantum wells,” Appl. Phys. Lett. 50(26), 1885–1887 (1987).
[Crossref]

M. S. Skolnick, P. R. Tapster, S. J. Bass, A. D. Pitt, N. Apsley, and S. P. Aldred, “Investigation of InGaAs-InP quantum wells by optical spectroscopy,” Semicond. Sci. Techn. 1(1), 29–40 (1986).
[Crossref]

Bauerdick, S.

Baumberg, J. J.

S. Christopoulos, G. Baldassari Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

Bayraktaroglu, A.

Benndorf, G.

R. Schmidt-Grund, B. Rheinländer, C. Czkalla, G. Benndorf, H. Hochmuth, M. Lorenz, and M. Grundmann, “Excitonpolariton formation at room temperature in a planar ZnO resonator structure,” Appl. Phys. B 93(2), 331–337 (2008).
[Crossref]

Bhattacharya, P.

Bigenwald, P.

M. Leroux, N. Grandjean, M. Laügt, J. Massies, B. Gil, P. Lefebvre, and P. Bigenwald, “Quantum confined Stark effect due to built-in internal polarization fields in (Al,Ga)N/GaN quantum wells,” Phys. Rev. B 58(20), R13371 (1998).
[Crossref]

Bloch, J.

H. Deng, G. Weihs, D. Snoke, J. Bloch, and Y. Yamamoto, “Polariton lasing vs. photon lasing in a semiconductor microcavity,” Proc. Nat. Acad. Sci. 100(26), 15318–15323 (2003).
[Crossref] [PubMed]

Bouchoule, S.

F. Li, L. Orosz, O. Kamoun, S. Bouchoule, C. Brimont, P. Disseix, T. Guillet, X. Lafosse, M. Leroux, J. Leymarie, M. Mexis, M. Mihailovic, G. Patriarche, F. Réveret, D. Solnyshkov, J. Zuniga-Perez, and G. Malpuech, “From excitonic to photonic polariton condensate in a ZnO-Based microcavity,” Phys. Rev. Lett. 110(19), 196406 (2013).
[Crossref] [PubMed]

Bowers, J. E.

T. Ishikawa and J. E. Bowers, “Band lineup and in-plane effective mass of InGaAsP or InGaAlAs on InP strained-layer quantum well,” IEEE J. Quantum Electron. 30(2), 562–570 (1994).
[Crossref]

Brimont, C.

F. Li, L. Orosz, O. Kamoun, S. Bouchoule, C. Brimont, P. Disseix, T. Guillet, X. Lafosse, M. Leroux, J. Leymarie, M. Mexis, M. Mihailovic, G. Patriarche, F. Réveret, D. Solnyshkov, J. Zuniga-Perez, and G. Malpuech, “From excitonic to photonic polariton condensate in a ZnO-Based microcavity,” Phys. Rev. Lett. 110(19), 196406 (2013).
[Crossref] [PubMed]

Buller, G. S.

G. S. Buller, S. J. Fancey, J. S. Massa, A. C. Walker, S. Cova, and A. Lacaita, “Time-resolved photoluminescence measurements of InGaAs/InP multiple-quantum-well structures at 1.3-µ m wavelengths by use of germanium single-photon avalanche photodiodes,” Appl. Opt. 25(6), 916–921 (1996).
[Crossref]

Butté, R.

S. Christopoulos, G. Baldassari Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

Byrne, D.

N. Antoine-Vincent, F. Natali, D. Byrne, A. Vasson, P. Disseix, J. Leymarie, M. Leroux, F. Semond, and J. Massies, “Observation of Rabi splitting in a bulk GaN microcavity grown on silicon,” Phys. Rev. B 68(15), 153313 (2003).
[Crossref]

Byrnes, T.

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(11), 803–813 (2014).
[Crossref]

Cao, H.

Y. Yamamoto, F. Tassone, and H. Cao, Semiconductor Cavity Quantum Electrodynamics (Springer-Verlag, 2000).

Carlin, J.-F.

S. Christopoulos, G. Baldassari Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

Carusotto, I.

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85(1), 299–366 (2013).
[Crossref]

Chang, S.-K.

S.-K. Chang, A. V. Nurmikko, J.-W. Wu, L. A. Kolodziejski, and R. L. Gunshor, “Band offsets and excitons in CdTe/(Cd, Mn) Te quantum wells,” Phys. Rev. B 37(3), 1191–1198 (1988).
[Crossref]

Chang, T. Y.

G. Livescu, D. A. B. Miller, D. S. Chemla, M. Ramaswamy, T. Y. Chang, N. Sauer, A. C. Goassard, and J. H. English, “Free carrier and many-body effects in absorption spectra of modulation-doped quantum wells,” IEEE J. Quantum Electron. 24(8), 1677–1689 (1988).
[Crossref]

Chemla, D. S.

S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, “Linear and nonlinear optical properties of semiconductor quantum wells,” Adv. Phys. 38(2), 89–188 (1989).
[Crossref]

G. Livescu, D. A. B. Miller, D. S. Chemla, M. Ramaswamy, T. Y. Chang, N. Sauer, A. C. Goassard, and J. H. English, “Free carrier and many-body effects in absorption spectra of modulation-doped quantum wells,” IEEE J. Quantum Electron. 24(8), 1677–1689 (1988).
[Crossref]

S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B 32(10), 6601–6609 (1985).
[Crossref]

Christmann, G.

S. Christopoulos, G. Baldassari Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

Christopoulos, S.

S. Christopoulos, G. Baldassari Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007).
[Crossref] [PubMed]

Ciuti, C.

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85(1), 299–366 (2013).
[Crossref]

Clark, C.

D. M. Coles, P. Michetti, C. Clark, W. C. Tsoi, A. M. Adawi, J.-S. Kim, and D. G. Lidzey, “Vibrationally assisted polariton-relaxation processes in strongly coupled organic-semiconductor microcavities,” Adv. Functional Mater. 21(19), 3691–3696 (2011).
[Crossref]

Claxton, P.A.

M. S. Skolnick, K. J. Nash, M. K. Saker, S. J. Bass, P.A. Claxton, and J. S. Roberts, “Free-carrier effects on luminescence linewidths in quantum wells,” Appl. Phys. Lett. 50(26), 1885–1887 (1987).
[Crossref]

Coles, D. M.

D. M. Coles, P. Michetti, C. Clark, W. C. Tsoi, A. M. Adawi, J.-S. Kim, and D. G. Lidzey, “Vibrationally assisted polariton-relaxation processes in strongly coupled organic-semiconductor microcavities,” Adv. Functional Mater. 21(19), 3691–3696 (2011).
[Crossref]

Cova, S.

G. S. Buller, S. J. Fancey, J. S. Massa, A. C. Walker, S. Cova, and A. Lacaita, “Time-resolved photoluminescence measurements of InGaAs/InP multiple-quantum-well structures at 1.3-µ m wavelengths by use of germanium single-photon avalanche photodiodes,” Appl. Opt. 25(6), 916–921 (1996).
[Crossref]

Czkalla, C.

R. Schmidt-Grund, B. Rheinländer, C. Czkalla, G. Benndorf, H. Hochmuth, M. Lorenz, and M. Grundmann, “Excitonpolariton formation at room temperature in a planar ZnO resonator structure,” Appl. Phys. B 93(2), 331–337 (2008).
[Crossref]

Damm, T.

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Figures (9)

Fig. 1
Fig. 1

(a) Slanted pore photonic crystal sandwiching a thin planar slab containing quantum wells. The pores are approximately 160 nm in radius. Three quantum wells are embedded in the central slab layer, which is approximately 36 nm in width. (b) Band structure for the heterostructure shown in Fig. 1(a) in the first Brillouin Zone of −π/a ≤ kx,ky ≤ π/a. The shaded grey areas represent the bulk 3D bands of the slanted pore crystal. The curves in the photonic band gap denote confined 2D guided modes introduced in the central slab layer, of which the lowest one is labelled in magenta. (c) A closer view of the band diagram around the photonic band gap. The excitonic recombination energy of E0 = 944 meV (dashed black line) is detuned above the lowest guided photonic band by Δ = 35 meV. The lower and upper polariton branches are shown in blue and red respectively. An exciton-photon coupling of ℏΩ = 13.7 meV is used in obtaining the polariton dispersion curves.

Fig. 2
Fig. 2

(a) Electric field intensity in the QW region for the lowest guided mode over the area occupied by one unit cell of slanted pore photonic crystal. The slice is in the x-y plane at a height of z = 0, through the middle of the central slab layer. The patterned areas indicate the regions where the air pores make contact with the central slab layer. (b) Average in-plane field intensity for the lowest guided photonic mode at wave vector Q ( Y ) = ( 0 , 0.5 ) 2 π a (dotted line) 1 S S α = L , T ( u Q ( Y ) ( ρ , z ) n ^ α ) 2 d 2 ρ, and that of the z-component (solid line, multiplied by a factor of 10) 1 S S ( u Q ( Y ) ( ρ , z ) n ^ Z ) 2 d 2 ρ as a function of the vertical position z in the heterostructure. (c) Photonic dispersion ℏωk for the lowest guided photonic mode over the first photonic Brillouin Zone. The lattice constant a = 495 nm is chosen so that the exciton is resonant with the lowest guided photonic mode.

Fig. 3
Fig. 3

(a) The collective coupling strength ℏΩk over the high symmetry path in the first photonic Brillouin Zone. We compute ℏΩk assuming there are three QWs in the central slab layer and a detuning of Δ = 35 meV. (b) The dispersion of the lower polariton branch from Eq. (9). The collective coupling strength is ℏΩ = 13.7 meV for three QWs placed in the central slab layer. The lattice constant is a = 495 nm to enforce a detuning of Δ = 0. In both Figs. (a) and (b), the QWs are composed of 3 nm InGaAs wells surrounded by 7 nm InP barriers and the central slab layer is 0.07a thick. (c) The dispersion depth V and the detuning Δ. The excitonic dispersion (dashed green), lowest guided 2D photonic band dispersion (dash-dot blue) and the lower and upper polariton dispersions (solid red) are shown from the local photonic minimum at k = Q(Y) to k = 0.

Fig. 4
Fig. 4

The collective coupling strength ℏΩ as a function of the number of (3 nm thick) InGaAs QWs (with 7 nm InP barriers) embedded in the heterostructure. The lattice constant a = 516 nm provides an exciton-photon detuning of Δ = 35 meV. The first three QWs are placed in the central slab layer, and subsequent QWs are placed in the photonic crystal above and below the central slab layer.

Fig. 5
Fig. 5

(a) The exciton recombination energy E0 (circles) and the exciton binding energy (triangles) in InGaAs quantum wells of varying widths surrounded by 7 nm InP barriers. (c) The lattice constant a (circles) required to enforce a detuning of Δ = 35 meV for each QW width. For each QW width, the central slab layer accomodates three QWs. (c) The collective coupling strength versus the QW width, assuming there are only QWs in the central slab layer (circles) and that the first unit cell of SP2 above and below the central slab layer are saturated with QWs (triangles). (d) The relationship between detuning Δ and the lattice constant a for a 0.07a central slab layer sandwiched by SP2 photonic crystal with a pore radius of 0.305a. The exciton recombination energy is 944 meV, which is that for 3 nm InGaAs QWs surrounded by 7 nm InP barriers.

Fig. 6
Fig. 6

The critical temperature for the onset of an exciton-polariton BEC as a function of the detuning Δ and (a) the cavity length, (b) coupling strength and (c) the number of QWs in the system. In (a), we assume that there are three QWs in the central slab layer yielding a coupling strength of ℏΩ = 13.7 meV. In (b) and (c), the cavity length is taken to be 50 µm. In all cases, the polariton density per QW is (6.2aB)−2 = 260 µm−2 where aB is the exciton Bohr radius.

Fig. 7
Fig. 7

The BEC critical temperature as a function of the polariton density and (a) cavity length, (b) number of QWs in the system and (c) detuning. In (a), we consider three QWs in the central slab layer yielding a collective coupling strength of ℏΩ = 13.7 meV and a detuning of Δ = 35 meV. In (b), we consider a cavity length of D = 50 µm−2 and a detuning of Δ = 35 meV. In (c), we consider a cavity length of D = 50 µm−2 and three quantum wells in the central slab layer (ℏΩ = 13.7 meV). The maximum polariton density per QW is chosen to be (2.8aB)−2 = 1.2 × 103 µm−2.

Fig. 8
Fig. 8

(a) The remaining PBG between the LP and the lower 3D band edge, relative to the central band gap frequency versus pore radius rp in the slanted pore photonic crystal. (b) The upper 3D band edge (upper red curve), the lower 3D band edge (lower blue curve) and the LP ground state (middle cyan curve) energies versus pore radius rp. The shaded area represents the intersection set of photonic band gaps generated by each pore radius. (c) The detuning Δ (blue curve) and the collective coupling strength ℏΩ (red curve) and (d) the dispersion depth V versus the pore radius rp. In all cases, there are three InGaAs/InP QWs embedded in a 0.07a = 36 nm thick central slab layer layer. In Figs. 8(a), 8(b) and 8(c), the lattice constant is held at a = 516 nm to enforce a detuning of Δ = 35 meV when the pore radius is rp = 0.305a = 157 nm. In Fig. 8(d), the lattice constant is a = 516 nm (lower blue curve) and a = 519 nm (upper green curve) to enforce detunings of Δ = 35 meV and Δ = 40 meV, respectively, when the pore radius is 0.305a.

Fig. 9
Fig. 9

(a) The root mean square deviation of the dispersion depth V (circles) and the vacuum Rabi splitting Δ 2 + 4 2 Ω 2 (triangles) as a function of the exciton inhomogeneous broadening ΔErms. (b) The root mean square deviation of the critical temperature Tc as a function of the exciton inhomogeneous broadening ΔErms. The red dashed line indicates the value of ΔErms.

Equations (18)

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E p , k ( ρ , z ) = ω p , k 2 ε 0 S u p , k ( ρ , z ) e i k ρ ,
H ^ = H ^ exc + H ^ ph + H ^ int ,
H ^ exc = l , n , α , k E exc ( k + G n ) β l , α , k + G n β l , α , k + G n ,
H ^ ph = p , k ω p , k a ^ p , k a ^ p , k ,
H ^ int = l , α , n , p , k i Ω ˜ l , α , n , p , k β l , α , k + G n a p , k + h . c . ,
Ω ˜ l , α , n , p , k = E exc ( k + G n ) 2 ω p , k ε 0 ϕ ( 0 ) d α ( u p , k + G n ( ρ , z l ) n ^ α ) ,
E exc ( k ) = E 0 + 2 2 m exc k 2 ,
ω k = ω 0 + 2 2 ( ( k x Q x ( Y ) ) 2 m x ( Y ) + ( k y Q y ( Y ) ) 2 m y ( Y ) ) .
H ^ = H ^ 0 + H ^ int ,
H ^ 0 = k [ E exc ( k ) b ^ k b ^ k + ω k a ^ k a ^ k ] ,
H ^ int = k i Ω k ( b ^ k a ^ k b ^ k a ^ k ) ,
b ^ k = l , α , n Ω ˜ l , α , n , k Ω k β l , α , k + G n ,
Ω k = l , n , α Ω ˜ l , α , n , k Ω ˜ l , α , n , k .
Ω k = E 0 2 ω k ε 0 S | ϕ ( 0 ) | | d | [ l S | u k ( ρ , z l ) | 2 d 2 ρ ] 1 / 2 .
E LP ( k ) = 1 2 ( E exc ( k ) + ω k ( E exc ( k ) ω k ) 2 + 4 2 Ω 2 ) ,
V = [ E exc ( k ) E LP ( k ) ] k = Q ( Y ) = Δ / 2 + ( Δ / 2 ) 2 + 2 Ω 2 ,
n x , n y > 1 1 exp ( E LP ( k n x , n y ) / k B T c ) 1 = N ,
V = Δ / 2 + Re [ ( Δ i Γ ) 2 + 4 2 Ω 2 ] 1 / 2 / 2 .

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