Abstract

We consider theoretically nonlinear effects in a semiconductor quantum well embedded inside a photonic microcavity. Two-photon absorption by a 2p exciton state is considered and investigated; the matrix element of two-photon absorption is calculated. We compute the emission spectrum of the sample and demonstrate that under coherent pumping the nonlinearity of the two photon absorption process gives rise to bistability.

© 2013 OSA

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  1. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymanska, R. Andre, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
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  2. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
    [Crossref] [PubMed]
  3. C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, “Coherent zero-state and p-state in an exciton-polariton condensate array,” Nature 450(7169), 529–532 (2007).
    [Crossref] [PubMed]
  4. A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaitre, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Vina, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
    [Crossref] [PubMed]
  5. A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdre, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nature Phys.,  5, 805–810 (2009).
    [Crossref]
  6. I. Carusotto and C. Ciuti, “Probing microcavity polariton superfluidity through resonant Rayleigh scattering,” Phys. Rev. Lett., 93(16), 166401 (2004).
    [Crossref]
  7. K. G. Lagoudakis, B. Pietka, M. Wouters, R. Andre, and B. Deveaud-Pledran, “Coherent oscillations in an exciton-polariton Josephson junction,” Phys. Rev. Lett. 105(12), 120403 (2010).
    [Crossref] [PubMed]
  8. K. G. Lagoudakis, T. Ostatnicky, A. V. Kavokin, Y. G. Rubo, R. Andre, and B. Deveaud-Pledran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 13(5955), 974–976 (2009).
    [Crossref]
  9. K. G. Lagoudakis, F. Manni, B. Pietka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. Andre, and B. Deveaud-Pledran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106(11), 115301 (2011).
    [Crossref] [PubMed]
  10. G. Nardin, G. Grosso, Y. Leger, B. Pietka, F. Morier-Genoud, and B. Deveaud-Pledran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nature Phys. 7, 635–641 (2011).
    [Crossref]
  11. A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332(6034), 1167–1170 (2011).
    [Crossref] [PubMed]
  12. G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107(24), 245301 (2011).
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  13. M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Mndez, K. Biermann, R. Hey, and P. V. Santoset, “Observation of bright polariton solitons in a semiconductor microcavity,” Nature Photon. 6, 50–55 (2012).
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  15. F. Manni, K. G. Lagoudakis, T. C. H. Liew, R. Andre, and B. Deveaud-Pledran, “Spontaneous pattern formation in a polariton condensate,” Phys. Rev. Lett. 107(10), 106401 (2011).
    [Crossref] [PubMed]
  16. G. Christmann, G. Tosi, N. G. Berloff, P. Tsotsis, P. S. Eldridge, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Polariton ring condensates and sunflower ripples in an expanding quantum liquid,” Phys. Rev. B 85(23), 235303 (2012).
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  19. Ayan Das, Junseok Heo, Marc Jankowski, Wei Guo, Lei Zhang, Hui Deng, and Pallab Bhattacharya, “Room temperature ultralow threshold GaN nanowire polariton laser,” Phys. Rev. Lett. 107(6), 066405 (2011).
    [Crossref] [PubMed]
  20. R. Schmidt-Grund, B. Rheinlnder, C. Czekalla, G. Benndorf, H. Hochmut, A. Rahm, M. Lorenz, and M. Grundmann, “ZnO based planar and micropillar resonators,” Superlattic. Microstruct. 41(5–6), 360–363 (2007).
    [Crossref]
  21. S. Kena-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nature Photonics 4, 371–375 (2010).
    [Crossref]
  22. T. C. H. Liew, I. A. Shelykh, and G. Malpuech, “Polaritonic devices,” Physica E 43(9), 1543–1568 (2011).
    [Crossref]
  23. K. V. Kavokin, M. A. Kaliteevski, R. A. Abram, A. V. Kavokin, S. Sharkova, and I. A. Shelykh, “Stimulated emission of terahertz radiation by exciton-polariton lasers,” Appl. Phys. Lett. 97(20), 201111 (2010).
    [Crossref]
  24. A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108(19), 197401 (2012).
    [Crossref] [PubMed]
  25. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
    [Crossref] [PubMed]
  26. I. G. Savenko, O. V. Kibis, and I. A. Shelykh, “Asymmetric quantum dot in a microcavity as a nonlinear optical element,” Phys. Rev. A 85(5), 053818 (2012).
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  28. V. D. Kulakovskii, A. I. Tartakovskii, D. N. Krizhanovskii, A. Armitage, J. S. Roberts, and M. S. Skolnick, “Two-dimensional excitonic polaritons and their interaction,” Phys. Usp. 43(8), 853–857 (2000).
    [Crossref]
  29. N. A. Gippius, S. G. Tikhodeev, V. D. Kulakovskii, D. N. Krizhanovskii, and A. I. Tartakovskii, “Nonlinear dynamics of polariton scattering in semiconductor microcavity: Bistability vs. stimulated scattering,” Europhys. Lett. 67(6), 997 (2004).
    [Crossref]
  30. D. M. Whittaker, “Effects of polariton-energy renormalization in the microcavity optical parametric oscillator,” Phys. Rev. B 71(11), 115301 (2005).
    [Crossref]
  31. A. Baas, J. P. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Optical bistability in semiconductor microcavities in the nondegenerate parametric oscillation regime: Analogy with the optical parametric oscillator,” Phys. Rev. B 70(16), 161307(R) (2004).
    [Crossref]
  32. N. A. Gippius, I. A. Shelykh, D. D. Solnyshkov, S. S. Gavrilov, Yuri G. Rubo, A. V. Kavokin, S. G. Tikhodeev, and G. Malpuech, “Polarization multistability of cavity polaritons,” Phys. Rev. Lett. 98(23), 236401 (2007).
    [Crossref] [PubMed]
  33. T. K. Paraïso, M. Wouters, Y. Léger, F. Morier-Genoud, and B. Deveaud-Plédran, “Multistability of a coherent spin ensemble in a semiconductor microcavity,” Nature Mater. 9, 655–660 (2010).
    [Crossref]
  34. D. Bajoni, E. Semenova, A. Lematre, S. Bouchoule, E. Wertz, P. Senellart, S. Barbay, R. Kuszelewicz, and J. Bloch, “Optical bistability in a GaAs-based polariton diode,” Phys. Rev. Lett. 101(26), 266402 (2008).
    [Crossref] [PubMed]
  35. T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 100(11), 116401 (2008).
    [PubMed]
  36. A. Amo, T. H. C. Liew, C. Adrados, R. Houdre, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nature Photon. 4, 361–366 (2010).
    [Crossref]
  37. D. Sarkar, S. S. Gavrilov, M. Sich, J. H. Quilter, R. A. Bradley, N. A. Gippius, K. Guda, V. D. Kulakovskii, M. S. Skolnick, and D. N. Krizhanovskii, “Polarization bistability and resultant spin rings in semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216402 (2010).
    [Crossref]
  38. C. Adrados, A. Amo, T. C. H. Liew, R. Hivet, R. Houdr, E. Giacobino, A. V. Kavokin, and A. Bramati, “Spin rings in bistable planar semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216403 (2010).
    [Crossref]
  39. T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 101(1), 016402 (2008).
    [Crossref] [PubMed]
  40. T. C. H. Liew, A. V. Kavokin, T. Ostatnický, M. Kaliteevski, I. A. Shelykh, and R. A. Abram, “Exciton-polariton integrated circuits,” Phys. Rev. B 82(3), 033302 (2010).
    [Crossref]
  41. I. G. Savenko, I. A. Shelykh, and M. A. Kaliteevski, “Nonlinear terahertz emission in semiconductor microcavities,” Phys. Rev. Lett. 107(2), 027401 (2011).
    [Crossref] [PubMed]
  42. 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]
  43. I. A. Shelykh, A. V. Kavokin, Yuri G. Rubo, T. C. H. Liew, and G. Malpuech, “Polariton polarization-sensitive phenomena in planar semiconductor microcavities”, Semicond. Sci. Technol. 25(1), 013001 (2010).
    [Crossref]
  44. A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
    [Crossref]
  45. B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Generation of entangled photon holes using quantum interference,” Phys. Rev. A 74(4), 010303()R (2006).
  46. X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, and W. Y. Ching, “Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory,” Phys.Rev. A 43(3), 1186–1196 (1991).
    [Crossref] [PubMed]

2012 (6)

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Mndez, K. Biermann, R. Hey, and P. V. Santoset, “Observation of bright polariton solitons in a semiconductor microcavity,” Nature Photon. 6, 50–55 (2012).
[Crossref]

R. Hivet, H. Flayac, D. D. Solnyshkov, D. Tanese, T. Boulier, D. Andreoli, E. Giacobino, J. Bloch, A. Bramati, G. Malpuech, and A. Amo, “Half-solitons in a polariton quantum fluid behave like magnetic monopoles,” Nature Phys. 8, 724–728 (2012).
[Crossref]

G. Christmann, G. Tosi, N. G. Berloff, P. Tsotsis, P. S. Eldridge, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Polariton ring condensates and sunflower ripples in an expanding quantum liquid,” Phys. Rev. B 85(23), 235303 (2012).
[Crossref]

E. Kammann, T. C. H. Liew, H. Ohadi, P. Cilibrizzi, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, A. V. Kavokin, and P. G. Lagoudakis, “Nonlinear optical spin Hall effect and long-range spin transport in polariton lasers,” Phys. Rev. Lett. 109(3), 036404 (2012).
[Crossref] [PubMed]

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108(19), 197401 (2012).
[Crossref] [PubMed]

I. G. Savenko, O. V. Kibis, and I. A. Shelykh, “Asymmetric quantum dot in a microcavity as a nonlinear optical element,” Phys. Rev. A 85(5), 053818 (2012).
[Crossref]

2011 (8)

T. C. H. Liew, I. A. Shelykh, and G. Malpuech, “Polaritonic devices,” Physica E 43(9), 1543–1568 (2011).
[Crossref]

Ayan Das, Junseok Heo, Marc Jankowski, Wei Guo, Lei Zhang, Hui Deng, and Pallab Bhattacharya, “Room temperature ultralow threshold GaN nanowire polariton laser,” Phys. Rev. Lett. 107(6), 066405 (2011).
[Crossref] [PubMed]

F. Manni, K. G. Lagoudakis, T. C. H. Liew, R. Andre, and B. Deveaud-Pledran, “Spontaneous pattern formation in a polariton condensate,” Phys. Rev. Lett. 107(10), 106401 (2011).
[Crossref] [PubMed]

K. G. Lagoudakis, F. Manni, B. Pietka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. Andre, and B. Deveaud-Pledran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106(11), 115301 (2011).
[Crossref] [PubMed]

G. Nardin, G. Grosso, Y. Leger, B. Pietka, F. Morier-Genoud, and B. Deveaud-Pledran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nature Phys. 7, 635–641 (2011).
[Crossref]

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332(6034), 1167–1170 (2011).
[Crossref] [PubMed]

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107(24), 245301 (2011).
[Crossref]

I. G. Savenko, I. A. Shelykh, and M. A. Kaliteevski, “Nonlinear terahertz emission in semiconductor microcavities,” Phys. Rev. Lett. 107(2), 027401 (2011).
[Crossref] [PubMed]

2010 (9)

T. K. Paraïso, M. Wouters, Y. Léger, F. Morier-Genoud, and B. Deveaud-Plédran, “Multistability of a coherent spin ensemble in a semiconductor microcavity,” Nature Mater. 9, 655–660 (2010).
[Crossref]

I. A. Shelykh, A. V. Kavokin, Yuri G. Rubo, T. C. H. Liew, and G. Malpuech, “Polariton polarization-sensitive phenomena in planar semiconductor microcavities”, Semicond. Sci. Technol. 25(1), 013001 (2010).
[Crossref]

T. C. H. Liew, A. V. Kavokin, T. Ostatnický, M. Kaliteevski, I. A. Shelykh, and R. A. Abram, “Exciton-polariton integrated circuits,” Phys. Rev. B 82(3), 033302 (2010).
[Crossref]

K. G. Lagoudakis, B. Pietka, M. Wouters, R. Andre, and B. Deveaud-Pledran, “Coherent oscillations in an exciton-polariton Josephson junction,” Phys. Rev. Lett. 105(12), 120403 (2010).
[Crossref] [PubMed]

K. V. Kavokin, M. A. Kaliteevski, R. A. Abram, A. V. Kavokin, S. Sharkova, and I. A. Shelykh, “Stimulated emission of terahertz radiation by exciton-polariton lasers,” Appl. Phys. Lett. 97(20), 201111 (2010).
[Crossref]

S. Kena-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nature Photonics 4, 371–375 (2010).
[Crossref]

A. Amo, T. H. C. Liew, C. Adrados, R. Houdre, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nature Photon. 4, 361–366 (2010).
[Crossref]

D. Sarkar, S. S. Gavrilov, M. Sich, J. H. Quilter, R. A. Bradley, N. A. Gippius, K. Guda, V. D. Kulakovskii, M. S. Skolnick, and D. N. Krizhanovskii, “Polarization bistability and resultant spin rings in semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216402 (2010).
[Crossref]

C. Adrados, A. Amo, T. C. H. Liew, R. Hivet, R. Houdr, E. Giacobino, A. V. Kavokin, and A. Bramati, “Spin rings in bistable planar semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216403 (2010).
[Crossref]

2009 (3)

K. G. Lagoudakis, T. Ostatnicky, A. V. Kavokin, Y. G. Rubo, R. Andre, and B. Deveaud-Pledran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 13(5955), 974–976 (2009).
[Crossref]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaitre, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Vina, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
[Crossref] [PubMed]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdre, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nature Phys.,  5, 805–810 (2009).
[Crossref]

2008 (3)

T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 101(1), 016402 (2008).
[Crossref] [PubMed]

D. Bajoni, E. Semenova, A. Lematre, S. Bouchoule, E. Wertz, P. Senellart, S. Barbay, R. Kuszelewicz, and J. Bloch, “Optical bistability in a GaAs-based polariton diode,” Phys. Rev. Lett. 101(26), 266402 (2008).
[Crossref] [PubMed]

T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 100(11), 116401 (2008).
[PubMed]

2007 (5)

N. A. Gippius, I. A. Shelykh, D. D. Solnyshkov, S. S. Gavrilov, Yuri G. Rubo, A. V. Kavokin, S. G. Tikhodeev, and G. Malpuech, “Polarization multistability of cavity polaritons,” Phys. Rev. Lett. 98(23), 236401 (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(5827), 1007–1010 (2007).
[Crossref] [PubMed]

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, “Coherent zero-state and p-state in an exciton-polariton condensate array,” Nature 450(7169), 529–532 (2007).
[Crossref] [PubMed]

R. Schmidt-Grund, B. Rheinlnder, C. Czekalla, G. Benndorf, H. Hochmut, A. Rahm, M. Lorenz, and M. Grundmann, “ZnO based planar and micropillar resonators,” Superlattic. Microstruct. 41(5–6), 360–363 (2007).
[Crossref]

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. 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]

2006 (3)

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

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
[Crossref]

B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Generation of entangled photon holes using quantum interference,” Phys. Rev. A 74(4), 010303()R (2006).

2005 (1)

D. M. Whittaker, “Effects of polariton-energy renormalization in the microcavity optical parametric oscillator,” Phys. Rev. B 71(11), 115301 (2005).
[Crossref]

2004 (3)

A. Baas, J. P. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Optical bistability in semiconductor microcavities in the nondegenerate parametric oscillation regime: Analogy with the optical parametric oscillator,” Phys. Rev. B 70(16), 161307(R) (2004).
[Crossref]

N. A. Gippius, S. G. Tikhodeev, V. D. Kulakovskii, D. N. Krizhanovskii, and A. I. Tartakovskii, “Nonlinear dynamics of polariton scattering in semiconductor microcavity: Bistability vs. stimulated scattering,” Europhys. Lett. 67(6), 997 (2004).
[Crossref]

I. Carusotto and C. Ciuti, “Probing microcavity polariton superfluidity through resonant Rayleigh scattering,” Phys. Rev. Lett., 93(16), 166401 (2004).
[Crossref]

2000 (1)

V. D. Kulakovskii, A. I. Tartakovskii, D. N. Krizhanovskii, A. Armitage, J. S. Roberts, and M. S. Skolnick, “Two-dimensional excitonic polaritons and their interaction,” Phys. Usp. 43(8), 853–857 (2000).
[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]

1992 (1)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[Crossref] [PubMed]

1991 (1)

X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, and W. Y. Ching, “Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory,” Phys.Rev. A 43(3), 1186–1196 (1991).
[Crossref] [PubMed]

Abram, R. A.

K. V. Kavokin, M. A. Kaliteevski, R. A. Abram, A. V. Kavokin, S. Sharkova, and I. A. Shelykh, “Stimulated emission of terahertz radiation by exciton-polariton lasers,” Appl. Phys. Lett. 97(20), 201111 (2010).
[Crossref]

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T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 101(1), 016402 (2008).
[Crossref] [PubMed]

T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 100(11), 116401 (2008).
[PubMed]

N. A. Gippius, I. A. Shelykh, D. D. Solnyshkov, S. S. Gavrilov, Yuri G. Rubo, A. V. Kavokin, S. G. Tikhodeev, and G. Malpuech, “Polarization multistability of cavity polaritons,” Phys. Rev. Lett. 98(23), 236401 (2007).
[Crossref] [PubMed]

Sich, M.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Mndez, K. Biermann, R. Hey, and P. V. Santoset, “Observation of bright polariton solitons in a semiconductor microcavity,” Nature Photon. 6, 50–55 (2012).
[Crossref]

D. Sarkar, S. S. Gavrilov, M. Sich, J. H. Quilter, R. A. Bradley, N. A. Gippius, K. Guda, V. D. Kulakovskii, M. S. Skolnick, and D. N. Krizhanovskii, “Polarization bistability and resultant spin rings in semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216402 (2010).
[Crossref]

Skolnick, M. S.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Mndez, K. Biermann, R. Hey, and P. V. Santoset, “Observation of bright polariton solitons in a semiconductor microcavity,” Nature Photon. 6, 50–55 (2012).
[Crossref]

D. Sarkar, S. S. Gavrilov, M. Sich, J. H. Quilter, R. A. Bradley, N. A. Gippius, K. Guda, V. D. Kulakovskii, M. S. Skolnick, and D. N. Krizhanovskii, “Polarization bistability and resultant spin rings in semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216402 (2010).
[Crossref]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaitre, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Vina, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
[Crossref] [PubMed]

V. D. Kulakovskii, A. I. Tartakovskii, D. N. Krizhanovskii, A. Armitage, J. S. Roberts, and M. S. Skolnick, “Two-dimensional excitonic polaritons and their interaction,” Phys. Usp. 43(8), 853–857 (2000).
[Crossref]

Skryabin, D. V.

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Mndez, K. Biermann, R. Hey, and P. V. Santoset, “Observation of bright polariton solitons in a semiconductor microcavity,” Nature Photon. 6, 50–55 (2012).
[Crossref]

Snoke, D.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

Solnyshkov, D. D.

R. Hivet, H. Flayac, D. D. Solnyshkov, D. Tanese, T. Boulier, D. Andreoli, E. Giacobino, J. Bloch, A. Bramati, G. Malpuech, and A. Amo, “Half-solitons in a polariton quantum fluid behave like magnetic monopoles,” Nature Phys. 8, 724–728 (2012).
[Crossref]

N. A. Gippius, I. A. Shelykh, D. D. Solnyshkov, S. S. Gavrilov, Yuri G. Rubo, A. V. Kavokin, S. G. Tikhodeev, and G. Malpuech, “Polarization multistability of cavity polaritons,” Phys. Rev. Lett. 98(23), 236401 (2007).
[Crossref] [PubMed]

Staehli, J. L.

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

Szymanska, M. H.

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

Tanese, D.

R. Hivet, H. Flayac, D. D. Solnyshkov, D. Tanese, T. Boulier, D. Andreoli, E. Giacobino, J. Bloch, A. Bramati, G. Malpuech, and A. Amo, “Half-solitons in a polariton quantum fluid behave like magnetic monopoles,” Nature Phys. 8, 724–728 (2012).
[Crossref]

Tartakovskii, A. I.

N. A. Gippius, S. G. Tikhodeev, V. D. Kulakovskii, D. N. Krizhanovskii, and A. I. Tartakovskii, “Nonlinear dynamics of polariton scattering in semiconductor microcavity: Bistability vs. stimulated scattering,” Europhys. Lett. 67(6), 997 (2004).
[Crossref]

V. D. Kulakovskii, A. I. Tartakovskii, D. N. Krizhanovskii, A. Armitage, J. S. Roberts, and M. S. Skolnick, “Two-dimensional excitonic polaritons and their interaction,” Phys. Usp. 43(8), 853–857 (2000).
[Crossref]

Tassone, F.

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]

Taylor, T.

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108(19), 197401 (2012).
[Crossref] [PubMed]

Tejedor, C.

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaitre, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Vina, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
[Crossref] [PubMed]

Tikhodeev, S. G.

N. A. Gippius, I. A. Shelykh, D. D. Solnyshkov, S. S. Gavrilov, Yuri G. Rubo, A. V. Kavokin, S. G. Tikhodeev, and G. Malpuech, “Polarization multistability of cavity polaritons,” Phys. Rev. Lett. 98(23), 236401 (2007).
[Crossref] [PubMed]

N. A. Gippius, S. G. Tikhodeev, V. D. Kulakovskii, D. N. Krizhanovskii, and A. I. Tartakovskii, “Nonlinear dynamics of polariton scattering in semiconductor microcavity: Bistability vs. stimulated scattering,” Europhys. Lett. 67(6), 997 (2004).
[Crossref]

Tosi, G.

G. Christmann, G. Tosi, N. G. Berloff, P. Tsotsis, P. S. Eldridge, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Polariton ring condensates and sunflower ripples in an expanding quantum liquid,” Phys. Rev. B 85(23), 235303 (2012).
[Crossref]

Tsotsis, P.

G. Christmann, G. Tosi, N. G. Berloff, P. Tsotsis, P. S. Eldridge, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Polariton ring condensates and sunflower ripples in an expanding quantum liquid,” Phys. Rev. B 85(23), 235303 (2012).
[Crossref]

E. Kammann, T. C. H. Liew, H. Ohadi, P. Cilibrizzi, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, A. V. Kavokin, and P. G. Lagoudakis, “Nonlinear optical spin Hall effect and long-range spin transport in polariton lasers,” Phys. Rev. Lett. 109(3), 036404 (2012).
[Crossref] [PubMed]

Utsunomiya, S.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, “Coherent zero-state and p-state in an exciton-polariton condensate array,” Nature 450(7169), 529–532 (2007).
[Crossref] [PubMed]

Verger, A.

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
[Crossref]

Vina, L.

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaitre, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Vina, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
[Crossref] [PubMed]

Weisbuch, C.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[Crossref] [PubMed]

Wertz, E.

D. Bajoni, E. Semenova, A. Lematre, S. Bouchoule, E. Wertz, P. Senellart, S. Barbay, R. Kuszelewicz, and J. Bloch, “Optical bistability in a GaAs-based polariton diode,” Phys. Rev. Lett. 101(26), 266402 (2008).
[Crossref] [PubMed]

West, K.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

Whittaker, D. M.

D. M. Whittaker, “Effects of polariton-energy renormalization in the microcavity optical parametric oscillator,” Phys. Rev. B 71(11), 115301 (2005).
[Crossref]

Wong, K. W.

X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, and W. Y. Ching, “Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory,” Phys.Rev. A 43(3), 1186–1196 (1991).
[Crossref] [PubMed]

Wouters, M.

K. G. Lagoudakis, F. Manni, B. Pietka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. Andre, and B. Deveaud-Pledran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106(11), 115301 (2011).
[Crossref] [PubMed]

K. G. Lagoudakis, B. Pietka, M. Wouters, R. Andre, and B. Deveaud-Pledran, “Coherent oscillations in an exciton-polariton Josephson junction,” Phys. Rev. Lett. 105(12), 120403 (2010).
[Crossref] [PubMed]

T. K. Paraïso, M. Wouters, Y. Léger, F. Morier-Genoud, and B. Deveaud-Plédran, “Multistability of a coherent spin ensemble in a semiconductor microcavity,” Nature Mater. 9, 655–660 (2010).
[Crossref]

Yamamoto, Y.

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, “Coherent zero-state and p-state in an exciton-polariton condensate array,” Nature 450(7169), 529–532 (2007).
[Crossref] [PubMed]

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]

Yang, X. L.

X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, and W. Y. Ching, “Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory,” Phys.Rev. A 43(3), 1186–1196 (1991).
[Crossref] [PubMed]

Zhang, Lei

Ayan Das, Junseok Heo, Marc Jankowski, Wei Guo, Lei Zhang, Hui Deng, and Pallab Bhattacharya, “Room temperature ultralow threshold GaN nanowire polariton laser,” Phys. Rev. Lett. 107(6), 066405 (2011).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

K. V. Kavokin, M. A. Kaliteevski, R. A. Abram, A. V. Kavokin, S. Sharkova, and I. A. Shelykh, “Stimulated emission of terahertz radiation by exciton-polariton lasers,” Appl. Phys. Lett. 97(20), 201111 (2010).
[Crossref]

Europhys. Lett. (1)

N. A. Gippius, S. G. Tikhodeev, V. D. Kulakovskii, D. N. Krizhanovskii, and A. I. Tartakovskii, “Nonlinear dynamics of polariton scattering in semiconductor microcavity: Bistability vs. stimulated scattering,” Europhys. Lett. 67(6), 997 (2004).
[Crossref]

Nature (3)

C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, “Coherent zero-state and p-state in an exciton-polariton condensate array,” Nature 450(7169), 529–532 (2007).
[Crossref] [PubMed]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaitre, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Vina, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
[Crossref] [PubMed]

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

Nature Mater. (1)

T. K. Paraïso, M. Wouters, Y. Léger, F. Morier-Genoud, and B. Deveaud-Plédran, “Multistability of a coherent spin ensemble in a semiconductor microcavity,” Nature Mater. 9, 655–660 (2010).
[Crossref]

Nature Photon. (2)

A. Amo, T. H. C. Liew, C. Adrados, R. Houdre, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nature Photon. 4, 361–366 (2010).
[Crossref]

M. Sich, D. N. Krizhanovskii, M. S. Skolnick, A. V. Gorbach, R. Hartley, D. V. Skryabin, E. A. Cerda-Mndez, K. Biermann, R. Hey, and P. V. Santoset, “Observation of bright polariton solitons in a semiconductor microcavity,” Nature Photon. 6, 50–55 (2012).
[Crossref]

Nature Photonics (1)

S. Kena-Cohen and S. R. Forrest, “Room-temperature polariton lasing in an organic single-crystal microcavity,” Nature Photonics 4, 371–375 (2010).
[Crossref]

Nature Phys. (3)

R. Hivet, H. Flayac, D. D. Solnyshkov, D. Tanese, T. Boulier, D. Andreoli, E. Giacobino, J. Bloch, A. Bramati, G. Malpuech, and A. Amo, “Half-solitons in a polariton quantum fluid behave like magnetic monopoles,” Nature Phys. 8, 724–728 (2012).
[Crossref]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdre, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nature Phys.,  5, 805–810 (2009).
[Crossref]

G. Nardin, G. Grosso, Y. Leger, B. Pietka, F. Morier-Genoud, and B. Deveaud-Pledran, “Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid,” Nature Phys. 7, 635–641 (2011).
[Crossref]

Phys. Rev. A (2)

I. G. Savenko, O. V. Kibis, and I. A. Shelykh, “Asymmetric quantum dot in a microcavity as a nonlinear optical element,” Phys. Rev. A 85(5), 053818 (2012).
[Crossref]

B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Generation of entangled photon holes using quantum interference,” Phys. Rev. A 74(4), 010303()R (2006).

Phys. Rev. B (6)

T. C. H. Liew, A. V. Kavokin, T. Ostatnický, M. Kaliteevski, I. A. Shelykh, and R. A. Abram, “Exciton-polariton integrated circuits,” Phys. Rev. B 82(3), 033302 (2010).
[Crossref]

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]

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
[Crossref]

D. M. Whittaker, “Effects of polariton-energy renormalization in the microcavity optical parametric oscillator,” Phys. Rev. B 71(11), 115301 (2005).
[Crossref]

A. Baas, J. P. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Optical bistability in semiconductor microcavities in the nondegenerate parametric oscillation regime: Analogy with the optical parametric oscillator,” Phys. Rev. B 70(16), 161307(R) (2004).
[Crossref]

G. Christmann, G. Tosi, N. G. Berloff, P. Tsotsis, P. S. Eldridge, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Polariton ring condensates and sunflower ripples in an expanding quantum liquid,” Phys. Rev. B 85(23), 235303 (2012).
[Crossref]

Phys. Rev. Lett. (16)

E. Kammann, T. C. H. Liew, H. Ohadi, P. Cilibrizzi, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, A. V. Kavokin, and P. G. Lagoudakis, “Nonlinear optical spin Hall effect and long-range spin transport in polariton lasers,” Phys. Rev. Lett. 109(3), 036404 (2012).
[Crossref] [PubMed]

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. 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]

Ayan Das, Junseok Heo, Marc Jankowski, Wei Guo, Lei Zhang, Hui Deng, and Pallab Bhattacharya, “Room temperature ultralow threshold GaN nanowire polariton laser,” Phys. Rev. Lett. 107(6), 066405 (2011).
[Crossref] [PubMed]

K. G. Lagoudakis, F. Manni, B. Pietka, M. Wouters, T. C. H. Liew, V. Savona, A. V. Kavokin, R. Andre, and B. Deveaud-Pledran, “Probing the dynamics of spontaneous quantum vortices in polariton superfluids,” Phys. Rev. Lett. 106(11), 115301 (2011).
[Crossref] [PubMed]

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, “Soliton instabilities and vortex street formation in a polariton quantum fluid,” Phys. Rev. Lett. 107(24), 245301 (2011).
[Crossref]

K. G. Lagoudakis, B. Pietka, M. Wouters, R. Andre, and B. Deveaud-Pledran, “Coherent oscillations in an exciton-polariton Josephson junction,” Phys. Rev. Lett. 105(12), 120403 (2010).
[Crossref] [PubMed]

N. A. Gippius, I. A. Shelykh, D. D. Solnyshkov, S. S. Gavrilov, Yuri G. Rubo, A. V. Kavokin, S. G. Tikhodeev, and G. Malpuech, “Polarization multistability of cavity polaritons,” Phys. Rev. Lett. 98(23), 236401 (2007).
[Crossref] [PubMed]

D. Sarkar, S. S. Gavrilov, M. Sich, J. H. Quilter, R. A. Bradley, N. A. Gippius, K. Guda, V. D. Kulakovskii, M. S. Skolnick, and D. N. Krizhanovskii, “Polarization bistability and resultant spin rings in semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216402 (2010).
[Crossref]

C. Adrados, A. Amo, T. C. H. Liew, R. Hivet, R. Houdr, E. Giacobino, A. V. Kavokin, and A. Bramati, “Spin rings in bistable planar semiconductor microcavities,” Phys. Rev. Lett. 105(21), 216403 (2010).
[Crossref]

T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 101(1), 016402 (2008).
[Crossref] [PubMed]

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108(19), 197401 (2012).
[Crossref] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992).
[Crossref] [PubMed]

F. Manni, K. G. Lagoudakis, T. C. H. Liew, R. Andre, and B. Deveaud-Pledran, “Spontaneous pattern formation in a polariton condensate,” Phys. Rev. Lett. 107(10), 106401 (2011).
[Crossref] [PubMed]

I. G. Savenko, I. A. Shelykh, and M. A. Kaliteevski, “Nonlinear terahertz emission in semiconductor microcavities,” Phys. Rev. Lett. 107(2), 027401 (2011).
[Crossref] [PubMed]

D. Bajoni, E. Semenova, A. Lematre, S. Bouchoule, E. Wertz, P. Senellart, S. Barbay, R. Kuszelewicz, and J. Bloch, “Optical bistability in a GaAs-based polariton diode,” Phys. Rev. Lett. 101(26), 266402 (2008).
[Crossref] [PubMed]

T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Phys. Rev. Lett. 100(11), 116401 (2008).
[PubMed]

Phys. Rev. Lett., (1)

I. Carusotto and C. Ciuti, “Probing microcavity polariton superfluidity through resonant Rayleigh scattering,” Phys. Rev. Lett., 93(16), 166401 (2004).
[Crossref]

Phys. Usp. (1)

V. D. Kulakovskii, A. I. Tartakovskii, D. N. Krizhanovskii, A. Armitage, J. S. Roberts, and M. S. Skolnick, “Two-dimensional excitonic polaritons and their interaction,” Phys. Usp. 43(8), 853–857 (2000).
[Crossref]

Phys.Rev. A (1)

X. L. Yang, S. H. Guo, F. T. Chan, K. W. Wong, and W. Y. Ching, “Analytic solution of a two-dimensional hydrogen atom. I. Nonrelativistic theory,” Phys.Rev. A 43(3), 1186–1196 (1991).
[Crossref] [PubMed]

Physica E (1)

T. C. H. Liew, I. A. Shelykh, and G. Malpuech, “Polaritonic devices,” Physica E 43(9), 1543–1568 (2011).
[Crossref]

Science (3)

K. G. Lagoudakis, T. Ostatnicky, A. V. Kavokin, Y. G. Rubo, R. Andre, and B. Deveaud-Pledran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 13(5955), 974–976 (2009).
[Crossref]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Lemnager, R. Houdr, E. Giacobino, C. Ciuti, and A. Bramati, “Polariton superfluids reveal quantum hydrodynamic solitons,” Science 332(6034), 1167–1170 (2011).
[Crossref] [PubMed]

Semicond. Sci. Technol. (1)

I. A. Shelykh, A. V. Kavokin, Yuri G. Rubo, T. C. H. Liew, and G. Malpuech, “Polariton polarization-sensitive phenomena in planar semiconductor microcavities”, Semicond. Sci. Technol. 25(1), 013001 (2010).
[Crossref]

Superlattic. Microstruct. (1)

R. Schmidt-Grund, B. Rheinlnder, C. Czekalla, G. Benndorf, H. Hochmut, A. Rahm, M. Lorenz, and M. Grundmann, “ZnO based planar and micropillar resonators,” Superlattic. Microstruct. 41(5–6), 360–363 (2007).
[Crossref]

Other (1)

A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, (2007)).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Geometry of the structure. We consider a microcavity, which is made by Bragg mirrors, with the quantum well inside, where a 2p excitonic state can be excited by two photons(red curves) with energy h̄ω2c each.

Fig. 2
Fig. 2

(a) Energy levels of the QW with 2p excitonic transition placed inside the micro-cavity. We consider the case when the exciton energy is h̄ωp and the photon energy is ω2cωp/2. Possible transitions for N = 1, 2, 3, 4 manifolds for the ideal cavity are represented on the right side of the figure (a). (b) Emission spectrum of the system. The intensity of transitions from individual levels is presented by the blue lines. We consider the case when ω2cωp/2 = 0.71eV, g = 0.025meV and the average number of the excitations in the system 〈N〉 = 30 and the statistics of photons is Poissonian. Including a Lorentzian broadening of each transition line, gives the double peak spectrum of emission shown by the red curve. We consider broadening equals 0.05meV. One can define the value of the Rabi splitting in the system as the distance between the two peaks.

Fig. 3
Fig. 3

Considering the finite lifetime of the photons and external coherent pumping of the cavity, we observed a bistable behaviour of the number of photons on intensity of the coherent pump. (a) The parameters are varied for detuning of the system: (red dashed line) Δa = 0.375meV, Δp = 0.75meV; (green dot line) Δa = 0.25meV, Δp = 0.5meV; (blue bold line) Δa = 0.125meV, Δp = 0.25meV. The influence of the exciton-exciton interaction on the hysteresis curve is illustrated in figure (b), where the cases of αp=0 (red dashed curve) and α p = 6 E B a B 2 / S (red solid curve) are presented. The detuning parameters are Δa = 0.375meV, Δp = 0.75meV.

Equations (52)

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^ = h ¯ ω p p ^ p ^ + h ¯ ω 2 c a ^ a ^ + g ( p ^ a ^ a ^ + p ^ a ^ a ^ ) ,
g = S 2 ( q A 0 μ ) 2 n i E g m 0 2 2 m * Φ n ( 0 ) d r R 21 ( r ) r R 10 ( r ) 2 ω ( E g E n + ω ) i m 0 h ¯ 2 ( E 2 p E n s ) ,
A = e A 0 , A 0 = h ¯ 2 ε ε 0 ω L S ,
2 = ( 2 h ¯ ω 2 c g 2 g 2 h ¯ ω p ) , 3 = ( 3 h ¯ ω 2 c g 6 g 6 h ¯ ( ω p + ω 2 c ) ) ,
E 2 = 2 h ¯ ω c ± g 2 , E 3 = 3 h ¯ ω c ± g 6 .
p ( λ ; N ) = λ N e λ N ! .
Δ Ω R 4 g 2 N ( γ a γ p ) 2 4 .
i h ¯ d p ^ d t = [ p ^ , ^ ] = h ¯ ω p p ^ + g a ^ 2 ,
i h ¯ d a ^ d t = [ a ^ , ^ ] = h ¯ ω a a ^ + 2 g p ^ a ^ .
d p ^ d t = ( i ω p + γ p h ¯ ) p ^ i Ω p a ^ 2 ,
d a ^ d t = ( i ω a + γ a h ¯ ) a ^ 2 i Ω p p ^ a ^ * i h ¯ P e i ω t .
( i h ¯ Δ p + γ p ) p + i h ¯ Ω p a 2 = 0 ,
( i h ¯ Δ a + γ a ) a + 2 i h ¯ Ω p p a * = i P ,
( i h ¯ Δ a + γ a ) a + 2 h ¯ 2 Ω p 2 i h ¯ Δ p + γ p | a | 2 a + i P = 0 .
N a [ 1 + c 1 N a + c 2 N a 2 ] = I a ,
N p = g 2 N a 2 γ p 2 + h ¯ 2 Δ p 2 ,
c 1 = 4 g 2 ( γ a γ p h ¯ 2 Δ a Δ p ) ( h ¯ 2 Δ p 2 + γ p 2 ) ( h ¯ 2 Δ a 2 + γ a 2 ) ,
c 2 = 4 g 4 ( h ¯ 2 Δ p 2 + γ p 2 ) ( h ¯ 2 Δ a 2 + γ a 2 ) ,
I a = | P | 2 h ¯ 2 Δ a 2 + γ a 2 .
int = α p 2 p ^ p ^ p ^ p ^ ,
d p ^ d t = ( i ω p + γ p h ¯ ) p ^ i Ω p a ^ 2 i h ¯ α p p ^ p ^ p ^ ,
d a ^ d t = ( i ω a + γ a h ¯ ) a ^ 2 i Ω p p ^ a ^ * i h ¯ P e i ω t ,
n a + 4 ( ( γ a γ p h ¯ 2 Δ a Δ p ) n p h ¯ Δ a α p n p 2 ) ( h ¯ 2 Δ a 2 + γ a 2 ) + 4 g 2 n p n a ( h ¯ 2 Δ a 2 + γ a 2 ) = I a .
^ = ( p ^ e q e A e ) 2 2 m e + ( p ^ h q h A h ) 2 2 m h + U ( r e r h ) ,
A e = A h = e A 0 , A 0 = h ¯ 2 ε ε 0 ω V ,
W ^ = q A 0 μ e p ^ ,
^ = p ^ 2 2 μ + U ( r ) .
( h ¯ 2 2 μ [ 2 r 2 + 1 r r + 1 r 2 2 ϕ 2 ] q 2 4 π ε 0 ε r ) ψ ( r , ϕ ) = ( E E g ) ψ ( r , ϕ ) ,
ψ ( r , ϕ ) = R ( r ) Φ ( ϕ ) ,
Φ ( ϕ ) = 1 ( 2 π ) 1 / 2 e i l ϕ , l = 0 , ± 1 , ± 2 ,
R n l ( r ) = β n ( 2 | l | ) ! [ ( n | l | 1 ) ! ( 2 n 1 ) ( n | l | 1 ) ! ] 1 / 2 ( β n r ) | l | e β n r / 2 F 1 1 ( n + | l | + 1 , 2 | l | + 1 , β n r ) ,
β n = 2 4 π ε 0 ε ( n 1 / 2 ) μ e 2 h ¯ 2 ,
E n = E g 1 2 ( 4 π ε 0 ε ) 2 ( n 1 / 2 ) μ q 4 h ¯ 2 .
M f i = ξ f | W ^ | ξ ξ | V ^ ( 1 ) | i E i E η + f | V ^ ( 2 ) | i .
| i = δ ( r e r h ) , E i = 2 ω ,
| η = F η ( r e , r h ) = e i P c h ¯ R c S ψ η ( r ) , E η = E g E n + ω .
η | V ^ ( 1 ) | i = q A 0 μ ( e p ^ ) c v d r e d r h δ ( r e r h ) F η ( r e ; r h ) = = q A 0 μ ( e p ^ ) c v R η ( 0 ) 1 S ( 2 π h ¯ ) 2 δ ( P c ) ,
f | W ^ | η = q A 0 μ d R c d r F η * ( r e ; r h ) e p ^ F η ( ( r e ; r h ) ) = = q A 0 μ δ ( P c P c ) 1 S ( 2 π h ¯ ) 2 d r R η * ( r ) e p ^ R η ( r ) = = q A 0 μ ( e p ^ ) η η 1 S ( 2 π h ¯ ) 2 δ ( P c P c ) ,
M f i = S ( q A 0 μ ) 2 η ( e p ^ ) η η ( e p ^ ) c v ψ η ( 0 ) 2 ω ( E g E n + ω ) .
1 m * 2 | ( e p ^ ) c v | 2 E g m 0 2 ,
i h ¯ d x ^ d t = i h ¯ p ^ m 0 = [ x ^ ; ^ ] c | p ^ | v i h ¯ m 0 a E g .
( e p ^ ) c v i h ¯ E g a m 0 ,
p ^ = i h ¯ ^ = i h ¯ ( r ^ r + ϕ ^ 1 r ϕ ) ,
e p ^ = i h ¯ 2 e i ϕ ( r + i 1 r ϕ ) .
R n 0 = β n 1 2 n 1 e β n r 2 F 1 1 ( n 1 , 1 , β n r ) = = β n 1 2 n 1 e β n r 2 L n 1 0 ( β n r ) .
R 21 = β 2 2 6 r e β 2 r 2 .
2 p | p ^ | 1 s = 2 p | m 0 i h ¯ [ ^ , r ^ ] | 1 s = i m 0 h ¯ ( E 2 p E 1 s ) 2 p | r ^ | 1 s .
f | W ^ | η = q A 0 μ δ ( P c P c ) ( 2 π h ¯ ) 2 S δ ( P c P c ) d r R η * ( r ) e p ^ R η ( r ) = = q A 0 μ δ ( P c P c ) ( 2 π h ¯ ) 2 S d r R η * ( r ) e i ϕ 2 ( i h ¯ r ) R η ( r ) = = q A 0 μ δ ( P c P c ) ( 2 π h ¯ ) 2 S d r e i ϕ 2 i m 0 h ¯ ( E η E η ) R η * ( r ) r R η ( r ) ,
2 p | W ^ | n s = q A 0 μ δ ( P c P c ) e i ϕ 2 i m 0 h ¯ ( E 2 p E n s ) ( 2 π h ¯ ) 2 S d r R 2 p * ( r ) r R 1 s ( r ) .
d r R 21 ( r ) r R n 0 ( r ) = 243 ( n 2 ) n 3 ( n + 1 ) n 2 ( 2 n 1 ) 5 ( μ q 2 / ( π ε 0 ε h ¯ 2 ) ) 4 β 2 2 β n 6 ( 2 n 1 ) .
M 2 p , i = S ( q A 0 μ ) 2 n i E g m 0 2 2 m * Φ n ( 0 ) d r R 21 ( r ) r R 10 ( r ) 2 ω ( E g E n + ω ) i m 0 h ¯ 2 ( E 2 p E n s ) .
M 2 p , i = 2 p | ^ | 2 ω = g 2 p | p ^ a ^ + a + + p ^ + a ^ a ^ | 2 ω = g 2 .

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