204
6 Effects of Quantisation
24. A. Rahimi-Iman, C. Schneider, J. Fischer, S. Holzinger, M. Amthor, S. Höfling, S. Reitzenstein, L. Worschech, M. Kamp, A. Forchel, Zeeman splitting and diamagnetic shift of spatially confined quantum-well exciton polaritons in an external magnetic field. Phys. Rev. B
84, 165325 (2011)
25. K. Winkler, C. Schneider, J. Fischer, A. Rahimi-Iman, M. Amthor, A. Forchel, S. Reitzenstein,
S. Höfling, M. Kamp, Electroluminescence from spatially confined exciton polaritons in a
textured microcavity. Appl. Phys. Lett. 102, 041101 (2013)
26. M. Bayer, T. Gutbrod, J.P. Reithmaier, A. Forchel, T.L. Reinecke, P.A. Knipp, A.A. Dremin,
V.D. Kulakovskii, Optical modes in photonic molecules. Phys. Rev. Lett. 81, 2582–2585
(1998)
27. M. Bayer, T. Gutbrod, A. Forchel, T.L. Reinecke, P.A. Knipp, R. Werner, J.P. Reithmaier,
Optical demonstration of a crystal band structure formation. Phys. Rev. Lett. 83, 5374–5377
(1999)
28. C.W. Lai, N.Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M.D. Fraser, T. Byrnes, P. Recher,
N. Kumada, T. Fujisawa, Y. Yamamoto, Coherent zero-state and π -state in an exciton-polariton
condensate array. Nature 450, 529–532 (2007)
29. N.Y. Kim, K. Kusudo, C. Wu, N. Masumoto, A. Löffler, S. Höfling, N. Kumada, L. Worschech,
A. Forchel, Y. Yamamoto, Dynamical d-wave condensation of exciton-polaritons in a twodimensional square-lattice potential. Nat. Phys. 7, 681–686 (2011)
30. N.Y. Kim, K. Kusudo, A. Löffler, S. Höfling, A. Forchel, Y. Yamamoto, Exciton-polariton
condensates near the Dirac point in a triangular lattice. New J. Phys. 15, 035032 (2013)
31. K. Winkler, J. Fischer, A. Schade, M. Amthor, R. Dall, J. Geßler, M. Emmerling, E.A. Ostrovskaya, M. Kamp, C. Schneider, S. Höfling, A polariton condensate in a photonic crystal
potential landscape. New J. Phys. 17, 023001 (2015)
32. M.A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D.N. Christodoulides, M. Khajavikhan, Topological insulator laser: experiments. Science 359, eaar4005 (2018)
33. G. Harari, M.A. Bandres, Y. Lumer, M.C. Rechtsman, Y.D. Chong, M. Khajavikhan, D.N.
Christodoulides, M. Segev, Topological insulator laser: theory. Science 359, eaar4003 (2018)
34. R. Ge, W. Broer, T.C.H. Liew, Floquet topological polaritons in semiconductor microcavities.
Phys. Rev. B 97, 195305 (2018)
35. S. Klembt, T.H. Harder, O.A. Egorov, K. Winkler, R. Ge, M.A. Bandres, M. Emmerling, L.
Worschech, T.C.H. Liew, M. Segev, C. Schneider, S. Höfling, Exciton-polariton topological
insulator. Nature 562, 552–556 (2018)
36. N.N. Bogoliubov, On the theory of superfluidity. J. Phys. USSR 11, 23 (1947)
37. O. Penrose, L. Onsager, Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576
(1956)
38. V. Savona, D. Sarchi, Bose-Einstein condensation of microcavity polaritons. Phys. Status
Solidi B 242, 2290–2301 (2005)
39. H. Deng, H. Haug, Y. Yamamoto, Exciton-polariton Bose-Einstein condensation. Rev. Mod.
Phys. 82, 1489 (2010)
40. A. Imamoglu, R.J. Ram, S. Pau, Y. Yamamoto, Nonequilibrium condensates and lasers without
inversion: exciton-polariton lasers. Phys. Rev. A 53, 4250 (1996)
41. A. Kavokin, G. Malpuech, F.P. Laussy, Polariton laser and polariton superfluidity in microcavities. Phys. Lett. A 306, 187–199 (2003)
42. D. Solnyshkov, E. Petrolati, A. Di Carlo, G. Malpuech, Theory of an electrically injected bulk
polariton laser. Appl. Phys. Lett. 94, 011110–3 (2009)
43. D. Snoke, Spontaneous Bose coherence of excitons and polaritons. Science 298(5597), 1368–
1372 (2002)
44. D. Sarchi, V. Savona, Long-range order in the Bose-Einstein condensation of polaritons. Phys.
Rev. B 75, 115326 (2007)
45. D.D. Solnyshkov, H. Tercas, K. Dini, G. Malpuech, Hybrid Boltzmann-Gross-Pitaevskii theory of Bose-Einstein condensation and superfluidity in open driven-dissipative systems. Phys.
Rev. A: At. Mol. Opt. Phys. 89, 033626 (2014)
6 Effects of Quantisation
24. A. Rahimi-Iman, C. Schneider, J. Fischer, S. Holzinger, M. Amthor, S. Höfling, S. Reitzenstein, L. Worschech, M. Kamp, A. Forchel, Zeeman splitting and diamagnetic shift of spatially confined quantum-well exciton polaritons in an external magnetic field. Phys. Rev. B
84, 165325 (2011)
25. K. Winkler, C. Schneider, J. Fischer, A. Rahimi-Iman, M. Amthor, A. Forchel, S. Reitzenstein,
S. Höfling, M. Kamp, Electroluminescence from spatially confined exciton polaritons in a
textured microcavity. Appl. Phys. Lett. 102, 041101 (2013)
26. M. Bayer, T. Gutbrod, J.P. Reithmaier, A. Forchel, T.L. Reinecke, P.A. Knipp, A.A. Dremin,
V.D. Kulakovskii, Optical modes in photonic molecules. Phys. Rev. Lett. 81, 2582–2585
(1998)
27. M. Bayer, T. Gutbrod, A. Forchel, T.L. Reinecke, P.A. Knipp, R. Werner, J.P. Reithmaier,
Optical demonstration of a crystal band structure formation. Phys. Rev. Lett. 83, 5374–5377
(1999)
28. C.W. Lai, N.Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M.D. Fraser, T. Byrnes, P. Recher,
N. Kumada, T. Fujisawa, Y. Yamamoto, Coherent zero-state and π -state in an exciton-polariton
condensate array. Nature 450, 529–532 (2007)
29. N.Y. Kim, K. Kusudo, C. Wu, N. Masumoto, A. Löffler, S. Höfling, N. Kumada, L. Worschech,
A. Forchel, Y. Yamamoto, Dynamical d-wave condensation of exciton-polaritons in a twodimensional square-lattice potential. Nat. Phys. 7, 681–686 (2011)
30. N.Y. Kim, K. Kusudo, A. Löffler, S. Höfling, A. Forchel, Y. Yamamoto, Exciton-polariton
condensates near the Dirac point in a triangular lattice. New J. Phys. 15, 035032 (2013)
31. K. Winkler, J. Fischer, A. Schade, M. Amthor, R. Dall, J. Geßler, M. Emmerling, E.A. Ostrovskaya, M. Kamp, C. Schneider, S. Höfling, A polariton condensate in a photonic crystal
potential landscape. New J. Phys. 17, 023001 (2015)
32. M.A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D.N. Christodoulides, M. Khajavikhan, Topological insulator laser: experiments. Science 359, eaar4005 (2018)
33. G. Harari, M.A. Bandres, Y. Lumer, M.C. Rechtsman, Y.D. Chong, M. Khajavikhan, D.N.
Christodoulides, M. Segev, Topological insulator laser: theory. Science 359, eaar4003 (2018)
34. R. Ge, W. Broer, T.C.H. Liew, Floquet topological polaritons in semiconductor microcavities.
Phys. Rev. B 97, 195305 (2018)
35. S. Klembt, T.H. Harder, O.A. Egorov, K. Winkler, R. Ge, M.A. Bandres, M. Emmerling, L.
Worschech, T.C.H. Liew, M. Segev, C. Schneider, S. Höfling, Exciton-polariton topological
insulator. Nature 562, 552–556 (2018)
36. N.N. Bogoliubov, On the theory of superfluidity. J. Phys. USSR 11, 23 (1947)
37. O. Penrose, L. Onsager, Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576
(1956)
38. V. Savona, D. Sarchi, Bose-Einstein condensation of microcavity polaritons. Phys. Status
Solidi B 242, 2290–2301 (2005)
39. H. Deng, H. Haug, Y. Yamamoto, Exciton-polariton Bose-Einstein condensation. Rev. Mod.
Phys. 82, 1489 (2010)
40. A. Imamoglu, R.J. Ram, S. Pau, Y. Yamamoto, Nonequilibrium condensates and lasers without
inversion: exciton-polariton lasers. Phys. Rev. A 53, 4250 (1996)
41. A. Kavokin, G. Malpuech, F.P. Laussy, Polariton laser and polariton superfluidity in microcavities. Phys. Lett. A 306, 187–199 (2003)
42. D. Solnyshkov, E. Petrolati, A. Di Carlo, G. Malpuech, Theory of an electrically injected bulk
polariton laser. Appl. Phys. Lett. 94, 011110–3 (2009)
43. D. Snoke, Spontaneous Bose coherence of excitons and polaritons. Science 298(5597), 1368–
1372 (2002)
44. D. Sarchi, V. Savona, Long-range order in the Bose-Einstein condensation of polaritons. Phys.
Rev. B 75, 115326 (2007)
45. D.D. Solnyshkov, H. Tercas, K. Dini, G. Malpuech, Hybrid Boltzmann-Gross-Pitaevskii theory of Bose-Einstein condensation and superfluidity in open driven-dissipative systems. Phys.
Rev. A: At. Mol. Opt. Phys. 89, 033626 (2014)