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Phase Diagram and Excitations of the Jaynes-Cummings-Hubbard Model

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Quantum Simulations with Photons and Polaritons

Part of the book series: Quantum Science and Technology ((QST))

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Abstract

The Jaynes-Cummings-Hubbard model (JCHM) has emerged as a fundamental model at the interface of quantum optics and condensed matter physics. It describes strongly correlated photons in a coupled qubit-cavity array and predicts a superfluid-Mott insulator transition of polaritons under quasi-equilibrium conditions. Here, we review recent analytical as well as numerical results for the phase diagram, elementary excitations and critical exponents of the JCHM and compare them to closely related models such as the Bose-Hubbard and the Dicke model. We comment on the fate of these results in open dissipative systems and outline schemes for their experimental verifiability.

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References

  1. A.D. Greentree, C. Tahan, J.H. Cole, L. Hollenberg, Nat. Phys. 2, 856 (2006)

    Article  Google Scholar 

  2. D. Angelakis, M. Santos, S. Bose, Phys. Rev. A 76, 031805 (2007)

    Article  ADS  Google Scholar 

  3. J. Cho, D.G. Angelakis, S. Bose, Phys. Rev. A 78, 062338 (2008)

    Article  ADS  Google Scholar 

  4. G. Zhu, S. Schmidt, J. Koch, New J. Phys. 15, 115002 (2013)

    Article  ADS  Google Scholar 

  5. M. Hartmann, F. Brandão, M. Plenio, Phys. Rev. Lett. 99, 160501 (2007)

    Article  ADS  Google Scholar 

  6. M. Hartmann, F. Brandão, M. Plenio, Nat. Phys. 2, 849–855 (2006)

    Article  Google Scholar 

  7. D. Rossini, R. Fazio, Phys. Rev. Lett. 99, 186401 (2007)

    Article  ADS  Google Scholar 

  8. D. Rossini, R. Fazio, G. Santoro, Europhys. Lett. 83, 47011 (2008)

    Article  ADS  Google Scholar 

  9. M. Aichhorn, M. Hohenadler, C. Tahan, P. Littlewood, Phys. Rev. Lett. 100, 216401 (2008)

    Article  ADS  Google Scholar 

  10. M.J. Hartmann, F.G.S.L. Brandao, M.B. Plenio, New J. Phys. 10, 033011 (2008)

    Article  ADS  Google Scholar 

  11. J. Zhao, A.W. Sandvik, K. Ueda (2008). arXiv:0806.3603

  12. S. Schmidt, G. Blatter, Phys. Rev. Lett. 103, 086403 (2009)

    Article  ADS  Google Scholar 

  13. J. Koch, K.L. Hur, Phys. Rev. A 80, 023811 (2009)

    Article  ADS  Google Scholar 

  14. P. Pippan, H. Evertz, M. Hohenadler, Phys. Rev. A 80, 033612 (2009)

    Article  ADS  Google Scholar 

  15. P.A. Ivanov, S.S. Ivanov, N.V. Vitanov, A. Mering, M. Fleischhauer, K. Singer, Phys. Rev. A 80, 060301 (2009)

    Article  ADS  Google Scholar 

  16. M. Knap, E. Arrigoni, W. von der Linden, Phys. Rev. B 81, 104303 (2010)

    Article  ADS  Google Scholar 

  17. M. Knap, E. Arrigoni, W. von der Linden, Phys. Rev. B 82, 045126 (2010)

    Article  ADS  Google Scholar 

  18. S. Schmidt, G. Blatter, Phys. Rev. Lett. 104, 216402 (2010)

    Article  ADS  Google Scholar 

  19. A. Tomadin, V. Giovannetti, R. Fazio, D. Gerace, I. Carusotto, H. Türeci, A. Imamoglu, Phys. Rev. A 81, 061801 (2010)

    Article  ADS  Google Scholar 

  20. M. Hohenadler, M. Aichhorn, S. Schmidt, L. Pollet, Phys. Rev. A 84, 041608(R) (2011)

    Article  ADS  Google Scholar 

  21. K. Liu, L. Tan, C.H. Lv, W.M. Liu, Phys. Rev. A 83, 063840 (2011)

    Article  ADS  Google Scholar 

  22. M. Hohenadler, M. Aichhorn, L. Pollet, S. Schmidt, Phys. Rev. A 85, 013810 (2012)

    Article  ADS  Google Scholar 

  23. C. Nietner, A. Pelster, Phys. Rev. A 85, 043831 (2012)

    Article  ADS  Google Scholar 

  24. M. Schiró, M. Bordyuh, B. Öztop, H.E. Türeci, Phys. Rev. Lett. 109, 053601 (2012)

    Article  ADS  Google Scholar 

  25. F. Nissen, S. Schmidt, M. Biondi, G. Blatter, H.E. Türeci, J. Keeling, Phys. Rev. Lett. 108, 233603 (2012)

    Article  ADS  Google Scholar 

  26. S. Schmidt, G. Blatter, J. Keeling, J. Phys. B: At. Mol. Opt. Phys. 46, 224020 (2013)

    Article  ADS  Google Scholar 

  27. T. Grujic, S.R. Clark, D. Jaksch, D.G. Angelakis, Phys. Rev. A 87, 053846 (2013)

    Article  ADS  Google Scholar 

  28. T. Yuge, K. Kamide, M. Yamaguchi, T. Ogawa (2014). arXiv:1401.6229

  29. D. Sarchi, I. Carusotto, M. Wouters, V. Savona, Phys. Rev. B 77, 125324 (2008)

    Article  ADS  Google Scholar 

  30. D. Gerace, H.E. Türeci, A. Imamoglu, V. Giovannetti, R. Fazio, Nat. Phys. 5, 281–284 (2009)

    Article  Google Scholar 

  31. S. Schmidt, D. Gerace, A. Houck, G. Blatter, H.E. Türeci, Phys. Rev. B 82, 100507 (2010)

    Article  ADS  Google Scholar 

  32. N. Schetakis, T. Grujic, S. Clark, D. Jaksch, D. Angelakis, J. Phys. B: At. Mol. Opt. Phys. 46, 224025 (2013)

    Article  ADS  Google Scholar 

  33. J. Raftery, D. Sadri, S. Schmidt, H.E. Türeci, A.A. Houck (2013). arXiv:1312.2963

  34. M. Hartmann, Phys. Rev. Lett. 104, 113601 (2010)

    Article  ADS  Google Scholar 

  35. T. Grujic, S.R. Clark, D.G. Angelakis, D. Jaksch, New J. Phys. 14, 103025 (2012)

    Article  Google Scholar 

  36. A.L. Boité, G. Orso, C. Ciuti, Phys. Rev. Lett. 110, 233601 (2013)

    Article  ADS  Google Scholar 

  37. J. Jin, D. Rossini, R. Fazio, M. Leib, M.J. Hartmann, Phys. Rev. Lett. 110, 163605 (2013)

    Article  ADS  Google Scholar 

  38. I. Carusotto, D. Gerace, H.E. Türeci, S. De Liberato, C. Ciuti, A. Imamoǧlu, Phys. Rev. Lett. 103, 033601 (2009)

    Article  ADS  Google Scholar 

  39. M. Kiffner, M. Hartmann, Phys. Rev. A 81, 021806 (2010)

    Article  ADS  Google Scholar 

  40. A.G. D’Souza, B.C. Sanders, D.L. Feder, Phys. Rev. A 88, 063801 (2013)

    Article  ADS  Google Scholar 

  41. J. Koch, A. Houck, K. Le Hur, S. Girvin, Phys. Rev. A 82, 043811 (2010)

    Article  ADS  Google Scholar 

  42. A. Nunnenkamp, J. Koch, S.M. Girvin, New J. Phys. 13, 095008 (2011)

    Article  ADS  Google Scholar 

  43. M. Hafezi, E.A. Demler, M.D. Lukin, J.M. Taylor, Nat. Phys. 7, 907–912 (2011)

    Article  Google Scholar 

  44. A. Kamal, J. Clarke, M.H. Devoret, Nat. Phys. 7, 311–315 (2011)

    Article  Google Scholar 

  45. R.O. Umucalilar, I. Carusotto, Phys. Rev. Lett. 108, 206809 (2012)

    Article  ADS  Google Scholar 

  46. M. Hafezi, S. Mittal, J. Fan, A. Migdall, J.M. Taylor, Nat. Photon 7, 1001–1005 (2013)

    Google Scholar 

  47. C.E. Bardyn, S.D. Huber, O. Zilberberg (2013). arXiv:1312.6894

  48. A. Petrescu, A.A. Houck, K. Le Hur, Phys. Rev. A 86, 053804 (2012)

    Article  ADS  Google Scholar 

  49. C.E. Bardyn, A. Imamoglu, Phys. Rev. Lett. 109, 253606 (2012)

    Article  ADS  Google Scholar 

  50. M.J. Hwang, M.S. Choi, Phys. Rev. B 87, 125404 (2013)

    Article  ADS  Google Scholar 

  51. B. Kumar, S. Jalal, Phys. Rev. A 88, 011802 (2013)

    Article  ADS  Google Scholar 

  52. A.A. Zvyagin, Phys. Rev. Lett. 110, 217207 (2013)

    Article  ADS  Google Scholar 

  53. J. Cho, D. Angelakis, S. Bose, Phys. Rev. Lett. 101, 246809 (2008)

    Article  ADS  Google Scholar 

  54. A. Hayward, A.M. Martin, A.D. Greentree, Phys. Rev. Lett. 108, 223602 (2012)

    Article  ADS  Google Scholar 

  55. M. Hafezi, M.D. Lukin, J.M. Taylor, New J. Phys. 15, 063001 (2013)

    Article  ADS  Google Scholar 

  56. R.O. Umucalilar, M. Wouters, I. Carusotto, Phys. Rev. A 89, 023803 (2014)

    Article  ADS  Google Scholar 

  57. M. Hartmann, F. Brandão, M. Plenio, Laser Photonics Rev. 2, 527–556 (2008)

    Article  Google Scholar 

  58. A. Tomadin, R. Fazio, J. Opt. Soc. Am. B 27, 130–136 (2010)

    Article  ADS  Google Scholar 

  59. A.A. Houck, H.E. Türeci, J. Koch, Nat. Phys. 8, 292–299 (2012)

    Article  Google Scholar 

  60. I. Carusotto, C. Ciuti, Rev. Mod. Phys. 85, 299 (2013)

    Article  ADS  Google Scholar 

  61. S. Schmidt, J. Koch, Annalen der Physik 525, 395–412 (2013)

    Article  ADS  Google Scholar 

  62. D.L. Underwood, W.E. Shanks, J. Koch, A.A. Houck, Phys. Rev. A 86, 023837 (2012)

    Article  ADS  Google Scholar 

  63. J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545–548 (2010)

    Article  ADS  Google Scholar 

  64. P. Kirton, J. Keeling, Phys. Rev. Lett. 111(Sep), 100404 (2013)

    Google Scholar 

  65. J. Schmitt, T. Damm, D. Dung, F. Vewinger, J. Klaers, M. Weitz, Phys. Rev. Lett. 112(Jan), 030401 (2014)

    Google Scholar 

  66. J. Klaers, J. Schmitt, T. Damm, D. Dung, F. Vewinger, M. Weitz, Proc. SPIE 8600, 8600L (2013)

    ADS  Google Scholar 

  67. H. Deng, H. Haug, Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010)

    Article  ADS  Google Scholar 

  68. O. Astafiev, A.M. Zagoskin, A.A. Abdumalikov, Y.A. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, J.S. Tsai, Science 327, 840 (2010)

    Article  ADS  Google Scholar 

  69. M.P.A. Fisher, P.B. Weichman, J. Watson, D.S. Fisher, G. Grinstein, Phys. Rev. B 40, 546 (1989)

    Article  ADS  Google Scholar 

  70. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (World Scientific, Singapore, 2006)

    Book  MATH  Google Scholar 

  71. H. Kleinert, S. Schmidt, A. Pelster, Annalen der Physik 14, 214 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  72. F.E.A. dos Santos, A. Pelster, Phys. Rev. A 79, 013614 (2009)

    Article  ADS  Google Scholar 

  73. N. Teichmann, D. Hinrichs, M. Holthaus, A. Eckardt, Phys. Rev. B 79, 100503 (2009)

    Article  ADS  Google Scholar 

  74. W. Metzner, Phys. Rev. B 43, 8549 (1991)

    Article  ADS  Google Scholar 

  75. M. Ohliger, A. Pelster (2008). arXiv:0810.4399

  76. S.D. Huber, E. Altman, H.P. Büchler, G. Blatter, Phys. Rev. B 75, 085106 (2007)

    Article  ADS  Google Scholar 

  77. B. Capogrosso-Sansone, S.G. Söyler, N. Prokof’ev, B. Svistunov, Phys. Rev. B 77, 015602 (2008)

    Article  ADS  Google Scholar 

  78. R. Dicke, Phys. Rev. 93, 99–110 (1954)

    Article  ADS  Google Scholar 

  79. K. Hepp, E.H. Lieb, Ann. Phys. 76, 360–404 (1973)

    Article  ADS  Google Scholar 

  80. Y.K. Wang, F.T. Hioe, Phys. Rev. A 7, 831 (1973)

    Article  ADS  Google Scholar 

  81. K. Hepp, E. Lieb, Phys. Rev. A 8, 2517–2525 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  82. M. Tavis, F.W. Cummings, Phys. Rev. 170, 379 (1968)

    Article  ADS  Google Scholar 

  83. J. Keeling, P.R. Eastham, M.H. Szymanska, P.B. Littlewood, Phys. Rev. Lett. 93, 226403 (2004)

    Article  ADS  Google Scholar 

  84. J. Keeling, P.R. Eastham, M.H. Szymanska, P.B. Littlewood, Phys. Rev. B 72, 115320 (2005)

    Article  ADS  Google Scholar 

  85. D. van Oosten, P. van der Straten, H.T.C. Stoof, Phys. Rev. A 63, 053601 (2001)

    Article  ADS  Google Scholar 

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Acknowledgements

We thank Martin Hohenadler, Markus Aichhorn, Jonathan Keeling and Lode Pollet for valuable discussions. This work was supported by a Ambizione award (S.S.) of the Swiss National Science Foundation.

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  1. Institute for Theoretical Physics, Eth Zurich, Zürich, Switzerland

    Sebastian Schmidt & Gianni Blatter

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  1. Sebastian Schmidt
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Correspondence to Sebastian Schmidt .

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  1. Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore

    Dimitris G. Angelakis

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Schmidt, S., Blatter, G. (2017). Phase Diagram and Excitations of the Jaynes-Cummings-Hubbard Model. In: Angelakis, D. (eds) Quantum Simulations with Photons and Polaritons. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-52025-4_2

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