Superfluid-Mott-insulator transition of light in the Jaynes-Cummings lattice

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 2, 2009, Pages

  Koch, Jens ^a   Le Hur, Karyn ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; BOSE HUBBARD MODEL; CRITICAL BEHAVIOR; ELECTROMAGNETIC RESONATORS; JAYNES-CUMMINGS; MEAN-FIELD THEORIES; MOTT-INSULATING PHASE; MULTICRITICAL POINT; POLARITONS; QUANTUM PHASE TRANSITIONS; REGULAR ARRAY; SIMILARITIES AND DIFFERENCES; SUPERFLUID PHASE; SUPERFLUID-MOTT-INSULATOR TRANSITION; TWO-LEVEL SYSTEM;

GRAPH THEORY; HUBBARD MODEL; INSULATION; MEAN FIELD THEORY;

PHASE TRANSITIONS;

EID: 68949147902     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.023811     Document Type: Article

References (39)

1. H. v. Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007). 10.1103/RevModPhys.79.1015 (Pubitemid 47364614)
2. E. Altman, W. Hofstetter, E. Demler, and M. D. Lukin, New J. Phys. 5, 113 (2003). 10.1088/1367-2630/5/1/113
3. J. Han, T. Zhang, Y. Wang, and W. Liu, Phys. Lett. A 332, 131 (2004). 10.1016/j.physleta.2004.09.059 (Pubitemid 40288164)
4. P. P. Orth, I. Stanic, and K. Le Hur, Phys. Rev. A 77, 051601 (R) (2008). 10.1103/PhysRevA.77.051601 (Pubitemid 351725939)
5. C. Emary and T. Brandes, Phys. Rev. Lett. 90, 044101 (2003). 10.1103/PhysRevLett.90.044101
6. R. H. Dicke, Phys. Rev. 93, 99 (1954). 10.1103/PhysRev.93.99
7. E. Jaynes and F. Cummings, Proc. IEEE 51, 89 (1963). 10.1109/PROC.1963. 1664
8. J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001). 10.1103/RevModPhys.73.565
9. R. J. Schoelkopf and S. M. Girvin, Nature (London) 451, 664 (2008). 10.1038/451664a (Pubitemid 351220557)
10. K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature (London) 436, 87 (2005). 10.1038/nature03804 (Pubitemid 40966189)
11. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, Nat. Phys. 2, 849 (2006). 10.1038/nphys462 (Pubitemid 44853583)
12. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, New J. Phys. 10, 033011 (2008). 10.1088/1367-2630/10/3/033011
13. D. E. Chang, V. Gritsev, G. Morigi, V. Vuletić, M. D. Lukin, and E. A. Demler, Nat. Phys. 4, 884 (2008). 10.1038/nphys1074
14. M. I. Makin, J. H. Cole, C. Tahan, L. C. L. Hollenberg, and A. D. Greentree, Phys. Rev. A 77, 053819 (2008). 10.1103/PhysRevA.77.053819 (Pubitemid 351725943)
15. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006). 10.1038/nphys466 (Pubitemid 44853584)
16. N. Na, S. Utsunomiya, L. Tian, and Y. Yamamoto, Phys. Rev. A 77, 031803 (R) (2008). 10.1103/PhysRevA.77.031803
17. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989). 10.1103/PhysRevB.40.546
18. D. Rossini and R. Fazio, Phys. Rev. Lett. 99, 186401 (2007). 10.1103/PhysRevLett.99.186401 (Pubitemid 350023215)
19. M. Aichhorn, M. Hohenadler, C. Tahan, and P. B. Littlewood, Phys. Rev. Lett. 100, 216401 (2008). 10.1103/PhysRevLett.100.216401 (Pubitemid 351777228)
20. J. Zhao, A. Sandvik, and K. Ueda, e-print arXiv:0806.3603.
21. P. Pippan, H. Evertz, and M. Hohenadler, e-print arXiv:0904.1350.
22. S. Schmidt and G. Blatter, e-print arXiv:0905.3344.
23. D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805 (R) (2007). 10.1103/PhysRevA.76.031805 (Pubitemid 47510818)
24. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, Laser Photonics Rev. 2, 527 (2008). 10.1002/lpor.200810046
25. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks-Cole, Belmont, MA, 1976).
26. P. R. Wallace, Phys. Rev. 71, 622 (1947). 10.1103/PhysRev.71.622
27. S. C. Lei and R. K. Lee, Phys. Rev. A 77, 033827 (2008). 10.1103/PhysRevA.77.033827
28. We note that for numerical purposes, it is convenient to carry out the minimization with respect to ψ̄ =κψ in order to avoid numerical problems in the limit of κ→0.
29. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 2000).
30. I. Herbut, A Modern Approach to Critical Phenomena (Cambridge University Press, New York, 2007).
31. P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928). 10.1007/BF01331938
32. E. Fradkin, Phys. Rev. Lett. 63, 322 (1989). 10.1103/PhysRevLett.63.322
33. C. D. Batista and G. Ortiz, Phys. Rev. Lett. 86, 1082 (2001). 10.1103/PhysRevLett.86.1082 (Pubitemid 32169232)
34. R. Friedberg, T. D. Lee, and H. C. Ren, Ann. Phys. 228, 52 (1993). 10.1006/aphy.1993.1088
35. Angelakis choose to call the model given by Eq. 49 an XY model. Here we rather follow the nomenclature used, e.g., by Sachdev.
36. J. W. Negele and H. Orland, Quantum Many-Particle Systems (Perseus Book Publishings, Cambridge, 1998).
37. We note that, as in the Bose-Hubbard case, the gauge transformation Eq. 63 actually leads out of the physical space since ω-μ acquires an imaginary part.
38. While the phase boundary 20 is obtained within the mean-field approximation and may acquire corrections when including the effects of fluctuations (see, e.g., Ref.), we emphasize that Eqs. 64 65 are exact.
39. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Nature (London) 431, 162 (2004). 10.1038/nature02851 (Pubitemid 39243464)