Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 85, Issue 4, 2012, Pages

  Nietner, Christian ^a   Pelster, Axel ^b,c  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b Hanse Wissenschaftskolleg   (Germany)

^c France   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTANT ORDERS; CUBIC LATTICE; EXCITATION SPECTRUM; FIRST ORDER; GINZBURG LANDAU THEORY; GINZBURG-LANDAU; HOPPING PARAMETERS; MEAN-FIELD; ORDER PARAMETER; POLARITONS; STATIC AND DYNAMIC; SUPERFLUID PHASE; TWO-LEVEL ATOM;

HUBBARD MODEL; PHOTONS;

SUPERCONDUCTING DEVICES;

EID: 84859997827     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.85.043831     Document Type: Article

References (88)

1. A. Kay and J. K. Pachos, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/6/1/126 6, 126 (2004). (Pubitemid 39350764)
2. P. Treutlein, T. Steinmetz, Y. Colombe, B. L. Lev, P. Hommelhoff, Fortschr. Phys. FPYKA6 0015-8208 10.1002/prop.200610325 54, 702 (2006). (Pubitemid 44368481)
3. R. P. Feynman, Int. J. Theor. Phys. IJTPBM 0020-7748 10.1007/BF02650179 21, 467 (1982).
4. H. S. J. van der Zant, F. C. Fritschy, W. J. Elion, L. J. Geerligs, and J. E. Mooij, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2971 69, 2971 (1992).
5. A. van Oudenaarden and J. E. Mooij, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4947 76, 4947 (1996).
6. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.546 40, 546 (1989).
7. M. Naraschewski, H. Wallis, A. Schenzle, J. I. Cirac, and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.2185 54, 2185 (1996).
8. M. R. Andrews, Science SCIEAS 0036-8075 10.1126/science.275.5300.637 275, 637 (1997). (Pubitemid 27061324)
9. K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.806 84, 806 (2000).
10. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Science SCIEAS 0036-8075 10.1126/science.1060182 292, 476 (2001).
11. S. Kling and A. Pelster, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.023609 76, 023609 (2007). (Pubitemid 47331071)
12. S. Kling and A. Pelster, Laser Physics LAPHEJ 1054-660X 10.1134/S1054660X0905034X 19, 1072 (2009).
13. D. M. Stamper-Kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H.-J. Miesner, J. Stenger, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2027 80, 2027 (1998).
14. F. Schreck, L. Khaykovich, K. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles, and C. Salomon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.080403 87, 080403 (2001).
15. S. Röthel and A. Pelster, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2007-00288-x 59, 343 (2007). (Pubitemid 350037078)
16. R. Graham and A. Pelster, Int. J. Bif. Chaos IJBEE4 0218-1274 10.1142/S0218127409024451 19, 2745 (2009).
17. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, Nature (London) NATUAS 0028-0836 10.1038/nature07000 453, 891 (2008). (Pubitemid 351832566)
18. G. Roati, C. D'Errico, L. Fallani, M. Fattori, C. Fort, Nature (London) NATUAS 0028-0836 10.1038/nature07071 453, 895 (2008). (Pubitemid 351832573)
19. A. Griesmaier, J. Werner, S. Hensler, J. Stuhler, and T. Pfau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.160401 94, 160401 (2005). (Pubitemid 40620281)
20. A. R. P. Lima and A. Pelster, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.021606 81, 021606 (2010).
21. T. van Zoest, N. Gaaloul, Y. Singh, H. Ahlers, W. Herr, Science SCIEAS 0036-8075 10.1126/science.1189164 328, 5985 (2010).
22. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3108 81, 3108 (1998).
23. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/415039a 415, 6867 (2002). (Pubitemid 34062442)
24. D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1975 82, 1975 (1999).
25. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, Nature (London) 425, 6961 (2008).
26. M. Riebe, H. Häffner, C. F. Roos, W. Hänsel, J. Benhelm, Nature (London) NATUAS 0028-0836 10.1038/nature02570 429, 6993 (2004). (Pubitemid 38833119)
27. C. F. Roos, G. P. T. Lancaster, M. Riebe, H. Häffner, W. Hänsel, S. Gulde, C. Becher, J. Eschner, R. Schmidt-Kaler, and R. Blatt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.220402 92, 220402 (2004).
28. L. Sanchez-Palencia and L. Santos, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.053607 72, 053607 (2005). (Pubitemid 41776191)
29. V. Ahufinger, L. Sanchez-Palencia, A. Kantian, A. Sanpera, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.063616 72, 063616 (2005).
30. D. Clément, A. F. Varón, M. Hugbart, J. A. Retter, P. Bouyer, L. Sanchez-Palencia, D. M. Gangardt, G. V. Shlyapnikov, and A. Aspect, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.170409 95, 170409 (2005). (Pubitemid 41777338)
31. K. V. Krutitsky, A. Pelster, and R. Graham, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/9/187 8, 187 (2006). (Pubitemid 44403692)
32. V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne, and C. J. Williams, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.043605 62, 043605 (2000).
33. S. J. J. M. F. Kokkelmans, H. M. J. Vissers, and B. J. Verhaar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.031601 63, 031601 (2001). (Pubitemid 33764955)
34. W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, Science SCIEAS 0036-8075 10.1126/science.1192368 329, 547 (2010).
35. P. Würtz, T. Langen, T. Gericke, A. Koglbauer, and H. Ott, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.080404 103, 080404 (2009).
36. N. Gemelke, X. Zhang, C.-L. Hung, and C. Chin, Nature (London) NATUAS 0028-0836 10.1038/nature08244 460, 995 (2009).
37. J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/nature09378 467, 68 (2010).
38. K. J. Vahala, Nature (London) NATUAS 0028-0836 10.1038/nature01939 424, 6950 (2003). (Pubitemid 37021719)
39. G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, Nature Phys. 1745-2473 10.1038/nphys227 2, 81 (2006). (Pubitemid 43731376)
40. T. M. Benson, S. V. Boriskina, P. Sewell, A. Vukovic, S. C. Greedy, Frontiers of Planar Lightwave Circuit Technology (Springer, Berlin, 2005), p. 39.
41. P. Grangier, G. Reymond, and N. Schlosser, Fortschr. Phys. FPYKA6 0015-8208 10.1002/1521-3978(200009)48:9/11<859::AID-PROP859>3.0.CO;2-N 48, 859 (2000).
42. M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.61.R11855 61, 11855 (2000).
43. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A.S. Zibrov, V. Vuletic, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.203902 102, 203902 (2009).
44. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, Nature Phys. 1745-2473 10.1038/nphys462 2, 849 (2006). (Pubitemid 44853583)
45. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nature Phys. 1745-2473 10.1038/nphys466 2, 856 (2006). (Pubitemid 44853584)
46. D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.031805 76, 031805 (2007). (Pubitemid 47510818)
47. H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, Science SCIEAS 0036-8075 10.1126/science.1074464 298, 199 (2002).
48. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, Nature (London) NATUAS 0028-0836 10.1038/nature05131 443, 7110 (2006). (Pubitemid 44477272)
49. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, Science SCIEAS 0036-8075 10.1126/science.1140990 316, 1007 (2007). (Pubitemid 46799484)
50. A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, Nature (London) NATUAS 0028-0836 10.1038/nature07640 457, 291 (2009).
51. A. Amo, J. Lefrère, S. Pigeon, C. Adrados, C. Ciuti, Nature Physics 1745-2473 10.1038/nphys1364 5, 805 (2009).
52. A. Z. Muradyan and G. A. Muradyan, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/35/19/304 35, 3995 (2002). (Pubitemid 35251023)
53. J.-Q. Liao, Z. R. Gong, L. Zhou, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.042304 81, 042304 (2010).
54. F. P. Laussy, E. del Valle, A. Gonzalez-Tudela, E. Cancellieri, D. Sanvitto, 18th Int. Symp. "Nanostructures: Physics and Technology " 298 (2010).
55. A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Bohm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.075305 82, 075305 (2010).
56. T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, Opt. Express OPEXFF 1094-4087 10.1364/OPEX.13.003558 13, 3558 (2005). (Pubitemid 40899410)
57. G. Ctistis, A. Hartsuiker, E. van der Pol, J. Claudon, W. L. Vos, and J. M. Gerad, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.195330 82, 195330 (2010).
58. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.043902 91, 043902 (2003).
59. F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hopkinson, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3487937 97, 111101 (2010).
60. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, Nature (London) NATUAS 0028-0836 10.1038/nature02851 431, 162 (2004). (Pubitemid 39243464)
61. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.29.001224 29, 1224 (2004).
62. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A.S. Zibrov, V. Vuletic, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.203902 102, 203902 (2009).
63. M. Trupke, J. Goldwin, B. Darquie, G. Dutier, S. Eriksson, J. Ashmore, and E. A. Hinds, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.063601 99, 063601 (2007). (Pubitemid 47253902)
64. F. Nissen, S. Schmidt, M. Biondi, G. Blatter, H. E. Türeci, and J. Keeling, e-print arXiv: 1202.1961.
65. B. Bradlyn, F. E. A. dos Santos, and A. Pelster, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.013615 79, 013615 (2009).
66. F. E. A. dos Santos and A. Pelster, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.013614 79, 013614 (2009).
67. T. D. Grass, F. E. A. dos Santos, and A. Pelster, Laser Physics LAPHEJ 1054-660X 10.1134/S1054660X11150096 21, 1459 (2011).
68. T. D. Grass, F. E. A. dos Santos, and A. Pelster, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.84.013613 84, 013613 (2011).
69. A. Hoffmann and A. Pelster, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053623 79, 053623 (2009).
70. D. McKay and B. DeMarco, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/74/5/054401 74, 054401 (2011).
71. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1995).
72. E. T. Jaynes and F. W. Cummings, P. IEEE IEEPAD 0018-9219 10.1109/PROC.1963.1664 51, 89 (1963).
73. S. Trotzky, L. Pollet, F. Gerbier, U. Schnorrberger, I. Bloch, Nat. Phys. 1745-2473 10.1038/nphys1799 6, 998 (2010).
74. F. Gerbier, S. Trotzky, S. Foelling, U. Schnorrberger, J. D. Thompson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.155303 101, 155303 (2008).
75. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
76. L. D. Landau and E. M. Lifschitz, Course of Theoretical Physics (Akademie Verlag, Berlin, 1970), Vol. 5.
77. J. W. Negele and H. Orland, Quantum Many-Particle Systems (Westview Press, Boulder, 1998).
78. W. Metzner, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.43.8549 43, 8549 (1991).
79. J. Koch and K. Le Hur, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80. 023811 80, 023811 (2009).
80. H. Kleinert and V. Schulte-Frohlinde, Critical Properties of φ 4 Theories (World Scientific Publishing Company, Singapore, 2001).
81. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 2002).
82. S. Schmidt and G. Blatter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.086403 103, 086403 (2009).
83. P. Buonsante and A. Vezzani, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.033608 70, 033608 (2004).
84. I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoglu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.033601 103, 033601 (2009).
85. J. Goldstone, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.127.965 127, 965 (1962).
86. M. Hohenadler, M. Aichhorn, S. Schmidt, and L. Pollet, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.84.041608 84, 041608 (2011).
87. S. Schmidt and G. Blatter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.216402 104, 216402 (2010).
88. C. Hei and W. von der Linden, e-print arXiv: 1105.2418.