Quantum-classical correspondence for a dc-biased cavity resonator-Cooperpair transistor system

Fluctuating Nonlinear Oscillators: From Nanomechanics to Quantum Superconducting Circuits

Volumn 9780199691388, Issue , 2012, Pages

  Blencowe, M P ^a   Armour, A D ^b   Rimberg, A J ^a  

^a Lamont Doherty Earth Observatory   (United States)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Chaos; Cooper pair transistor; Dynamical tunnelling; Macroscopic quantum dynamics; Nonlinear dynamics; Open quantum systems; Quantum classical correspondence; Superconducting circuits; Wigner function

Indexed keywords

CHAOS THEORY; QUANTUM OPTICS; TIMING CIRCUITS;

COOPER-PAIR TRANSISTORS; DC BIAS; DYNAMICAL TUNNELING; MACROSCOPIC QUANTUM; MACROSCOPIC QUANTUM DYNAMIC; OPEN QUANTUM SYSTEMS; QUANTUM DYNAMICS; QUANTUM-CLASSICAL CORRESPONDENCE; SUPERCONDUCTING CIRCUIT; WIGNER FUNCTIONS;

DYNAMICS;

EID: 84921746699     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780199691388.003.0002     Document Type: Chapter

References (80)

1. Armour, A.D. and Blencowe, M.P. (2008). New Journal of Physics, 10, 095004.
2. Bahr, B. and Korsch, H.J. (2007). Journal of Physics A: Mathematical and Theoretical, 40, 3959.
3. Berry, M.V. (1977). Philosophical Transactions of the Royal Society of London Series A, 287, 237.
4. Bhattacharya, T., Habib, S., and Jacobs, K. (2000). Phys. Rev. Lett., 85, 4852-4855.
5. Bizarro, J.P. (1994). Phys. Rev. A, 49, 3255.
6. Blencowe, M.P. and Armour, A.D. (2008). New Journal of Physics, 10, 095005.
7. Breuer, H.-P. and Petruccione, F. (2006). Theory of Open Quantum systems. Oxford University Press, Oxford, UK.
8. Brun, T.A., Percival, I.C., and Schack, R. (1996). Journal of Physics A: Mathematical and General, 29, 2077.
9. Burkard, G., Koch, R.H., and DiVincenzo, D.P. (2004). Phys. Rev. B, 69, 064503.
10. Casati, G. and Molinari, L. (1989). Progress of Theoretical Physics Supplement, 98, 287-322.
11. Chaudhury, S., Smith, A., Anderson, B.E., Ghose, S., and Jessen, P.S. (2009). Nature, 461, 768-771.
12. Chen, F., Sirois, A.J., Simmonds, R.W., and Rimberg, A.J. (2011). Applied Physics Letters, 98, 132509.
13. Chiorescu, I., Nakamura, Y., Harmans, C.J.P.M., and Mooij, J.E. (2003). Science, 299, 1869.
14. Clarke, J., Cleland, A.N., Devoret, M.H., Esteve, D., and Martinis, J.M. (1988). Science, 239, 992.
15. Cortés, E., West, B.J., and Lindenberg, K. (1985). Journal of Chemical Physics, 82, 2708.
16. Davis, M.J. and Heller, E.J. (1981). Journal of Chemical Physics, 75, 246.
17. Devoret, M.H. (1997). In Les Houches, Session LXIII, 1995 (ed. S. Reynaud, E. Giacobino, and J. Zinn-Justin), pp. 351-386. Elsevier, Amsterdam.
18. DiCarlo, L., Reed, M.D., Sun, L., Johnson, B.R., Chow, J.M., Gambetta, J.M., Frunzio, L., Girvin, S.M., Devoret, M.H., and Schoelkopf, R.J. (2010). Nature, 467, 574-578.
19. Dykman, M.I. (2007). Phys. Rev. E, 75, 011101.
20. Dykman, M.I. and Smelyanskiĭ, V.N. (1988). Sov. Phys. JETP, 67, 1769.
21. Everitt, M.J., Clark, T.D., Stifell, P.B., Ralph, J.F., Bulsara, A.R., and Harland, C.J. (2005). Phys. Rev. E, 72, 066209.
22. Fedorov, A., Macha, P., Feofanov, A.K., Harmans, C.J.P.M., and Mooij, J.E. (2011). Phys. Rev. Lett., 106, 170404.
23. Fox, R.F. and Elston, T.C. (1994). Phys. Rev. E, 49, 3683.
24. Fox, R.F. and Lan, B.L. (1990). Phys. Rev. A, 41, 2952.
25. Friedman, J.R., Patel, V., Chen, W., Tolpygo, S.K., and Lukens, J.E. (2000). Nature, 406, 43-46.
26. Gorin, T., Korsch, H.J., and Mirbach, B. (1997). Chemical Physics, 217, 145-153.
27. Graham, R. and Keymer, J. (1991). Phys. Rev. A, 44, 6281.
28. Graham, R., Schlautmann, M., and Shepelyansky, D.L. (1991). Phys. Rev. Lett., 67, 255-258.
29. Greenbaum, B.D., Habib, S., Shizume, K., and Sundaram, B. (2007). Phys. Rev. E, 76, 046215.
30. Haake, F. (2010). Quantum Signatures of Chaos (3rd edn). Volume 54. Springer Verlag.
31. Habib, S., Jacobs, K., Mabuchi, H., Ryne, R., Shizume, K., and Sundaram, B. (2002). Phys. Rev. Lett., 88, 40402.
32. Habib, S., Shizume, K., and Zurek, W.H. (1998). Phys. Rev. Lett., 80, 4361-4365.
33. Hofeinz, M., Portier, F., Baudouin, Q., Joyez, P., Vion, D., Bertet, P., Roche, P., and Esteve, D. (2011). Phys. Rev. Lett., 106, 217005.
34. Holst, T., Esteve, D., Urbina, C., and Devoret, M.H. (1994). Phys. Rev. Lett., 73, 3455-3458.
35. Hori, T. (1927). Z. f. Physik, 44, 834.
36. Hudson, R.L. (1974). Reports on Mathematical Physics, 6, 249-252.
37. Ingold, G.L., Grabert, H., and Eberhardt, U. (1994). Phys. Rev. B, 50, 395.
38. Ingold, G.L. and Nazarov, Y.V. (1992). In Single Charge Tunneling (ed. H. Grabert and M. Devoret). Plenum Press, New York.
39. Josephson, B.D. (1962). Phys. Lett., 1 251-253.
40. Kastrup, H.A. (2006). Phys. Rev. A, 73, 052104.
41. Katz, I., Lifshitz, R., Retzker, A., and Straub, R. (2008). New Journal of Physics, 10, 125023.
42. Ketzmerick, R. and Wustmann, W. (2010). Phys. Rev. E, 82, 021114.
43. Koch, J., Yu, T.M., Gambetta, J., Houck, A.A., Schuster, D.I., Majer, J., Blais, A., Devoret, M.H., Girvin, S.M., and Schoelkopf, R.J. (2007). Phys. Rev. A, 76, 042319.
44. Kohler, S., Dittrich, T., and Hänggi, P. (1997). Phys. Rev. E, 55, 300.
45. Kohler, S., Utermann, R., Hänggi, P., and Dittrich, T. (1998). Phys. Rev. E, 58, 7219.
46. Kowalski, K., Rembielinski, J., and Papaloucas, L.C. (1996). Journal of Physics A:Mathematical and General, 29, 4149.
47. Lan, B.L. and Fox, R.F. (1991). Phys. Rev. A, 43, 646.
48. Latka, M., Grigolini, P., and West, B.J. (1994). Phys. Rev. A, 50, 1071.
49. Lee, S.B. and Feit, M.D. (1993). Phys. Rev. E, 47, 4552.
50. Leggett, A. J. (2009). Contemporary Physics, 50, 243-258.
51. Leppäkangas, J. and Tuneberg, E. (2008). Phys. Rev. B, 78, 144518.
52. Leppäkangas, J., Tuneberg, E., Lindell, R., and Hakonen, P. (2006). Phys. Rev. B, 74, 054504.
53. Lin, W.A. and Ballentine, L.E. (1990). Phys. Rev. Lett., 65, 2927-2930.
54. Marthaler, M. and Dykman, M.I. (2006). Phys. Rev. A, 73, 042108.
55. Mirbach, B. and Korsch, H.J. (1995). Phys. Rev. Lett., 75, 362-365.
56. Monteoliva, D. and Paz, J.P. (2001). Phys. Rev. E, 64, 056238.
57. Mouchet, A., Eltschka, C., and Schlagheck, P. (2006). Phys. Rev. E, 74, 026211.
58. Mouchet, A., Miniatura, C., Kaiser, R., Grémaud, B., and Delande, D. (2001). Phys. Rev. E, 64, 016221.
59. Mukunda, N. (1979). American Journal of Physics, 47, 182.
60. Neeley, M., Bialczak, R.C., Lenander, M., Lucero, E., Mariantoni, M., O'Connell, A.D., Sank, D., Wang, H., Weides, M., Wenner, J., Yin, Y., Yamamoto, T., Cleland, A.N., and Martinis, J.M. (2010). Nature, 467, 570-573.
61. Pashkin, Yu. A., Im, H., Leppäkangas, J., Li, T.F., Astafev, O., Abdumalikov, Jr., A.A., Tuneberg, E., and Tsai, J.S. (2011). Phys. Rev. B, 83, 020502.
62. Peano, V. and Torwart, M. (2004). Phys. Rev. B, 70, 235401.
63. Prance, R.J., Mutton, J.E., Prance, H., Clark, T.D., Widom, A., and Megaloudis, G. (1983). Helvetica Physica Acta, 56, 789-95.
64. Reichl, L.E. (2004). The Transition to Chaos: Conservative Classical Systems and Quantum Manifestations (2nd edn). Springer Verlag.
65. Rigas, I., Sánchez-Soto, L.L., Klimov, A.B., Řeháček, J., and Hradil, Z. (2008). Phys. Rev. A, 78, 060101.
66. Rigas, I., Sánchez-Soto, L.L., Klimov, A.B., Řeháček, J., and Hradil, Z. (2010). Phys. Rev. A, 81, 012101.
67. Serban, I. and Wilhelm, F.K. (2007). Phys. Rev. Lett., 99, 137001.
68. Smith, T.I. (1974). Journal of Applied Physics, 45, 1875-1879.
69. Srivastava, Y. and Widom, A. (1987). Physics Reports, 148, 1-65.
70. Steck, D.A., Oskay, W.H., and Raizen, M.G. (2001). Science, 293, 274.
71. Takahashi, K. (1989). Progress of Theoretical Physics Supplement, 98, 109-156.
72. Toda, M., Adachi, S., and Ikeda, K. (1989). Progress of Theoretical Physics Supplement, 98, 323-375.
73. Tomsovic, S. and Ullmo, D. (1994). Phys. Rev. E, 50, 145.
74. Verso, A. and Ankerhold, J. (2010). Phys. Rev. A, 81, 022110.
75. Vijay, R., Devoret, M.H., and Siddiqi, I. (2009). Review of Scientifc Instruments, 80, 111101.
76. Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Huang, R.S., Majer, J., Kumar, S., Girvin, S.M., and Schoelkopf, R.J. (2004). Nature, 431, 162-167.
77. Werthamer, N.R. and Shapiro, S. (1967). Phys Rev, 164, 523.
78. Yurke, B. and Denker, J.S. (1984). Phys. Rev. A, 29, 1419-1437.
79. Zimmerman, J.E. (1971). Journal of Applied Physics, 42, 30-37.
80. Zurek, W.H. and Paz, J.P. (1994). Phys. Rev. Lett., 72, 2508-2511.