Low-lying bifurcations in cavity quantum electrodynamics

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 6, 2006, Pages

  Armen, M A ^a   Mabuchi, H ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFUSION; DYNAMICS; ELECTRODYNAMICS; SENSORS; STOCHASTIC CONTROL SYSTEMS;

INTRACAVITY OPTICAL FIELD; QUANTUM STATIONARY STATES; STOCHASTIC TRANSITIONS;

QUANTUM THEORY;

EID: 33744796814     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.063801     Document Type: Article

References (62)

1. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Westview Press, MA, 2001).
2. L. Perko, Differential Equations and Dynamical Systems, 3rd ed. (Springer-Verlag, New York, 2006).
3. R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, cond-mat/0511587.
4. C. H. Tseng, D. Enzer, G. Gabrielse, and F. L. Walls, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.2094 59, 2094 (1999).
5. I. Siddiqi, R. Vijay, F. Pierre, C. M. Wilson, M. Metcalfe, C. Rigetti, L. Frunzio, and M. H. Devoret, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.207002 93, 207002 (2004).
6. E. Abraham and S. D. Smith, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/45/8/001 45, 815 (1982).
7. M. F. Yanik, S. Fan, M. Soljačić, and J. D. Joannopoulos, Opt. Lett. OPLEDP 0146-9592 28, 2506 (2003).
8. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, Opt. Express OPEXFF 1094-4087 10.1364/OPEX.13.009623 13, 9623 (2005).
9. D. T. Gillespie, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100540a008 81, 2340 (1977).
10. L. Arnold, Random Dynamical Systems (Springer-Verlag, Berlin, 1998).
11. E. C. Zeeman, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/1/1/005 1, 115 (1988).
12. M. B. Elowitz and S. Leibler, Nature (London) NATUAS 0028-0836 10.1038/35002125 403, 335 (2000).
13. H. Qian, S. Saffarian, and E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.152007599 99, 10376 (2002).
14. R. Steuer, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2004.01.012 228, 293 (2004).
15. G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.1727 67, 1727 (1991).
16. H. Mabuchi and A. C. Doherty, Science SCIEAS 0036-8075 10.1126/science.1078446 298, 1372 (2002).
17. C. M. Savage and H. J. Carmichael, IEEE J. Quantum Electron. IEJQA7 0018-9197 10.1109/3.7075 24, 1495 (1988).
18. S. Ya. Kilin and T. B. Krinitskaya, J. Opt. Soc. Am. B JOBPDE 0740-3224 8, 2289 (1991).
19. A. V. Kozlovskii and A. N. Oraevskii, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/1.558897 88, 1095 (1999).
20. C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.4157 80, 4157 (1998).
21. P. Alsing and H. J. Carmichael, Quantum Opt. QUOPET 0954-8998 10.1088/0954-8998/3/1/003 3, 13 (1991).
22. T. Wellens and A. Buchleitner, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(01)00291-9 268, 131 (2001).
23. Hu Gang, C. Z. Ning, and H. Haken, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.2702 41, 2702 (1990).
24. H. Gang, C. Z. Ning, and H. Haken, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.3975 41, 3975 (1990).
25. Cavity Quantum Electrodynamics, edited by, P. R. Berman, (Academic Press, San Diego, 1994).
26. P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press, Cambridge, England, 1997).
27. H. M. Wiseman and A. C. Doherty, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.070405 94, 070405 (2005).
28. S. Habib, K. Jacobs, and K. Shizume, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.010403 96, 010403 (2006).
29. For a complementary perspective, see A. Vardi and J. R. Anglin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.568 86, 568 (2001).
30. H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
31. A. T. Rosenberger, L. A. Orozco, H. J. Kimble, and P. D. Drummond, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.43.6284 43, 6284 (1991).
32. L. A. Lugiato, in Progress in Optics, edited by, E. Wolf, (North-Holland, Amsterdam, 1984), Vol. XXI.
33. H. J. Carmichael, in Frontiers in Quantum Optics, edited by, E. R. Pike, and, S. Sarkar, (Adam Hilger, Bristol, 1986).
34. L. A. Orozco, H. J. Kimble, A. T. Rosenberger, L. A. Lugiato, M. L. Asquini, M. Brambilla, and L. M. Narducci, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.39.1235 39, 1235 (1989).
35. Hu Gang and Guo-jian Yang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.1979 38, 1979 (1988).
36. K. Wiesenfeld and B. McNamara, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.33.629 33, 629 (1986);
37. K. A. Shore, J. Opt. Soc. Am. B JOBPDE 0740-3224 5, 1211 (1988);
38. V. M. Eguíluz, M. Ospeck, Y. Choe, A. J. Hudspeth, and M. O. Magnasco, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5232 84, 5232 (2000).
39. H. Mabuchi and H. M. Wiseman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.4620 81, 4620 (1998);
40. misprint corrected in Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1798 82, 1798 (1999).
41. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
42. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1995).
43. H. M. Wiseman and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.47.642 47, 642 (1993).
44. L. Bouten, R. van Handel, and M. R. James, math.OC/0601741.
45. S. M. Tan, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 10.1088/1464-4266/1/4/312 1, 424 (1999).
46. R. van Handel and H. Mabuchi, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 7, S226 (2005).
47. A. C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S. M. Tan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.012105 62, 012105 (2000).
48. R. van Handel, J. K. Stockton, and H. Mabuchi, IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/TAC.2005.849193 50, 768 (2005).
49. B. Macke, J. Zemmouri, and N. E. Fettouhi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.47.R1609 47, R1609 (1993).
50. L. Yaowen, P. Huican, Z. Hong, and W. Yinghai, Phys. Lett. A PYLAAG 0375-9601 262, 416 (1999).
51. E. H. Abed and J. H. Fu, Syst. Control Lett. SCLEDC 0167-6911 10.1016/0167-6911(86)90095-2 7, 11 (1986).
52. G. Chen, J. L. Moiola, and H. O. Wang, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1016/S0218-1274(00)00036-0 10, 511 (2000).
53. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.032109 69, 032109 (2004).
54. S. D. Robinson, F. Moss, and P. V. E. McClintock, J. Phys. A JPHAC5 0305-4470 18, L89 (1985).
55. L. Fronzoni, R. Mannella, P. V. E. McClintock, and F. Moss, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.36.834 36, 834 (1987).
56. K. Wiesenfeld, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01010430 38, 1071 (1985).
57. W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology (Springer, Berlin, 1984).
58. L. Arnold and P. Boxler, in Diffusion Processes and Related Problems in Analysis, edited by, M. A. Pinsky, and, V. Wihstutz, (Birkhäuser, Boston, 1992), Vol. II.
59. L. Arnold, G. Bleckert, and K.-R. Schenk-Hoppé, in Stochastic Dynamics, edited by, H. Crauel, and, M. Grundlach, (Springer-Verlag, New York, 1999).
60. R. Wackerbauer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.2872 59, 2872 (1999).
61. H. J. Carmichael, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.33.3262 33, 3262 (1986).
62. C. Z. Ning, J. Phys. A JPHAC5 0305-4470 21, L491 (1988).