A basic two-state model for bosonic field theories with a cubic nonlinearity

Journal of Physics A: Mathematical and General

Volumn 38, Issue 16, 2005, Pages 3505-3516

  Ishkhanyan, Artur ^a,c   Javanainen, Juha ^b   Nakamura, Hiroki ^c  

^a Armenian NAS   (Armenia)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c INSTITUTE FOR MOLECULAR SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24144476540     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/16/003     Document Type: Review

References (54)

1. Anderson M H, Ensher J R, Matthews M R, Wieman C E and Cornell E A 1995 Science 269 198
2. Davis K B, Mewes M-O, Andrews M R, van Druten N J, Durfee D S, Kurn D M and Ketterle W 1995 Phys. Rev. Lett. 75 3969
3. Bradley C C, Sackett C A, Tollett J J and Hulet R G 1995 Plys. Rev. Lett. 75 1687
4. Anglin J R and Ketterle W 2002 Nature 416 211
5. Javanainen J and Mackie M 1999 Phys. Rev. A 59 R3186
6. Kostrun M, Mackie M, Cote R and Javanainen J 2000 Phys. Rev. A 62 063616
7. Mackie M and Javanainen J 1999 Phys. Rev. A 60 3174
8. Drummond P D, Kheruntsyan K V and He H 1998 Phys. Rev. Lett. 81 3055
9. Heinzen D J, Wynar R, Drummond P D and Kheruntsyan K V 2000 Phys. Rev. Lett. 84 5029
10. Timmermans E, Tommasini P, Hussein M and Kernan A 1999 Phys. Rep. C 315 199
11. van Abeelen F A and Verhaar B J 1999 Phys. Rev. Lett. 83 1550
12. Shen Y R 2002 The Principles of Nonlinear Optics (New York: Wiley)
13. Boyd R W 1992 Nonlinear Optics (Boston, MA: Academic)
14. Yariv A 1989 Quantum Electronics (New York: Wiley)
15. Butcher P N and Cotter D 1991 The Elements of Nonlinear Optics (Cambridge: Cambridge University Press)
16. Akhmanov S A and Khokhlov R V 1972 Problems of Nonlinear Optics (New York: Gordon and Breach)
17. Shore B W 1990 The Theory of Coherent Atomic Excitation (New York: Wiley)
18. Nikitin E E and Umanski S Ya 1984 Theory of Slow Atomic Collisions (Berlin: Springer)
19. Vitanov N V and Garraway B M 1996 Phys. Rev. A 53 4288
20. Vitanov N V and Garraway B M 1996 Phys. Rev. A 54 5458(E)
21. Ishkhanyan A, Chernikov G P and Nakamura H 2004 Rabi problem in photoassociation of atomic Bose-Einstein condensates Phys. Rev. A 70 053611
22. Landau L D 1932 Phys. Z. Sowjetunion 2 46
23. Zener C 1932 Proc. R. Soc. A 137 696
24. Abramowitz M and Stegun I A 1965 Handbook of Mathematical Functions (New York: Dover)
25. Erdelyi A, Magnus W, Oberhettinger F and Tricomi F G 1953 Higher Transcendental Functions (New York: McGraw-Hill)
26. Slater L J 1966 Generalized Hypergeometric Functions (Cambridge: Cambridge University Press)
27. Ishkhanyan A M 2000 J. Phys. A: Math. Gen. 33 5539
28. Ishkhanyan A M 2000 Opt. Commun. 176 155
29. Ishkhanyan A M 1997 J. Phys. A: Math. Gen. 30 1203
30. Ishkhanyan A M and Suominen K-A 2001 J. Phys. A: Math. Gen. 34 6301
31. Ishkhanyan A, Mackie M, Carmichael A, Gould P L and Javanainen J 2004 Landau-Zener problem for trilinear systems Phys. Rev. A 69 043612
32. Ishkhanyan A M and Chernikov G P 2004 Weak interaction limit in the theory of photoassociation of cold atoms J. Contemp. Phys. (Armenian Academy of Science) 39 1
33. Nayfeh A H 1985 Perturbation Methods (New York: Wiley)
34. Kevorkian J and Cole J D 1985 Perturbation Methods in Applied Mathematics (Heidelberg: Springer)
35. Kevorkian J and Cole J D 1996 Multiple Scale and Singular Perturbation Metltods (New York: Springer)
36. Tricomi F G 1985 Integral Equations (New York: Dover)
37. Brunner H and van der Houwen P J 1986 The Numerical Solution of Volterra Equations (Amsterdam: North Holland)
38. Burton T A 1983 Volterra Integral and Differential Equations (New York: Academic)
39. Baker C T H 1978 The Numerical Treatment of Integral Equations (Oxford: Clarendon)
40. Miller R K 1971 Nonlinear Volterra Integral Equations (New York: Benjamin)
41. Ishkhanyan A, Mackie M, Gould Ph and Javanainen J 2003 Interactions in Ultracold Gases: From Atoms to Molecules ed M Weidemuller and C Zimmermann (Berlin: Wiley) p 470
42. Sommerfeld A 1896 Math. Ann. 47 317
43. Born M and Wolf E 1999 Principles of Optics (Cambridge: Cambridge University Press)
44. Demkov Yu N and Kunike M 1969 Vest. Leningr. Univ. Fiz. Khim 16 39
45. Suominen K-A and Garraway B M 1992 Phys. Rev. A 45 374
46. Vitanov N V and Garraway B M 1996 Phys. Rev. A 53 4288
47. Vitanov N V and Garraway B M 1996 Phys. Rev. A 54 5458(E)
48. Nakamura 2002 Nonadiabatic Transition: Concepts, Basic Theories and Applications (Singapore: World Scientific)
49. Teranishi Y and Nakamura H 1998 Phys. Rev. Lett. 81 2032
50. Zhu C, Teranishi Y and Nakamura H 2001 Adv. Chem. Phys. 117 127
51. Teranishi Y and Nakamura H 1997 J. Chem. Phys. 107 1904
52. Yurovsky V A, Ben-Reuven A, Julienne P S and Williams C J 1999 Phys. Rev. A 60 R765
53. Yurovsky V A, Ben-Reuven A, Julienne P S and Williams C J 2000 Phys. Rev. A 62 043605
54. Weidemuller M and Zimmermann C (ed) 2003 Interactions in Ultracold Gases: From Atoms to Molecules (Berlin: Wiley)