Multidimensional quantum solitons with nondegenerate parametric interactions: photonic and Bose-Einstein condensate environments

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 6, 2000, Pages 063816-063811

  Kheruntsyan, K V ^a   Drummond, P D ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; BINDING ENERGY; EIGENVALUES AND EIGENFUNCTIONS; FERMI LEVEL; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; NONLINEAR OPTICS; PHOTONS; SOLITONS;

BOSE-EINSTEIN CONDENSATE; FERMI GAS; MULTIDIMENSIONAL QUANTUM SOLITON; NONDEGENERATE PARAMETRIC INTERACTION;

QUANTUM THEORY;

EID: 0033715115     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (95)

1. N.H. Christ and T.D. Lee, Phys, Rev. D 12, 1606 (1975); T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood, Switzerland, 1988).
2. N.H. Christ and T.D. Lee, Phys, Rev. D 12, 1606 (1975); T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood, Switzerland, 1988).
3. E.H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963); I.B. McGuire, J. Math. Phys. 5, 622 (1964); C.N. Yang, Phys. Rev. 168, 1920 (1967); H.B. Thacker, Rev. Mod. Phys. 53, 253 (1981).
4. E.H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963); I.B. McGuire, J. Math. Phys. 5, 622 (1964); C.N. Yang, Phys. Rev. 168, 1920 (1967); H.B. Thacker, Rev. Mod. Phys. 53, 253 (1981).
5. E.H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963); I.B. McGuire, J. Math. Phys. 5, 622 (1964); C.N. Yang, Phys. Rev. 168, 1920 (1967); H.B. Thacker, Rev. Mod. Phys. 53, 253 (1981).
6. E.H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963); I.B. McGuire, J. Math. Phys. 5, 622 (1964); C.N. Yang, Phys. Rev. 168, 1920 (1967); H.B. Thacker, Rev. Mod. Phys. 53, 253 (1981).
7. S.J. Carter, P.D. Drummond, M.D. Reid, and R.M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P.D. Drummond and S.J. Carter, J. Opt. Soc. Am. B 4, 1565 (1987).
8. S.J. Carter, P.D. Drummond, M.D. Reid, and R.M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P.D. Drummond and S.J. Carter, J. Opt. Soc. Am. B 4, 1565 (1987).
9. Y. Lai and H.A. Haus, Phys. Rev. A 40, 844 (1989); H.A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990).
10. Y. Lai and H.A. Haus, Phys. Rev. A 40, 844 (1989); H.A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990).
11. M. Rosenbluh and R.M. Shelby, Phys. Rev. Lett. 66, 153 (1991); P.D. Drummond, R.M. Shelby, S.R. Friberg, and Y. Yamamoto, Nature (London) 365, 307 (1993).
12. M. Rosenbluh and R.M. Shelby, Phys. Rev. Lett. 66, 153 (1991); P.D. Drummond, R.M. Shelby, S.R. Friberg, and Y. Yamamoto, Nature (London) 365, 307 (1993).
13. C.L. Schultz, M.J. Ablowitz, and O. BarYaacov, Phys. Rev. Lett. 59, 2825 (1987); G.D. Pang, F.-C. Pu, and B.-H. Zhao, ibid. 65, 3227 (1990); G.D. Pang, Phys. Lett. A 184, 163 (1994).
14. C.L. Schultz, M.J. Ablowitz, and O. BarYaacov, Phys. Rev. Lett. 59, 2825 (1987); G.D. Pang, F.-C. Pu, and B.-H. Zhao, ibid. 65, 3227 (1990); G.D. Pang, Phys. Lett. A 184, 163 (1994).
15. C.L. Schultz, M.J. Ablowitz, and O. BarYaacov, Phys. Rev. Lett. 59, 2825 (1987); G.D. Pang, F.-C. Pu, and B.-H. Zhao, ibid. 65, 3227 (1990); G.D. Pang, Phys. Lett. A 184, 163 (1994).
16. R.B. Laughlin, Phys. Rev. Lett. 50, 1385 (1983).
17. D.C. Tsui, H.L. Störmer, and H.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).
18. N.K. Wilkin, J.M.F. Gunn, and R.A. Smith, Phys. Rev. Lett. 80, 2265 (1998).
19. M.H. Anderson, J.R. Ensher, C.E. Wieman and E.A. Cornell, Science 269, 198 (1995); C.C. Bradley, C.A. Sackett, J.J. Tollett, and R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995); K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, ibid. 75, 3969 (1995).
20. M.H. Anderson, J.R. Ensher, C.E. Wieman and E.A. Cornell, Science 269, 198 (1995); C.C. Bradley, C.A. Sackett, J.J. Tollett, and R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995); K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, ibid. 75, 3969 (1995).
21. M.H. Anderson, J.R. Ensher, C.E. Wieman and E.A. Cornell, Science 269, 198 (1995); C.C. Bradley, C.A. Sackett, J.J. Tollett, and R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995); K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, ibid. 75, 3969 (1995).
22. K.V. Kheruntsyan and P.D. Drummond, Phys. Rev. A 58, 2488 (1998).
23. R. Friedberg and T.D. Lee, Phys. Rev. B 40, 6745 (1989).
24. Y. Wang, Phys. Lett. A 176, 19 (1993).
25. P.D. Drummond and H. He, Phys. Rev. A 56, R1107 (1997).
26. A.A. Kanashov and A.M. Rubenchik, Physica D 4, 122 (1981).
27. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); L. Torner, C.R. Menyuk, W.E. Torruellas, and G.I. Stegeman, Opt. Lett. 20, 13 (1995); L. Bergé, V.K. Mezentsev, J.J. Rasmussen, and J. Wyller, Phys. Rev. A 52, R28 (1995); H. He, M.J. Werner, and P.D. Drummond, Phys. Rev. E 54, 896 (1996); A.V. Buryak and Yu. Kivshar, Phys. Rev. Lett. 77, 5210 (1996).
28. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); L. Torner, C.R. Menyuk, W.E. Torruellas, and G.I. Stegeman, Opt. Lett. 20, 13 (1995); L. Bergé, V.K. Mezentsev, J.J. Rasmussen, and J. Wyller, Phys. Rev. A 52, R28 (1995); H. He, M.J. Werner, and P.D. Drummond, Phys. Rev. E 54, 896 (1996); A.V. Buryak and Yu. Kivshar, Phys. Rev. Lett. 77, 5210 (1996).
29. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); L. Torner, C.R. Menyuk, W.E. Torruellas, and G.I. Stegeman, Opt. Lett. 20, 13 (1995); L. Bergé, V.K. Mezentsev, J.J. Rasmussen, and J. Wyller, Phys. Rev. A 52, R28 (1995); H. He, M.J. Werner, and P.D. Drummond, Phys. Rev. E 54, 896 (1996); A.V. Buryak and Yu. Kivshar, Phys. Rev. Lett. 77, 5210 (1996).
30. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); L. Torner, C.R. Menyuk, W.E. Torruellas, and G.I. Stegeman, Opt. Lett. 20, 13 (1995); L. Bergé, V.K. Mezentsev, J.J. Rasmussen, and J. Wyller, Phys. Rev. A 52, R28 (1995); H. He, M.J. Werner, and P.D. Drummond, Phys. Rev. E 54, 896 (1996); A.V. Buryak and Yu. Kivshar, Phys. Rev. Lett. 77, 5210 (1996).
31. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); L. Torner, C.R. Menyuk, W.E. Torruellas, and G.I. Stegeman, Opt. Lett. 20, 13 (1995); L. Bergé, V.K. Mezentsev, J.J. Rasmussen, and J. Wyller, Phys. Rev. A 52, R28 (1995); H. He, M.J. Werner, and P.D. Drummond, Phys. Rev. E 54, 896 (1996); A.V. Buryak and Yu. Kivshar, Phys. Rev. Lett. 77, 5210 (1996).
32. B.A. Malomed, P.D. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).
33. W.E. Torruellas, Z. Wang, D.J. Hagan, E.W. Van Stryland, G.I. Stegeman, L. Torner, and C.R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schick, Y. Baek, and G.I. Stegeman, Phys. Rev. E 53, 1138 (1996).
34. W.E. Torruellas, Z. Wang, D.J. Hagan, E.W. Van Stryland, G.I. Stegeman, L. Torner, and C.R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schick, Y. Baek, and G.I. Stegeman, Phys. Rev. E 53, 1138 (1996).
35. K.V. Kheruntsyan and P.D. Drummond, Phys. Rev. A 58, R2676 (1998).
36. P.D. Drummond, K.V. Kheruntsyan, and H. He, J. Opt. B: Quantum Semiclass Opt. 1, 387 (1999).
37. I.H. Deutsch and R.Y. Chiao, Phys. Rev. Lett. 69, 3627 (1992); Z. Cheng and G. Kurizki, ibid. 75, 3430 (1995); I.H. Deutsch, R.Y. Chiao, and J.C. Garrison, Phys. Rev. A 47, 3330 (1993); A.G. Shnirman, B.A. Malomed, and E. Ben-Jacob, ibid. 50, 3453 (1994).
38. I.H. Deutsch and R.Y. Chiao, Phys. Rev. Lett. 69, 3627 (1992); Z. Cheng and G. Kurizki, ibid. 75, 3430 (1995); I.H. Deutsch, R.Y. Chiao, and J.C. Garrison, Phys. Rev. A 47, 3330 (1993); A.G. Shnirman, B.A. Malomed, and E. Ben-Jacob, ibid. 50, 3453 (1994).
39. I.H. Deutsch and R.Y. Chiao, Phys. Rev. Lett. 69, 3627 (1992); Z. Cheng and G. Kurizki, ibid. 75, 3430 (1995); I.H. Deutsch, R.Y. Chiao, and J.C. Garrison, Phys. Rev. A 47, 3330 (1993); A.G. Shnirman, B.A. Malomed, and E. Ben-Jacob, ibid. 50, 3453 (1994).
40. I.H. Deutsch and R.Y. Chiao, Phys. Rev. Lett. 69, 3627 (1992); Z. Cheng and G. Kurizki, ibid. 75, 3430 (1995); I.H. Deutsch, R.Y. Chiao, and J.C. Garrison, Phys. Rev. A 47, 3330 (1993); A.G. Shnirman, B.A. Malomed, and E. Ben-Jacob, ibid. 50, 3453 (1994).
41. D.J. Heinzen, R.H. Wynar, P.D. Drummond, and K.V. Kheruntsyan, Phys. Rev. Lett. (to be published); see also D.J. Heinzen, P.D. Drummond, and K.V. Kheruntsyan, Bull. Am. Phys. Soc. 44(1), 1007 (1999).
42. D.J. Heinzen, R.H. Wynar, P.D. Drummond, and K.V. Kheruntsyan, Phys. Rev. Lett. (to be published); see also D.J. Heinzen, P.D. Drummond, and K.V. Kheruntsyan, Bull. Am. Phys. Soc. 44(1), 1007 (1999).
43. P.D. Drummond, K.V. Kheruntsyan, and H. He, Phys. Rev. Lett. 81, 3055 (1998).
44. C.J. Myatt et al., Phys. Rev. Lett. 78, 586 (1997); H. Pu and N.P. Bigelow, ibid. 80, 1130 (1998); C.K. Law et al., ibid. 79, 3105 (1997); B.D. Esry et al., ibid. 78, 3594 (1997) P. Öhberg, Phys. Rev. A 59, 634 (1999).
45. C.J. Myatt et al., Phys. Rev. Lett. 78, 586 (1997); H. Pu and N.P. Bigelow, ibid. 80, 1130 (1998); C.K. Law et al., ibid. 79, 3105 (1997); B.D. Esry et al., ibid. 78, 3594 (1997) P. Öhberg, Phys. Rev. A 59, 634 (1999).
46. C.J. Myatt et al., Phys. Rev. Lett. 78, 586 (1997); H. Pu and N.P. Bigelow, ibid. 80, 1130 (1998); C.K. Law et al., ibid. 79, 3105 (1997); B.D. Esry et al., ibid. 78, 3594 (1997) P. Öhberg, Phys. Rev. A 59, 634 (1999).
47. C.J. Myatt et al., Phys. Rev. Lett. 78, 586 (1997); H. Pu and N.P. Bigelow, ibid. 80, 1130 (1998); C.K. Law et al., ibid. 79, 3105 (1997); B.D. Esry et al., ibid. 78, 3594 (1997) P. Öhberg, Phys. Rev. A 59, 634 (1999).
48. C.J. Myatt et al., Phys. Rev. Lett. 78, 586 (1997); H. Pu and N.P. Bigelow, ibid. 80, 1130 (1998); C.K. Law et al., ibid. 79, 3105 (1997); B.D. Esry et al., ibid. 78, 3594 (1997) P. Öhberg, Phys. Rev. A 59, 634 (1999).
49. A.V. Buryak, Yu.S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); M.A. Karpierz, ibid. 20, 1677 (1995); S. Trillo, A.V. Buryak, and Yu.S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997); L. Bergé, O. Bang, J.J. Rassmussen, and V.K. Mezentsev, Phys. Rev. E 55, 3555 (1997); O. Bang, Yu.S. Kivshar, A.V. Buryak, A. De Rossi, and S. Trillo, ibid. 58, 5057 (1998).
50. A.V. Buryak, Yu.S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); M.A. Karpierz, ibid. 20, 1677 (1995); S. Trillo, A.V. Buryak, and Yu.S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997); L. Bergé, O. Bang, J.J. Rassmussen, and V.K. Mezentsev, Phys. Rev. E 55, 3555 (1997); O. Bang, Yu.S. Kivshar, A.V. Buryak, A. De Rossi, and S. Trillo, ibid. 58, 5057 (1998).
51. A.V. Buryak, Yu.S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); M.A. Karpierz, ibid. 20, 1677 (1995); S. Trillo, A.V. Buryak, and Yu.S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997); L. Bergé, O. Bang, J.J. Rassmussen, and V.K. Mezentsev, Phys. Rev. E 55, 3555 (1997); O. Bang, Yu.S. Kivshar, A.V. Buryak, A. De Rossi, and S. Trillo, ibid. 58, 5057 (1998).
52. A.V. Buryak, Yu.S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); M.A. Karpierz, ibid. 20, 1677 (1995); S. Trillo, A.V. Buryak, and Yu.S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997); L. Bergé, O. Bang, J.J. Rassmussen, and V.K. Mezentsev, Phys. Rev. E 55, 3555 (1997); O. Bang, Yu.S. Kivshar, A.V. Buryak, A. De Rossi, and S. Trillo, ibid. 58, 5057 (1998).
53. A.V. Buryak, Yu.S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); M.A. Karpierz, ibid. 20, 1677 (1995); S. Trillo, A.V. Buryak, and Yu.S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997); L. Bergé, O. Bang, J.J. Rassmussen, and V.K. Mezentsev, Phys. Rev. E 55, 3555 (1997); O. Bang, Yu.S. Kivshar, A.V. Buryak, A. De Rossi, and S. Trillo, ibid. 58, 5057 (1998).
54. A.V. Buryak, Yu.S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995); M.A. Karpierz, ibid. 20, 1677 (1995); S. Trillo, A.V. Buryak, and Yu.S. Kivshar, Opt. Commun. 122, 200 (1996); O. Bang, J. Opt. Soc. Am. B 14, 51 (1997); L. Bergé, O. Bang, J.J. Rassmussen, and V.K. Mezentsev, Phys. Rev. E 55, 3555 (1997); O. Bang, Yu.S. Kivshar, A.V. Buryak, A. De Rossi, and S. Trillo, ibid. 58, 5057 (1998).
55. T.D. Lee, Phys. Rev. 54, 1329 (1954); L. Van Hove, Physica (Amsterdam) 21, 901 (1955); see also S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson, New York, 1961).
56. T.D. Lee, Phys. Rev. 54, 1329 (1954); L. Van Hove, Physica (Amsterdam) 21, 901 (1955); see also S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson, New York, 1961).
57. T.D. Lee, Phys. Rev. 54, 1329 (1954); L. Van Hove, Physica (Amsterdam) 21, 901 (1955); see also S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson, New York, 1961).
58. K. Huang, Statistical Mechanics (Wiley, New York, 1963).
59. K. Huang and C.N. Yang, Phys. Rev. 105, 767 (1957); T.D. Lee, K. Huang, and C.N. Yang, ibid. 106, 1135 (1957).
60. K. Huang and C.N. Yang, Phys. Rev. 105, 767 (1957); T.D. Lee, K. Huang, and C.N. Yang, ibid. 106, 1135 (1957).
61. C.M. Caves and D.D. Crouch, J. Opt. Soc. Am. B 4, 1535 (1987); M.G. Raymer, P.D. Drummond, and S.J. Carter, Opt. Lett. 16, 1189 (1991); M. Hillery and L.D. Mlodinov, Phys. Rev. A 30, 1860 (1984); P.D. Drummond, ibid. 42, 6845 (1990).
62. C.M. Caves and D.D. Crouch, J. Opt. Soc. Am. B 4, 1535 (1987); M.G. Raymer, P.D. Drummond, and S.J. Carter, Opt. Lett. 16, 1189 (1991); M. Hillery and L.D. Mlodinov, Phys. Rev. A 30, 1860 (1984); P.D. Drummond, ibid. 42, 6845 (1990).
63. C.M. Caves and D.D. Crouch, J. Opt. Soc. Am. B 4, 1535 (1987); M.G. Raymer, P.D. Drummond, and S.J. Carter, Opt. Lett. 16, 1189 (1991); M. Hillery and L.D. Mlodinov, Phys. Rev. A 30, 1860 (1984); P.D. Drummond, ibid. 42, 6845 (1990).
64. C.M. Caves and D.D. Crouch, J. Opt. Soc. Am. B 4, 1535 (1987); M.G. Raymer, P.D. Drummond, and S.J. Carter, Opt. Lett. 16, 1189 (1991); M. Hillery and L.D. Mlodinov, Phys. Rev. A 30, 1860 (1984); P.D. Drummond, ibid. 42, 6845 (1990).
65. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963); N.N. Bogolyubov, J. Phys. (USSR) 11, 23 (1947); K.A. Brueckner and K. Sawada, Phys. Rev. 106, 1117 (1957); K. Huang, C.N. Yang, and J.M. Luttinger, ibid. 105, 776 (1957); N.P. Proukakis, K. Burnett, and H.T.C. Stoof, Phys. Rev. A 57, 1230 (1998).
66. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963); N.N. Bogolyubov, J. Phys. (USSR) 11, 23 (1947); K.A. Brueckner and K. Sawada, Phys. Rev. 106, 1117 (1957); K. Huang, C.N. Yang, and J.M. Luttinger, ibid. 105, 776 (1957); N.P. Proukakis, K. Burnett, and H.T.C. Stoof, Phys. Rev. A 57, 1230 (1998).
67. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963); N.N. Bogolyubov, J. Phys. (USSR) 11, 23 (1947); K.A. Brueckner and K. Sawada, Phys. Rev. 106, 1117 (1957); K. Huang, C.N. Yang, and J.M. Luttinger, ibid. 105, 776 (1957); N.P. Proukakis, K. Burnett, and H.T.C. Stoof, Phys. Rev. A 57, 1230 (1998).
68. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963); N.N. Bogolyubov, J. Phys. (USSR) 11, 23 (1947); K.A. Brueckner and K. Sawada, Phys. Rev. 106, 1117 (1957); K. Huang, C.N. Yang, and J.M. Luttinger, ibid. 105, 776 (1957); N.P. Proukakis, K. Burnett, and H.T.C. Stoof, Phys. Rev. A 57, 1230 (1998).
69. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963); N.N. Bogolyubov, J. Phys. (USSR) 11, 23 (1947); K.A. Brueckner and K. Sawada, Phys. Rev. 106, 1117 (1957); K. Huang, C.N. Yang, and J.M. Luttinger, ibid. 105, 776 (1957); N.P. Proukakis, K. Burnett, and H.T.C. Stoof, Phys. Rev. A 57, 1230 (1998).
70. J.M. Vogels et al., Phys. Rev. A 56, R1067 (1997); P.S. Julienne et al., ibid. 58, R797 (1998); Y.B. Band and P.S. Julienne, Phys. Rev. A 51, R4317 (1995); A. Vardi et al., J. Chem. Phys. 107, 6166 (1997); R. Côté and A. Dalgarno, Chem. Phys. Lett. 279, 50 (1997).
71. J.M. Vogels et al., Phys. Rev. A 56, R1067 (1997); P.S. Julienne et al., ibid. 58, R797 (1998); Y.B. Band and P.S. Julienne, Phys. Rev. A 51, R4317 (1995); A. Vardi et al., J. Chem. Phys. 107, 6166 (1997); R. Côté and A. Dalgarno, Chem. Phys. Lett. 279, 50 (1997).
72. J.M. Vogels et al., Phys. Rev. A 56, R1067 (1997); P.S. Julienne et al., ibid. 58, R797 (1998); Y.B. Band and P.S. Julienne, Phys. Rev. A 51, R4317 (1995); A. Vardi et al., J. Chem. Phys. 107, 6166 (1997); R. Côté and A. Dalgarno, Chem. Phys. Lett. 279, 50 (1997).
73. J.M. Vogels et al., Phys. Rev. A 56, R1067 (1997); P.S. Julienne et al., ibid. 58, R797 (1998); Y.B. Band and P.S. Julienne, Phys. Rev. A 51, R4317 (1995); A. Vardi et al., J. Chem. Phys. 107, 6166 (1997); R. Côté and A. Dalgarno, Chem. Phys. Lett. 279, 50 (1997).
74. J.M. Vogels et al., Phys. Rev. A 56, R1067 (1997); P.S. Julienne et al., ibid. 58, R797 (1998); Y.B. Band and P.S. Julienne, Phys. Rev. A 51, R4317 (1995); A. Vardi et al., J. Chem. Phys. 107, 6166 (1997); R. Côté and A. Dalgarno, Chem. Phys. Lett. 279, 50 (1997).
75. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965); P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, Cambridge, 1990).
76. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965); P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, Cambridge, 1990).
77. Z. Chen et al., Appl. Phys. Lett. 61, 2401 (1992); H. Xie, W.I. Wang, J.R. Meyer, and L.R. Ram-Mohan, ibid. 65, 2048 (1994); M. Seto, et al., ibid. 65, 2969 (1994).
78. Z. Chen et al., Appl. Phys. Lett. 61, 2401 (1992); H. Xie, W.I. Wang, J.R. Meyer, and L.R. Ram-Mohan, ibid. 65, 2048 (1994); M. Seto, et al., ibid. 65, 2969 (1994).
79. Z. Chen et al., Appl. Phys. Lett. 61, 2401 (1992); H. Xie, W.I. Wang, J.R. Meyer, and L.R. Ram-Mohan, ibid. 65, 2048 (1994); M. Seto, et al., ibid. 65, 2969 (1994).
80. M.S. Wong, F. Pan, M. Bösch, R. Spreiter, C. Bosshard, P. Günter, and V. Gramlich, J. Opt. Soc. Am. B 15, 426 (1998); R. Spreiter, Ch. Bosshard, G. Knöpfle, P. Günter, R.R. Tykwinski, M. Schreiber, and F. Diederich, J. Phys. Chem. B 102, 29 (1998).
81. M.S. Wong, F. Pan, M. Bösch, R. Spreiter, C. Bosshard, P. Günter, and V. Gramlich, J. Opt. Soc. Am. B 15, 426 (1998); R. Spreiter, Ch. Bosshard, G. Knöpfle, P. Günter, R.R. Tykwinski, M. Schreiber, and F. Diederich, J. Phys. Chem. B 102, 29 (1998).
82. P. Tommasini, E. Timmermans, M. Hussein, and A. Kerman, cond-mat/9804015.
83. J. Javanainen and M. Mackie, Phys. Rev. A 59, R3186 (1999).
84. S. Inouye et al., Nature (London) 392, 151 (1998); Ph. Courteille, R.S. Freeland, and D.J. Heinzen, Phys. Rev. Lett. 81, 69 (1998).
85. S. Inouye et al., Nature (London) 392, 151 (1998); Ph. Courteille, R.S. Freeland, and D.J. Heinzen, Phys. Rev. Lett. 81, 69 (1998).
86. J. Stenger, S. Inouye, M.R. Andrews, H.-J. Miesner, D.M. Stamper-Kurn, and W. Ketterle, Phys. Rev. Lett. 82, 2422 (1999).
87. D. J. Heinzen (private communication); R.S. Freeland, R.H. Wynar, D.J. Han, and D.J. Heinzen, Bull. Am. Phys. Soc. 44(1), 1007 (1999).
88. D. J. Heinzen (private communication); R.S. Freeland, R.H. Wynar, D.J. Han, and D.J. Heinzen, Bull. Am. Phys. Soc. 44(1), 1007 (1999).
89. X. Liu, L.J. Qian, and F.W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
90. E. Timmermans, P. Tommasini, R Côte, M. Hussein, and A. Kerman, e-print cond-mat/9805323; A.N. Salguero, M.C. Nemes, M.D. Sampaio, and A.F.R. de Toledo Piza, e-print quant-ph/9809003.
91. E. Timmermans, P. Tommasini, R Côte, M. Hussein, and A. Kerman, e-print cond-mat/9805323; A.N. Salguero, M.C. Nemes, M.D. Sampaio, and A.F.R. de Toledo Piza, e-print quant-ph/9809003.
92. S.A. Morgan, R.J. Ballagh, and K. Burnett, Phys. Rev. A 55, 4338 (1997); W.P. Reinhard and C.W. Clark, J. Phys. B 30, L785 (1997); T.F. Scott, R.J. Ballagh, and K. Burnett, ibid. 31, L329 (1998); O. Zobay, S. Pötting, P. Meystre, and E.M. Wright, Phys. Rev. A 59, 643 (1999).
93. S.A. Morgan, R.J. Ballagh, and K. Burnett, Phys. Rev. A 55, 4338 (1997); W.P. Reinhard and C.W. Clark, J. Phys. B 30, L785 (1997); T.F. Scott, R.J. Ballagh, and K. Burnett, ibid. 31, L329 (1998); O. Zobay, S. Pötting, P. Meystre, and E.M. Wright, Phys. Rev. A 59, 643 (1999).
94. S.A. Morgan, R.J. Ballagh, and K. Burnett, Phys. Rev. A 55, 4338 (1997); W.P. Reinhard and C.W. Clark, J. Phys. B 30, L785 (1997); T.F. Scott, R.J. Ballagh, and K. Burnett, ibid. 31, L329 (1998); O. Zobay, S. Pötting, P. Meystre, and E.M. Wright, Phys. Rev. A 59, 643 (1999).
95. S.A. Morgan, R.J. Ballagh, and K. Burnett, Phys. Rev. A 55, 4338 (1997); W.P. Reinhard and C.W. Clark, J. Phys. B 30, L785 (1997); T.F. Scott, R.J. Ballagh, and K. Burnett, ibid. 31, L329 (1998); O. Zobay, S. Pötting, P. Meystre, and E.M. Wright, Phys. Rev. A 59, 643 (1999).