Feshbach resonances with large background scattering length: Interplay with open-channel resonances

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 1, 2004, Pages

  Marcelis, B ^a   Van Kempen, E G M ^a   Verhaar, B J ^a   Kokkelmans, S J J M F ^a,b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALKALI METALS; BINDING ENERGY; BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC WAVE SCATTERING; ENERGY ABSORPTION; MOLECULAR STRUCTURE;

ATOMIC COLLISIONS; INTERATOMIC POTENTIAL; OPEN-CHANNEL RESONANCE; WAVE FUNCTION;

RESONANCE;

EID: 19244365258     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.012701     Document Type: Article

References (73)

1. H. Feshbach, Ann. Phys. (N.Y.) 5, 357 (1958); 19, 287 (1962).
2. H. Feshbach, Ann. Phys. (N.Y.) 5, 357 (1958); 19, 287 (1962).
3. E. Tiesinga, A. J. Moerdijk, B. J. Verhaar, and H. T. C. Stoof, Phys. Rev. A 46, R1167 (1992); E. Tiesinga, B. J. Verhaar, and H. T. C. Stoof, ibid. 47, 4114 (1993).
4. E. Tiesinga, A. J. Moerdijk, B. J. Verhaar, and H. T. C. Stoof, Phys. Rev. A 46, R1167 (1992); E. Tiesinga, B. J. Verhaar, and H. T. C. Stoof, ibid. 47, 4114 (1993).
5. H. Heiselberg, Phys. Rev. A 63, 043606 (2001).
6. J. Carlson, S.-Y. Chang, V. R. Pandharipande, and K. E. Schmidt, Phys. Rev. Lett. 91, 050401 (2003).
7. T. L. Ho and E. J. Mueller, Phys. Rev. Lett. 92, 160404 (2004); T. L. Ho, Phys. Rev. Lett. 92, 090402 (2004).
8. T. L. Ho and E. J. Mueller, Phys. Rev. Lett. 92, 160404 (2004); T. L. Ho, Phys. Rev. Lett. 92, 090402 (2004).
9. S. J. J. M. F. Kokkelmans, G. V. Shlyapnikov, and C. Salomon, Phys. Rev. A 69, 031602 (2004).
10. Y. Ohashi and A. Griffin, Phys. Rev. Lett. 89, 130402 (2002).
11. J. N. Milstein, S. J. J. M. F. Kokkelmans, and M. J. Holland, Phys. Rev. A 66, 043604 (2002).
12. C. A. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett. 92, 040403 (2004).
13. J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, Nature (London) 396, 345 (1998).
14. F. A. van Abeelen and B. J. Verhaar, Phys. Rev. Lett. 83, 1550 (1999).
15. F. H. Mies, E. Tiesinga, and P. S. Julienne, Phys. Rev. A 61, 022721 (2000).
16. E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, Nature (London) 417, 529 (2002).
17. N. R. Claussen, S. J. J. M. F. Kokkelmans, S. T. Thompson, E. A. Donley, E. Hodby, and C. E. Wieman, Phys. Rev. A 67, 060701(R) (2003).
18. K. E. Strecker, G. B. Partridge, and R. G. Hulet, Phys. Rev. Lett. 91, 080406 (2003).
19. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, C. Chin, J. H. Denschlag, and R. Grimm, Phys. Rev. Lett. 91, 240402 (2003).
20. J. Cubizolles, T. Bourdel, S. J. J. M. F. Kokkelmans, G. V. Shlyapnikov, and C. Salomon, Phys. Rev. Lett. 91, 240401 (2003).
21. C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, Nature (London) 424, 47 (2003).
22. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, Science 302, 2101 (2003).
23. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. 91, 250401 (2003).
24. M. Greiner, C. A. Regal, and D. S. Jin, Nature (London) 426, 537 (2003).
25. K. Xu, T. Mukaiyama, J. R. Abo-Shaeer, J. K. Chin, D. E. Miller, and W. Ketterle, Phys. Rev. Lett. 91, 210402 (2003).
26. C. Chin, A. J. Kerman, V. Vuletić, and S. Chu, Phys. Rev. Lett. 90, 033201 (2003); J. Herbig, T. Kraemer, M. Mark, T. Weber, C. Chin, H.-C. NÄgerl, and R. Grimm, Science 301, 1510 (2003).
27. C. Chin, A. J. Kerman, V. Vuletić, and S. Chu, Phys. Rev. Lett. 90, 033201 (2003); J. Herbig, T. Kraemer, M. Mark, T. Weber, C. Chin, H.-C. NÄgerl, and R. Grimm, Science 301, 1510 (2003).
28. S. Dürr, T. Volz, A. Marte, and G. Rempe, Phys. Rev. Lett. 92, 020406 (2004).
29. G. F. Gribakin and V. V. Flambaum, Phys. Rev. A 48, 546 (1993).
30. Coupled-channel calculations: E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, Phys. Rev. Lett. 88, 093201 (2002). The binding energy data of Ref. [14] were used to optimize the potential parameters.
31. P. J. Leo, C. J. Williams, and P. S. Julienne, Phys. Rev. Lett. 85, 2721 (2000).
32. P. S. Julienne, E. Tiesinga, and T. Köhler, e-print cond-mat/0312492.
33. F. A. van Abeelen, B. J. Verhaar, and A. J. Moerdijk, Phys. Rev. A 55, 4377 (1997).
34. E. R. I. Abraham, W. I. McAlexander, J. M. Gerton, R. G. Hulet, R. Côté, and A. Dalgarno, Phys. Rev. A 55, R3299 (1997).
35. W. L. Wang and C. M. Shakin, Phys. Lett. 32B, 421 (1970); M. Micklinghoff, Nucl. Phys. A 295, 228 (1978); V. I. Kukulin and V. N. Pomerantsev, Ann. Phys. (N.Y.) 111, 330 (1978).
36. W. L. Wang and C. M. Shakin, Phys. Lett. 32B, 421 (1970); M. Micklinghoff, Nucl. Phys. A 295, 228 (1978); V. I. Kukulin and V. N. Pomerantsev, Ann. Phys. (N.Y.) 111, 330 (1978).
37. W. L. Wang and C. M. Shakin, Phys. Lett. 32B, 421 (1970); M. Micklinghoff, Nucl. Phys. A 295, 228 (1978); V. I. Kukulin and V. N. Pomerantsev, Ann. Phys. (N.Y.) 111, 330 (1978).
38. L. Rosenberg, Phys. Rev. A 30, 245 (1984).
39. W. Domcke, Phys. Rev. A 28, 2777 (1983).
40. A. J. Moerdijk, B. J. Verhaar, and A. Axelsson, Phys. Rev. A 51, 4852 (1995).
41. J. R. Taylor, Scattering Theory (Wiley, New York, 1972).
42. Note that virtual-state poles can collide on the negative imaginary k axis and move into the third and fourth quadrants of the complex k plane; see, e.g., [37]. However, these poles are located sufficiently far from the real k axis, such that they can be included in the background part of the scattering matrix.
43. H. M. Nussenzveig, Nucl. Phys. 11, 499 (1959).
44. H. Feshbach, Theoretical Nuclear Physics (Wiley, New York, 1992).
45. Note that similar behavior was found in the case of dipolemodified s-wave scattering of low-energy electrons from weakly dipolar molecules [40]. However, the physical mechanism responsible for this behavior is different, and the open channel studied in this reference does not contain a potential resonance. Moreover, in contrast to our approach, the work in this reference is based on a phenomenological parametrization of the decay width Γ(E).
46. W. Domcke, J. Phys. B 14, 4889 (1981).
47. C. J. Joachain, Quantum Collision Theory (North-Holland, New York, 1972).
48. n and without a cutoff, the Jost function has a branch point at the origin; see, e.g., [40,43], Within the finite-range approximation the Jost function is an entire function of k.
49. A. Herzenberg, J. Phys. B 17, 4213 (1984).
50. R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, Berlin, 1982).
51. F. W. Byron and R. W. Fuller, Mathematics of Classical and Quantum Physics (Dover, New York, 1992).
52. P 1 is not satisfied. This is related to the fact that the background part summarizes the effect of all distant poles and consists of a sum over these pole contributions. All these contributions are linear in k in the energy domain under consideration and so is their sum.
53. Note that the energy E can be any (complex) energy in this case, and it is not necessary to include the extra term iδ approaching zero. This small imaginary term only has to be included when calculating the physical scattering states, defined for real and positive energies E (see, for instance, Ref. [44]).
54. G. Gamow, Z. Phys. 51, 204 (1928).
55. W. J. Romo, Nucl. Phys. A 116, 618 (1968).
56. V. I. Kukulin, V. M. Krasnopol'sky, and J. Horáček, Theory of Resonances (Kluwer Academic, Dordrecht, 1989).
57. G. García-Calderón and R. Peierls, Nucl. Phys. A 265, 443 (1976).
58. W. J. Romo, Nucl. Phys. A 302, 61 (1978).
59. J. Bang, S. N. Ershov, F. A. Gareev, and G. S. Kazacha, Nucl. Phys. A 339, 89 (1980).
60. H. T. C. Stoof, J. M. V. A. Koelman, and B. J. Verhaar, Phys. Rev. B 38, 4688 (1988).
61. S. J. J. M. F. Kokkelmans, J. N. Milstein, M. L. Chiofalo, R. Walser, and M. J. Holland, Phys. Rev. A 65, 053617 (2002).
62. E. Timmermans, P. Tommasini, R. Côté, M. Hussein, and A. Kerman, Phys. Rev. Lett. 83, 2691 (1999).
63. J. W. Dunn, C. H. Greene, D. Blume, B. E. Granger, and M. J. Holland, e-print physics/0208031.
64. F. G. Fumi, Philos. Mag. 46, 1007 (1955).
65. L. Pricoupenko and Y. Castin, Phys. Rev. A 69, 051601 (2004).
66. S. J. J. M. F. Kokkelmans and M. J. Holland, Phys. Rev. Lett. 89, 180401 (2002).
67. M. Mackie, K.-A. Suominen, and J. Javanainen, Phys. Rev. Lett. 89, 180403 (2002).
68. T. Köhler, T. Gasenzer, and K. Burnett, Phys. Rev. A 67, 013601 (2003).
69. R. Combescot, Phys. Rev. Lett. 91, 120401 (2003); R. Combescot, New J. Phys. 5, 86 (2003).
70. R. Combescot, Phys. Rev. Lett. 91, 120401 (2003); R. Combescot, New J. Phys. 5, 86 (2003).
71. V. A. Yurovsky and A. Ben-Reuven, Phys. Rev. A 67, 043611 (2003).
72. R. A. Duine and H. T. C. Stoof, Phys. Rev. Lett. 91, 150405 (2003); Phys. Rep. 396, 115 (2004).
73. R. A. Duine and H. T. C. Stoof, Phys. Rev. Lett. 91, 150405 (2003); Phys. Rep. 396, 115 (2004).