Extension of Bogoliubov theory to quasicondensates

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 5, 2003, Pages 24-

  Mora, Christophe ^a   Castin, Yvan ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84876496666     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.67.053615     Document Type: Article

References (40)

1. A. Görlitz, J. M. Vogels, A. E. Leanhardt, C. Raman, T. L. Gustavson, J. R. Abo-Shaeer, A. P. Chikkatur, S. Gupta, S. Inouye, T. P. Rosenband, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 87, 130402 (2001).
2. F. Schreck, L. Khaykovich, K. L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles, and C. Salomon, Phys. Rev. Lett. 87, 080403 (2001).
3. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 22, 1133 (1966).
4. P. C. Hohenberg, Phys. Rev. 158, 383 (1967).
5. Y. Castin, R. Dum, E. Mandonnet, A. Minguzzi, and I. Carusotto, J. Mod. Opt. 47, 2671 (2000).
6. I. Carusotto and Y. Castin, J. Phys. B 34, 4589 (2001).
7. V. N. Popov, Theor. Math. Phys. 11, 565 (1972);Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983), Chap. 6.
8. D. S. Petrov, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 85, 3745 (2000).
9. D. S. Petrov, M. Holzmann, and G. V. Shlyapnikov, Phys. Rev. Lett. 84, 2551 (2000).
10. T.-L. Ho and M. Ma, J. Low Temp. Phys. 115, 61 (1999).
11. S. Dettmer, D. Hellweg, P. Ryytty, J. J. Arlt, W. Ertmer, K. Sengstock, D. S. Petrov, and G. V. Shlyapnikov, Phys. Rev. Lett. 87, 160406 (2001).
12. F. Gerbier, S. Richard, J. H. Thywissen, M. Hugbart, P. Bouyer, and A. Aspect, e-print cond-mat/0210206.
13. N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947).
14. C. Gardiner, Phys. Rev. A 56, 1414 (1997).
15. Y. Castin and R. Dum, Phys. Rev. A 57, 3008 (1998).
16. S. I. Shevchenko, Sov. J. Low Temp. Phys. 18, 223 (1992).
17. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1995), Chap. 28.
18. M. Girardeau and R. Arnowitt, Phys. Rev. 113, 755 (1959).
19. M. Schwartz, Phys. Rev. A 10, 1858 (1974).
20. J. O. Andersen, U. Al Khawaja, and H. T. C. Stoof, Phys. Rev. Lett. 88, 070407 (2002).
21. U. Al Khawaja, J. O. Andersen, N. P. Proukakis, and H. T. C. Stoof, Phys. Rev. A 66, 013615 (2002).
22. U. Al Khawaja, J. O. Andersen, N. P. Proukakis, and H. T. C. Stoof, Phys. Rev. A 66, 059902 (2002).
23. W.-C. Wu and A. Griffin, Phys. Rev. A 54, 4204 (1996).
24. This can be seen by taking the derivative of Eq. (11) with respect to (Formula presented)
25. We note that the same problem of course arises in the continuous version of the theory; in the above reasoning one has to replace (Formula presented) by the integral of (Formula presented) over a finite volume around the point (Formula presented)
26. A. Sinatra, C. Lobo, and Y. Castin, J. Phys. B 35, 3599 (2002).
27. M. Lewenstein and Li You, Phys. Rev. Lett. 77, 3489 (1996).
28. E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).
29. M. Gaudin, La Fonction d’Onde de Bethe (Masson, Paris, 1983).
30. V. Liu, Phys. Rev. Lett. 79, 4056 (1997).
31. L. P. Pitaevskii and S. Stringari, Phys. Lett. A 235, 398 (1997).
32. P. O. Fedichev and G. V. Shlyapnikov, Phys. Rev. A 58, 3146 (1998).
33. T. D. Lee and C. N. Yang, Phys. Rev. 105, 1119 (1957).
34. M. Schick, Phys. Rev. A 3, 1067 (1971).
35. D. M. Gangardt and G. V. Shlyapnikov, Phys. Rev. Lett. 90, 010401 (2003).
36. We have used the identity (Formula presented) where the cosine-integral function (Formula presented) tends to zero in the limit (Formula presented)
37. V. N. Popov, JETP Lett. 31, 526 (1980).
38. The trick is to use the rewriting (Formula presented) where (Formula presented) and (Formula presented) It is then clear that (Formula presented) can be extended to the domain (Formula presented) to form an even (Formula presented) function of k since one can extend (Formula presented) as an odd (Formula presented) function of k.
39. M. Schwartz, Phys. Rev. B 15, 1399 (1977).
40. M. Olshanii and V. Dunjko, e-print cond-mat/0210629.