Condensation of N bosons. III. Analytical results for all higher moments of condensate fluctuations in interacting and ideal dilute Bose gases via the canonical ensemble quasiparticle formulation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 5, 2000, Pages 536061-5360617

  Kocharovsky, V V ^a,b   Kocharovsky, Vl V ^b   Scully, Marlan O ^a,c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b INSTITUTE OF APPLIED PHYSICS   (Russian Federation)

^c MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347741586     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (69)

1. M. O. Scully, Phys. Rev. Lett. 82, 3927 (1999); henceforth referred to as CNB I.
2. V. V. Kocharovsky, M. O. Scully, S.-Y. Zhu, and S. Zubairy, Phys. Rev. A 61, 23609 (2000); henceforth referred to as CNB II.
3. M. Sargent, III, M. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, MA, 1974).
4. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).
5. The only exception known to the authors is the paper by M. Holthaus, E. Kalinowski, and K. Kirsten, Ann. Phys. (N.Y.) 270, 198 (1998), where the third moment of the ground-state occupation for ideal gas in a harmonic trap was discussed in Maxwell's demon ensemble approximation. Higher moments were also discussed on the basis of the master equation approach by M. O. Scully et al. in Refs. [1,2].
6. The only exception known to the authors is the paper by M. Holthaus, E. Kalinowski, and K. Kirsten, Ann. Phys. (N.Y.) 270, 198 (1998), where the third moment of the ground-state occupation for ideal gas in a harmonic trap was discussed in Maxwell's demon ensemble approximation. Higher moments were also discussed on the basis of the master equation approach by M. O. Scully et al. in Refs. [1,2].
7. M. Girardeau and R. Arnowitt, Phys. Rev. 113, 755 (1959).
8. V. N. Popov, Zh. Éksp. Teor. Fiz. 47, 1759 (1964) [Sov. Phys. JETP 20, 1185 (1965)]; Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983), Chap. 6.
9. V. N. Popov, Zh. Éksp. Teor. Fiz. 47, 1759 (1964) [Sov. Phys. JETP 20, 1185 (1965)]; Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983), Chap. 6.
10. V. N. Popov, Zh. Éksp. Teor. Fiz. 47, 1759 (1964) [Sov. Phys. JETP 20, 1185 (1965)]; Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983), Chap. 6.
11. H. Shi and A. Griffin, Phys. Rep. 304, 1 (1998).
12. N. N. Bogoliubov, Physica (Amsterdam) 26, 51 (1960).
13. P. W. Anderson, Lectures on the Many-Body Problem, edited by E. R. Caianiello (Academic Press, New York, 1964).
14. P. C. Hohenberg and P. C. Martin, Ann. Phys. (N.Y.) 34, 291 (1965).
15. E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics, Part 2 (Pergamon, Oxford, 1981).
16. R. M. Ziff, G. E. Uhlenbeck, and M. Kac, Phys. Rep. 32, 169 (1977).
17. N. L. Balazs and T. Bergeman, Phys. Rev. A 58, 2359 (1998).
18. M. O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, Phys. Rev. Lett. 78, 582 (1997); M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275, 637 (1997); B. P. Anderson and M. A. Kasevich, ibid. 282, 1686 (1998); I. Bloch, T. W. Mansch, and T. Esslinger, Phys. Rev. Lett. 82, 3008 (1999).
19. M. O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, Phys. Rev. Lett. 78, 582 (1997); M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275, 637 (1997); B. P. Anderson and M. A. Kasevich, ibid. 282, 1686 (1998); I. Bloch, T. W. Mansch, and T. Esslinger, Phys. Rev. Lett. 82, 3008 (1999).
20. M. O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, Phys. Rev. Lett. 78, 582 (1997); M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275, 637 (1997); B. P. Anderson and M. A. Kasevich, ibid. 282, 1686 (1998); I. Bloch, T. W. Mansch, and T. Esslinger, Phys. Rev. Lett. 82, 3008 (1999).
21. M. O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, Phys. Rev. Lett. 78, 582 (1997); M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 275, 637 (1997); B. P. Anderson and M. A. Kasevich, ibid. 282, 1686 (1998); I. Bloch, T. W. Mansch, and T. Esslinger, Phys. Rev. Lett. 82, 3008 (1999).
22. A. S. Parkins and D. F. Walls, Phys. Rep. 303, 1 (1998); see also the recent linewidth studies of R. Graham, Phys. Rev. Lett. 81, 5262 (1998).
23. A. S. Parkins and D. F. Walls, Phys. Rep. 303, 1 (1998); see also the recent linewidth studies of R. Graham, Phys. Rev. Lett. 81, 5262 (1998).
24. V. V. Kocharovsky, Vl. V. Kocharovsky, and M. O. Scully (unpublished).
25. C. W. Gardiner, Phys. Rev. A 56, 1414 (1997).
26. C. W. Gardiner and P. Zoller, Phys. Rev. A 55, 2902 (1997); D. Jaksch et al., ibid. 56, 575 (1997); 58, 1450 (1998).
27. C. W. Gardiner and P. Zoller, Phys. Rev. A 55, 2902 (1997); D. Jaksch et al., ibid. 56, 575 (1997); 58, 1450 (1998).
28. C. W. Gardiner and P. Zoller, Phys. Rev. A 55, 2902 (1997); D. Jaksch et al., ibid. 56, 575 (1997); 58, 1450 (1998).
29. M. D. Girardeau, Phys. Rev. A 58, 775 (1998).
30. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewood Cliffs, NJ, 1963).
31. T. N. Thiele, Theory of Observations (Oxford University Press, London, 1903); Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1972); C. W. Gardiner, Handbook of Stochastic Methods (Springer, Heidelberg, 1983).
32. T. N. Thiele, Theory of Observations (Oxford University Press, London, 1903); Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1972); C. W. Gardiner, Handbook of Stochastic Methods (Springer, Heidelberg, 1983).
33. T. N. Thiele, Theory of Observations (Oxford University Press, London, 1903); Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1972); C. W. Gardiner, Handbook of Stochastic Methods (Springer, Heidelberg, 1983).
34. H. Politzer, Phys. Rev. A 54, 5048 (1996); S. Grossmann and M. Holthaus, Phys. Rev. E 54, 3495 (1996); C. Herzog and M. Olshanii, Phys. Rev. A 55, 3254 (1997).
35. H. Politzer, Phys. Rev. A 54, 5048 (1996); S. Grossmann and M. Holthaus, Phys. Rev. E 54, 3495 (1996); C. Herzog and M. Olshanii, Phys. Rev. A 55, 3254 (1997).
36. H. Politzer, Phys. Rev. A 54, 5048 (1996); S. Grossmann and M. Holthaus, Phys. Rev. E 54, 3495 (1996); C. Herzog and M. Olshanii, Phys. Rev. A 55, 3254 (1997).
37. P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rzaz-wski, Phys. Rev. Lett. 79, 1789 (1997).
38. M. Wilkens and C. Weiss, J. Mod. Opt. 44, 1801 (1997); C. Weiss and M. Wilkens, Opt. Express 1, 272 (1997).
39. M. Wilkens and C. Weiss, J. Mod. Opt. 44, 1801 (1997); C. Weiss and M. Wilkens, Opt. Express 1, 272 (1997).
40. S. Grossmann and M. Holthaus, Phys. Rev. Lett. 79, 3557 (1997); e-print cond-mat/9709065; Opt. Express 1, 262 (1997).
41. S. Grossmann and M. Holthaus, Phys. Rev. Lett. 79, 3557 (1997); e-print cond-mat/9709065; Opt. Express 1, 262 (1997).
42. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 80, 5040 (1998).
43. S. R. de Groot, G. J. Hooyman, and C. A. ten Seldam, Proc. R. Soc. London, Ser. A 203, 266 (1950).
44. R. B. Dingle, Proc. Cambridge Philos. Soc. 45, 275 (1949); Adv. Phys. 1, 117 (1952); Asymptotic Expansions (Academic, New York, 1973), pp. 267-271.
45. R. B. Dingle, Proc. Cambridge Philos. Soc. 45, 275 (1949); Adv. Phys. 1, 117 (1952); Asymptotic Expansions (Academic, New York, 1973), pp. 267-271.
46. R. B. Dingle, Proc. Cambridge Philos. Soc. 45, 275 (1949); Adv. Phys. 1, 117 (1952); Asymptotic Expansions (Academic, New York, 1973), pp. 267-271.
47. A. R. Fraser, Philos. Mag. 42, 165 (1951).
48. F. Reif, Fundamentals in Thermal Physics (McGraw-Hill, New York, 1965).
49. E. H. Hauge, Phys. Norv. 4, 19 (1969).
50. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, San Francisco, 1971).
51. The term "squeezing" originates from the studies of a noise reduction in quantum optics [see a discussion after Eq. (74)].
52. F. Meier and W. Zwerger, e-print cond-mat/9906344.
53. C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker and C. M. Caves, ibid. 31, 3093 (1985).
54. C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker and C. M. Caves, ibid. 31, 3093 (1985).
55. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994), Chap. 5.
56. k)], introduced in Eq. (73), describes only the occupation of a pair of bear atom excitations k and - k [see Eqs. (66)-(69)] and, according to Eqs. (70),(71), the ground-state occupation. That is, it would be wrong to reduce the analysis of the thermodynamics and, in particular, the entropy of the interacting gas to this effective energy. Thermodynamics is determined by the original energy spectrum of the dressed canonical-ensemble quasiparticles, Eq. (65).
57. P. T. Landsberg, Thermodynamics - With Quantum Statistical Illustrations (Interscience, New York, 1961).
58. P. Borrmann and G. Franke, J. Chem. Phys. 98, 2484 (1993).
59. F. Brosens, J. J. Devreese, and L. F. Lemmens, Solid State Commun. 100, 123 (1996).
60. K. Chase, A. Mekjian, and L. Zamick, e-print cond-mat/9708070.
61. Z. Idziaszek, M. Gajda, P. Navez, M. Wilkens, and K. Rzazewski, Phys. Rev. Lett. 82, 4376 (1999).
62. R. Graham, Phys. Rev. Lett. 81, 5262 (1998); W. V. Lin, ibid. 79, 4056 (1997).
63. R. Graham, Phys. Rev. Lett. 81, 5262 (1998); W. V. Lin, ibid. 79, 4056 (1997).
64. L. V. Keldysh, Zh. Éksp. Teor. Fiz. 47, 352 (1964) [Sov. Phys. JETP 20, 235 (1965)].
65. L. V. Keldysh, Zh. Éksp. Teor. Fiz. 47, 352 (1964) [Sov. Phys. JETP 20, 235 (1965)].
66. E. M. Lifshits and L. P. Pitaevskii, Physical Kinetics (Pergamon Press, Oxford, 1981).
67. P. Danielewicz, Ann. Phys. (N.Y.) 152, 239 (1984).
68. H. T. C. Stoof, J. Low Temp. Phys. 114, 11 (1999).
69. M. Gajda, K. Rzazewski, Phys. Rev. Lett. 78, 2686 (1997).