Temporal coherence, anomalous moments, and pairing correlations in the classical-field description of a degenerate Bose gas

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 1, 2010, Pages

  Wright, T M ^a,b   Blakie, P B ^a   Ballagh, R J ^a  

^a UNIVERSITY OF OTAGO   (New Zealand)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BOSE CONDENSATION; BOSE GAS; BOSE-EINSTEIN CONDENSATES; COHERENCE PROPERTIES; FIELD DESCRIPTION; FIRST MOMENTS; ONSAGER; PAIRING CORRELATIONS; PHASE DIFFUSIONS; ROTATING FRAME; SHARP FEATURES; SHORT TIME SCALE; SLOW DIFFUSION; SPATIAL CORRELATION FUNCTIONS; SYMMETRY-BREAKING; TEMPERATURE DEPENDENCE; TEMPORAL BEHAVIOR; TEMPORAL COHERENCE; TEMPORAL CORRELATIONS; THERMAL DENSITY; TIME AVERAGING; TIME PERIODS;

HAMILTONIANS; MEAN FIELD THEORY; STATISTICAL MECHANICS; STEAM CONDENSERS; WAVE FUNCTIONS;

BOSONS;

EID: 77954847212     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.013621     Document Type: Article

References (49)

1. A. Griffin, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.53.9341 53, 9341 (1996).
2. K. Burnett, in Bose-Einstein Condensation in Atomic Gases, Proceedings of the International School of Physics "Enrico Fermi", Course CXL, edited by, M. Inguscio,, S. Stringari, and, C. E. Wieman, (IOS Press, Amsterdam, 1999).
3. D. A. W. Hutchinson, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/33/19/ 302 33, 3825 (2000).
4. A. J. Leggett, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.73.307 73, 307 (2001).
5. N. P. Proukakis and B. Jackson, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/41/20/203002 41, 203002 (2008).
6. C. W. Gardiner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.56.1414 56, 1414 (1997).
7. Y. Castin and R. Dum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57. 3008 57, 3008 (1998).
8. S. A. Morgan, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/33/19/303 33, 3847 (2000).
9. S. A. Gardiner and S. A. Morgan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.043621 75, 043621 (2007). (Pubitemid 46644536)
10. A. Sinatra, C. Lobo, and Y. Castin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.210404 87, 210404 (2001).
11. P. B. Blakie, A. S. Bradley, M. J. Davis, R. J. Ballagh, and C.W. Gardiner, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730802564254 57, 363 (2008).
12. K. Goral, M. Gajda, and K. Rzazewski, Opt. Express OPEXFF 1094-4087 10.1364/OE.8.000092 8, 92 (2001).
13. A. A. Norrie, R. J. Ballagh, and C. W. Gardiner, Phys. Rev. A 1050-2947 10.1103/PhysRevA.73.043617 73, 043617 (2006). (Pubitemid 43667763)
14. A. Polkovnikov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.033609 68, 033609 (2003).
15. P. B. Blakie and M. J. Davis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.063608 72, 063608 (2005). (Pubitemid 41776046)
16. T. M. Wright, R. J. Ballagh, A. S. Bradley, P. B. Blakie, and C.W. Gardiner, Phys. Rev. A 1050-2947 10.1103/PhysRevA.78.063601 78, 063601 (2008).
17. O. Penrose and L. Onsager, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.104.576 104, 576 (1956).
18. A. Sinatra and Y. Castin, Phys. Rev. A 1050-2947 10.1103/PhysRevA.78. 053615 78, 053615 (2008).
19. J. L. Lebowitz and O. Penrose, Phys. Today 26 (2), 23 (1973).
20. M. J. Davis, S. A. Morgan, and K. Burnett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.160402 87, 160402 (2001).
21. H. H. Rugh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.772 78, 772 (1997).
22. A. S. Bradley, C. W. Gardiner, and M. J. Davis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.033616 77, 033616 (2008). (Pubitemid 351416426)
23. T. M. Wright, A. S. Bradley, and R. J. Ballagh, Phys. Rev. A 1050-2947 10.1103/PhysRevA.80.053624 80, 053624 (2009).
24. T. M. Wright, A. S. Bradley, and R. J. Ballagh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.013610 81, 013610 (2010).
25. J.-P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1986).
26. R. Graham, Nonlinear Phenom. Complex Syst. (Dordrecht, Neth.) 5, 349 (2002).
27. Note that the cutoff energy refers only to the single-particle modes that the field is expanded on. The energies of excitations in the interacting field are raised because of the mean-field potential they experience (see also discussion in[16]).
28. A. L. Fetter, in Bose-Einstein Condensation in Atomic Gases, Proceedings of the International School of Physics "Enrico Fermi", Course CXL, edited by, M. Inguscio,, S. Stringari, and, C. E. Wieman, (IOS Press, Amsterdam, 1999).
29. C. Mora and Y. Castin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67. 053615 67, 053615 (2003).
30. The identification of the condensate and its eigenfrequency in this manner bears some resemblance to the method of Feit [M. D. Feit, J. A. Fleck Jr., and A. Steiger, J. Comput. Phys. 0021-9991 10.1016/0021-9991(82)90091-2 47, 412 (1982)] for the identification of Schrödinger eigenstates and eigenvalues from a spectral analysis of trajectories of the time-dependent Schrödinger equation. In contrast to that work, however, the condensate "eigenmode" we consider here emerges from the trajectories of a nonlinear equation of motion, and can only be obtained from an analysis of the real-time field trajectories [or some other sampling of the PGPE microcanonical density Eq.(5)].
31. We calculated (and fitted to) estimates of the powers at T = 4, 8,..., 400 ω r - 1, but for clarity indicate only every tenth such estimate in Fig. 2.
32. M. J. Davis and S. A. Morgan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.053615 68, 053615 (2003).
33. M. J. Davis and P. B. Blakie, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/48/001 38, 10259 (2005). (Pubitemid 41654858)
34. N. P. Proukakis, S. A. Morgan, S. Choi, and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.2435 58, 2435 (1998).
35. M. J. Davis, S. A. Morgan, and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.053618 66, 053618 (2002).
36. N. P. Proukakis and K. Burnett, J. Res. Natl. Inst. Stand. Technol. 101, 457 (1996).
37. M. Brewczyk, P. Borowski, M. Gajda, and K. Rza̧zewski, J.Phys. B JPAPEH 0953-4075 10.1088/0953-4075/37/13/010 37, 2725 (2004).
38. T. Bergeman, D. L. Feder, N. L. Balazs, and B. I. Schneider, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.063605 61, 063605 (2000).
39. J. F. Dobson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73. 2244 73, 2244 (1994).
40. C. J. Pethick and L. P. Pitaevskii, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.033609 62, 033609 (2000).
41. D. A. W. Hutchinson, R. J. Dodd, and K. Burnett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.2198 81, 2198 (1998).
42. C. W. Gardiner and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.536 58, 536 (1998).
43. C. W. Gardiner and M. J. Davis, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/36/23/010 36, 4731 (2003).
44. A. Bezett and P. B. Blakie, Phys. Rev. A 1050-2947 10.1103/PhysRevA.79. 033611 79, 033611 (2009).
45. C. W. Gardiner, Handbook of Stochastic Methods, 3rd ed. (Springer-Verlag, Berlin, 2004).
46. C. W. Gardiner and P. Zoller, Quantum Noise, 2nd ed. (Springer-Verlag, Berlin, 2000).
47. H. T. C. Stoof, in Coherent Atomic Matter Waves, Proceedings of the Les Houches Summer School of Theoretical Physics, Session LXXII, edited by, R. Kaiser,, C. Westbrook, and, F. David, (EDP Sciences & Springer-Verlag, Berlin, 2001).
48. A. Sinatra, Y. Castin, and E. Witkowska, Phys. Rev. A 1050-2947 10.1103/PhysRevA.75.033616 75, 033616 (2007). (Pubitemid 46494654)
49. Y. Castin, in Coherent Atomic Matter Waves, Proceedings of the Les Houches Summer School of Theoretical Physics, Session LXXII, edited by, R. Kaiser,, C. Westbrook, and, F. David, (EDP Sciences & Springer-Verlag, Berlin, 2001).