Many-body physics in the classical-field description of a degenerate Bose gas

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 84, Issue 2, 2011, Pages

  Wright, T M ^a   Proukakis, N P ^a,b   Davis, M J ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOSE GAS; CORRELATION FUNCTION; DENSITY FLUCTUATION; FIELD FLUCTUATIONS; MANY-BODY; MEAN-FIELD POTENTIAL; NON-GAUSSIAN; NORMAL PHASE; QUANTUM LADDERS; SYMMETRY-BREAKING;

MEAN FIELD THEORY;

BOSONS;

EID: 80051632869     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.84.023608     Document Type: Article

References (108)

1. M. H. Anderson, Science SCIEAS 0036-8075 10.1126/science.269.5221.198 269, 198 (1995).
2. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.3969 75, 3969 (1995).
3. C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.1687 75, 1687 (1995).
4. H. Shi and A. Griffin, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98) 00015-5 304, 1 (1998).
5. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.71.463 71, 463 (1999).
6. N. P. Proukakis and B. Jackson, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/41/20/203002 41, 203002 (2008).
7. N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).
8. S. T. Beliaev, Sov. Phys. JETP 7, 289 (1958).
9. A. Griffin, Excitations in a Bose-Condensed Liquid (Cambridge University Press, Cambridge, England, 1993).
10. H. T. C. Stoof, J. Low Temp. Phys. JLTPAC 0022-2291 10.1023/A: 1021897703053 114, 11 (1999).
11. M. Rusch, S. A. Morgan, D. A. W. Hutchinson, and K. Burnett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.4844 85, 4844 (2000). (Pubitemid 32871650)
12. S. A. Morgan, M. Rusch, D. A. W. Hutchinson, and K. Burnett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.250403 91, 250403 (2003).
13. S. A. Morgan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.023609 69, 023609 (2004).
14. A. Griffin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.53.9341 53, 9341 (1996).
15. J.-P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1986).
16. N. P. Proukakis and K. Burnett, J. Res. Natl. Inst. Stand. Technol. 101, 457 (1996).
17. N. M. Hugenholtz and D. Pines, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.116.489 116, 489 (1959).
18. M. Bijlsma and H. T. C. Stoof, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.498 55, 498 (1997).
19. H. Shi, G. Verechaka, and A. Griffin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.50.1119 50, 1119 (1994).
20. S. A. Morgan, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/33/19/303 33, 3847 (2000).
21. P. O. Fedichev and G. V. Shlyapnikov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.3146 58, 3146 (1998).
22. 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).
23. D. A. W. Hutchinson, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/33/19/ 302 33, 3825 (2000).
24. H. T. C. Stoof, M. Bijlsma, and M. Houbiers, J. Res. Natl. Inst. Stand. Technol. 101, 443 (1996).
25. N. P. Proukakis, K. Burnett, and H. T. C. Stoof, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.1230 57, 1230 (1998).
26. M. Bijlsma and H. T. C. Stoof, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.5085 54, 5085 (1996).
27. R. Walser, J. Williams, J. Cooper, and M. Holland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.3878 59, 3878 (1999).
28. R. Walser, J. Cooper, and M. Holland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.013607 63, 013607 (2000).
29. S. Giorgini, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.063615 61, 063615 (2000).
30. J. Wachter, R. Walser, J. Cooper, and M. Holland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.053612 64, 053612 (2001).
31. N. P. Proukakis, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/34/23/317 34, 4737 (2001). (Pubitemid 34061178)
32. M. Imamović-Tomasović and A. Griffin, J. Low Temp. Phys. JLTPAC 0022-2291 10.1023/A:1004860602930 122, 617 (2001). (Pubitemid 33638278)
33. P. B. Blakie, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730802564254 57, 363 (2008).
34. Y. Kagan and B. V. Svistunov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3331 79, 3331 (1997).
35. C. Lobo, A. Sinatra, and Y. Castin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.020403 92, 020403 (2004).
36. M. Brewczyk, M. Gajda, and K. Rzazewski, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/40/2/R01 40, R1 (2007). (Pubitemid 46476530)
37. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
38. G. Baym, J.-P. Blaizot, M. Holzmann, F. Laloe, and D. Vautherin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1703 83, 1703 (1999).
39. M. J. Steel, M. K. Olsen, L. I. Plimak, P. D. Drummond, S. M. Tan, M. J. Collett, D. F. Walls, and R. Graham, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.4824 58, 4824 (1998).
40. A. Sinatra, C. Lobo, and Y. Castin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.210404 87, 210404 (2001).
41. A. Polkovnikov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.053604 68, 053604 (2003).
42. A. A. Norrie, R. J. Ballagh, and C. W. Gardiner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.040401 94, 040401 (2005). (Pubitemid 40607203)
43. M. J. Davis, S. A. Morgan, and K. Burnett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.160402 87, 160402 (2001).
44. P. B. Blakie and M. J. Davis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.063608 72, 063608 (2005). (Pubitemid 41776046)
45. C. W. Gardiner and M. J. Davis, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/36/23/010 36, 4731 (2003).
46. M. J. Davis, S. A. Morgan, and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.053618 66, 053618 (2002).
47. M. Girardeau and R. Arnowitt, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.113.755 113, 755 (1959).
48. C. W. Gardiner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.56.1414 56, 1414 (1997).
49. Y. Castin and R. Dum, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57. 3008 57, 3008 (1998).
50. M. D. Girardeau, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.775 58, 775 (1998).
51. As noted in W. V. Liu, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.79. 4056 79, 4056 (1997)
52. due to the functional form of the Bose-gas equation of state, a "nearly pure" condensate with ∼ 90 % condensate fraction corresponds to a temperature of order half the critical temperature. For a typical system population of ∼ 10 5 atoms, the lowest-lying excitations of the condensate, with energies on the order of the trap spacing [S. Stringari, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.77.2360 77, 2360 (1996)], thus have thermal populations 10 atoms, significantly larger than the zero-point "vacuum" mode occupation. As these modes are most strongly affected by the presence of the condensate, it is logical to expect that they form the dominant contribution to the nontrivial correlations of the noncondensed component of the field.
53. J. O. Andersen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76. 599 76, 599 (2004). (Pubitemid 39063523)
54. M. J. Davis and P. B. Blakie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.060404 96, 060404 (2006). (Pubitemid 43271090)
55. T. M. Wright, P. B. Blakie, and R. J. Ballagh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.013621 82, 013621 (2010).
56. 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)
57. T. P. Simula and P. B. Blakie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.020404 96, 020404 (2006). (Pubitemid 43248202)
58. T. P. Simula, M. J. Davis, and P. B. Blakie, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.023618 77, 023618 (2008). (Pubitemid 351391411)
59. A. Bezett, E. Toth, and P. B. Blakie, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.023602 77, 023602 (2008). (Pubitemid 351321494)
60. A. Bezett and P. B. Blakie, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.023602 79, 023602 (2009).
61. R. N. Bisset, M. J. Davis, T. P. Simula, and P. B. Blakie, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.033626 79, 033626 (2009).
62. K. Damle, S. N. Majumdar, and S. Sachdev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.5037 54, 5037 (1996).
63. K. Goral, M. Gajda, and K. Rzazewski, Opt. Express OPEXFF 1094-4087 10.1364/OE.8.000092 8, 92 (2001).
64. N. G. Berloff and B. V. Svistunov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.013603 66, 013603 (2002).
65. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.263901 95, 263901 (2005). (Pubitemid 43061546)
66. A. Nunnenkamp, J. N. Milstein, and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.033604 75, 033604 (2007). (Pubitemid 46418235)
67. A. Sinatra, Y. Castin, and E. Witkowska, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.033616 75, 033616 (2007). (Pubitemid 46494654)
68. M. J. Davis and S. A. Morgan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.053615 68, 053615 (2003).
69. P. B. Blakie, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.026704 78, 026704 (2008).
70. T. M. Wright, R. J. Ballagh, A. S. Bradley, P. B. Blakie, and C. W. Gardiner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.063601 78, 063601 (2008).
71. H. H. Rugh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.772 78, 772 (1997).
72. K. Góral, M. Gajda, and K. Rzazewski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.051602 66, 051602 (2002).
73. O. Penrose and L. Onsager, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.104.576 104, 576 (1956).
74. H. Goldstein, Classical Mechanics (Addison-Wesley, Cambridge, MA, 1950).
75. E. C. G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective (Wiley, New York, 1974).
76. P. W. Anderson, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.38. 298 38, 298 (1966).
77. A. Leggett, in Bose-Einstein Condensation in Atomic Gases, edited by, A. Griffin, D. W. Snoke, and, S. Stringari, (Cambridge University Press, Cambridge, England, 1995).
78. A. L. Fetter, in Bose-Einstein Condensation in Atomic Gases, edited by, M. Inguscio, S. Stringari, and, C. E. Wieman, (IOS Press, Amsterdam, 1999).
79. S. A. Gardiner and S. A. Morgan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.043621 75, 043621 (2007). (Pubitemid 46644536)
80. A. Bezett and P. B. Blakie, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.033611 79, 033611 (2009).
81. C. W. Gardiner, Handbook of Stochastic Methods, 3rd ed., (Springer-Verlag, Berlin, 2000).
82. S. P. Cockburn, A. Negretti, N. P. Proukakis, and C. Henkel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.83.043619 83, 043619 (2011).
83. D. A. W. Hutchinson, E. Zaremba, and A. Griffin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.1842 78, 1842 (1997).
84. 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).
85. F. Lalöe, in Bose-Einstein Condensation in Atomic Gases, edited by, A. Griffin, D. W. Snoke, and, S. Stringari, (Cambridge University Press, Cambridge, England, 1995).
86. T. Köhler and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.033601 65, 033601 (2002).
87. E. Zaremba, T. Nikuni, and A. Griffin, J. Low Temp. Phys. JLTPAC 0022-2291 10.1023/A:1021846002995 116, 277 (1999).
88. C. W. Gardiner, J. R. Anglin, and T. I. A. Fudge, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/35/6/310 35, 1555 (2002). (Pubitemid 34404418)
89. C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, England, 2002).
90. L. Pitaevskii and E. Lifshitz, Statistical Physics Part 2: Theory of the condensed state, 2nd ed., (Pergamon, Oxford, 1980).
91. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003).
92. D. A. W. Hutchinson, R. J. Dodd, and K. Burnett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.2198 81, 2198 (1998).
93. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.63.214503 63, 214503 (2001).
94. N. Prokof'ev, O. Ruebenacker, and B. Svistunov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.270402 87, 270402 (2001).
95. C. W. Gardiner and P. Zoller, Quantum Noise, 2nd ed., (Springer-Verlag, Berlin, 2000).
96. V. Pietilä, T. P. Simula, and M. Möttönen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.033616 81, 033616 (2010).
97. R. J. Glauber, in Quantum Optics and Electronics, edited by, C. DeWitt, A. Blandin, and, C. Cohen-Tannoudji, (Gordon and Breach, New York, 1965), Chap. Optical Coherence and Photon Statistics.
98. R. Dodd, C. Clark, M. Edwards, and K. Burnett, Opt. Express OPEXFF 1094-4087 10.1364/OE.1.000284 1, 284 (1997).
99. C. W. Gardiner and A. S. Bradley, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/34/23/311 34, 4663 (2001). (Pubitemid 34061173)
100. T. M. Wright, A. S. Bradley, and R. J. Ballagh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.053624 80, 053624 (2009).
101. Y. Kagan, V. A. Kashurnikov, A. V. Krasavin, N. V. Prokof'ev, and B. V. Svistunov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.043608 61, 043608 (2000).
102. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, England, 1995).
103. H. Kleinert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.286 84, 286 (2000).
104. C. J. Foster, P. B. Blakie, and M. J. Davis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.023623 81, 023623 (2010).
105. H. T. C. Stoof and M. Bijlsma, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.47.939 47, 939 (1993).
106. M. D. Lee, S. A. Morgan, M. J. Davis, and K. Burnett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.043617 65, 043617 (2002).
107. U. Al Khawaja, J. O. Andersen, N. P. Proukakis, and H. T. C. Stoof, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.013615 66, 013615 (2002).
108. N. P. Proukakis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.023605 73, 023605 (2006). (Pubitemid 43270240)