Multi-mode description of an interacting Bose-Einstein condensate

Optics Express

Volumn 8, Issue 2, 2001, Pages 92-98

  Góral, Krzysztof ^a,c   Gajda, Mariusz ^b,c   Rza̧zewski, Kazimierz ^a,c  

^a CENTER FOR THEORETICAL PHYSICS   (Poland)

^b INSTITUTE OF PHYSICS   (Poland)

^c NONE   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONDENSATION; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PHASE TRANSITIONS; QUANTUM OPTICS; STATISTICAL MECHANICS;

BOSE CONDENSATION; FLUCTUATIONS; GENERAL; RELAXATIONS;

QUANTUM THEORY;

EID: 0038742279     PISSN: 10944087     EISSN: None     Source Type: Journal    
DOI: 10.1364/OE.8.000092     Document Type: Conference Paper

References (31)

1. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, "Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor," Science 269, 198-201 (1995).
2. K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, "Bose-Einstein condensation in a gas of sodium atoms," Phys. Rev. Lett. 75, 3969-3972 (1995).
3. C.C. Bradley, C.A. Sackett, J.J. Tollett, and R.G. Hulet, "Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions," Phys. Rev. Lett. 75, 1687-1690 (1995) and Erratum 79, 1170(E) (1997).
4. D.G. Fried, T.C. Killian, L. Willmann, D. Landhuis, S.C. Moss, D. Kleppner, and T.J. Greytak, "Bose-Einstein condensation of atomic hydrogen," Phys. Rev. Lett. 81, 3811-3814 (1998).
5. P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rza̧żewski, "Fourth statistical ensemble for the Bose-Einstein condensate," Phys. Rev. Lett. 79, 1789-1792 (1997).
6. M. Gajda and K. Rza̧żewski, "Fluctuations of Bose-Einstein condensate," Phys. Rev. Lett. 78, 2686-2689 (1997).
7. S. Grossmann and M. Holthaus, "Fluctuations of the particle number in a trapped Bose-Einstein condensate," Phys. Rev. Lett. 79, 3557-3560 (1997).
8. S. Grossmann and M. Holthaus, "Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps," Opt. Express 1, 262-271 (1997), http://www.opticsexpress.org/oearchive/source/2288.htm
9. H. D. Politzer, "Condensate fluctuations of a trapped, ideal Bose gas," Phys. Rev. A 54, 5048-5054 (1996).
10. M. Wilkens and C. Weiss, "Particle number fluctuations in an ideal Bose gas," J. Mod. Opt. 44, 1801-1814 (1997).
11. M. Wilkens and C. Weiss, "Particle number counting statistics in ideal Bose gases," Opt. Express 1, 272-283 (1997), http://www. optiesexpress.org/oearchive/source/2372.htm
12. S. Giorgini, L.P. Pitaevskii, and S. Stringari, "Anomalous fluctuations of the condensate in interacting Bose gases," Phys. Rev. Lett 80, 5040-5043 (1998).
13. Z. Idziaszek, M. Gajda, P. Navez, M. Wilkens, and K. Rza̧żewski, "Fluctuations of the weakly interacting Bose-Einstein condensate," Phys. Rev. Lett. 82, 4376-4379 (1999).
14. F. Meier and W. Zwerger, "Anomalous condensate fluctuations in strongly interacting superfluids," Phys. Rev. A 60, 5133-5135 (1999).
15. V.V. Kocharovsky, V.V. Kocharovsky, and M.O. Scully, "Condensate statistics in interacting and ideal dilute Bose gases," Phys. Rev. Lett. 84, 2306-2309 (2000).
16. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, "Theory of Bose-Einstein condensation in trapped gases," Rev. Mod. Phys. 71, 463-512 (1999).
17. R. Graham, "Condensate fluctuations in finite Bose-Einstein condensates at finite temperature," Phys. Rev. A 62, 023609 (2000).
18. R. Graham, "Decoherence of Bose-Einstein condensates in traps at finite temperature," Phys. Rev. Lett. 81, 5262-5265 (1998).
19. C.W. Gardiner and P. Zoller, "Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential," Phys. Rev. A 55, 2902-2921 (1997).
20. D. Jaksch, C.W. Gardiner, and P. Zoller, "Quantum kinetic theory. 2.Simulation of the quantum Boltzmann master equation," Phys. Rev. A 56, 575-586 (1997).
21. R. Walser, J. Williams, J. Cooper, and M. Holland, "Quantum kinetic theory for a condensed bosonic gas," Phys. Rev. A 59, 3878-3889 (1999).
22. R. Walser, J. Williams, and M. Holland, "Reversible and irreversible evolution of a condensed bosonic gas," preprint cond-mat/0004257, http://xxx.lanl.gov/abs/cond-mat/0004257
23. The case of boundary conditions different from the periodic ones (e.g. a rectangular trap) presents an interesting and challenging problem. In this case there are no universal eigenstates of a one-particle density matrix and therefore the definition of a condensate is unclear.
24. A.L. Fetter and J.D.Walecka, Quantum theory of many-particle systems (McGraw-Hill, New York, 1991).
25. E. Fermi, J. Pasta, and S. Ulam, "Studies of Nonlinear Problems. I," in Collected Papers of Enrico Fermi (Accademia Nazionale del Lincei and University of Chicago, Roma, 1965), Vol. II, p. 978.
26. P. Villain and M. Lewenstein, "Fermi-Pasta-Ulam problem revisited with a Bose-Einstein condensate," Phys. Rev. A 62, 043601 (2000).
27. F.M. Izrailev and B.V. Chirikov, "Statistical properties of a nonlinear string," Dokl. Akad. Nauk SSSR 166, 57-59 (1966) [Sov. Phys. Dokl. 11, 30-32 (1966)].
28. F.M. Izrailev and B.V. Chirikov, "Statistical properties of a nonlinear string," Dokl. Akad. Nauk SSSR 166, 57-59 (1966) [Sov. Phys. Dokl. 11, 30-32 (1966)].
29. J.H. Eberly, N.B. Narozhny, and J.J. Sanchez-Mondragon, "Periodic spontaneous collapse and revival in a simple quantum model," Phys. Rev. Lett. 44, 1323-1326 (1980).
30. In a recent preprint M.J. Davis, S.A. Morgan, and K. Burnett, "Simulations of Bose fields at finite temperature," preprint cond-mat/0011431, http://xxx.lanl.gov/abs/cond-mat/0011431, using similar methods, the authors establish a link between the energy and the temperature for temperatures below the critical region.
31. K. Góral, M. Gajda, and K. Rza̧żewski, "Multi-mode dynamics of a coupled ultracold atomic-molecular system," preprint cond-mat/0006192, http://xxx.lanl.gov/abs/cond-mat/0006192