Existence of Long-Range Order for Trapped Interacting Bosons

Physical Review Letters

Volumn 89, Issue 28, 2002, Pages

  Fischer, Uwe R ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BESSEL FUNCTIONS; ELECTRON GAS; ELECTRON SCATTERING; ELECTRON TRAPS; EQUATIONS OF MOTION; GROUND STATE; HAMILTONIANS; INTEGRAL EQUATIONS; STATISTICAL MECHANICS;

BOSON; HARMONICALLY TRAPPED DILUTE BOSE CONDENSATE; QUANTUM COHERENT SYSTEM; THOMAS-FERMI CONDENSATE;

QUANTUM THEORY;

EID: 0037207378     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.89.280402     Document Type: Article

References (25)

1. P.C. Hohenberg, Phys. Rev.10.1103/PhysRev.158.383 158, 383 (1967).
2. N.N. Bogoliubov, Selected Works, Pt. II: Quantum and Statistical Mechanics (Gordon and Breach, New York, 1991).
3. A. Görlitz et al, Phys. Rev. Lett.10.1103/PhysRevLett.87.130402 87, 130402 (2001).
4. S. Dettmer et al, Phys. Rev. Lett.10.1103/PhysRevLett.87.160406 87, 160406 (2001).
5. W. Hänsel, P. Hommelhoff, T.W. Hänsch, and J. Reichel, Nature (London)10.1038/35097032 413, 498 (2001).
6. H. Ott, J. Fortágh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, Phys. Rev. Lett.10.1103/PhysRevLett.87.230401 87, 230401 (2001).
7. M. Greiner, I. Bloch, O. Mandel, T.W. Hänsch, and T. Esslinger, Phys. Rev. Lett.10.1103/PhysRevLett.87.160405 87, 160405 (2001).
8. W. Ketterle and N.J. van Druten, Phys. Rev. A10.1103/PhysRevA.54.656 54, 656 (1996);
9. N.J. van Druten and W. Ketterle, Phys. Rev. Lett.10.1103/PhysRevLett.79.549 79, 549 (1997).
10. E.H. Lieb and W. Liniger, Phys. Rev.10.1103/PhysRev.130.1605 130, 1605 (1963).
11. D.S. Petrov, M. Holzmann, and G.V. Shlyapnikov, Phys. Rev. Lett.10.1103/PhysRevLett.84.2551 84, 2551 (2000);
12. D.S. Petrov, G.V. Shlyapnikov, and J.T.M. Walraven, Phys. Rev. Lett.10.1103/PhysRevLett.85.3745 85, 3745 (2000);
13. 87, 050404 (2001).
14. W.J. Mullin, J. Low Temp. Phys. 106, 615 (1997).
15. E.H. Lieb and R. Seiringer, Phys. Rev. Lett.10.1103/PhysRevLett.88.170409 88, 170409 (2002).
16. A.J. Leggett, Rev. Mod. Phys.10.1103/RevModPhys.73.307 73, 307 (2001).
17. D. Pines and P. Nozières, The Theory of Quantum Liquids: Volume I (Benjamin, New York, 1966).
18. T.-L. Ho and M. Ma, J. Low Temp. Phys. 115, 61 (1999).
19. V. Dunjko, V. Lorent, and M. Olshaniǐ, Phys. Rev. Lett.10.1103/PhysRevLett.86.5413 86, 5413 (2001);
20. M. Olshaniǐ, Phys. Rev. Lett.10.1103/PhysRevLett.81.938 81, 938 (1998).
21. J.M. Vogels and W. Ketterle (private communication).
22. Observe that, if (Formula presented) is close to the ideal gas prediction (Formula presented)
23. The point that the standard non-number-conserving Bogoliubov approach, when applied to the Bogoliubov inequality, is inconsistent with existing Bose-Einstein condensates has also been made by A.C. Olinto, Phys. Rev. A10.1103/PhysRevA.64.033606 64, 033606 (2001). However, it was claimed that, as a consequence, there is a need to modify the canonical commutation relations, leading to explicit dependence of the Bogoliubov inequality on particle interaction. It was shown here that this modification is not necessary, and that explicit dependence on interaction does not need to occur.
24. M.D. Girardeau and E.M. Wright, Phys. Rev. Lett.10.1103/PhysRevLett.87.210401 87, 210401 (2001).
25. S. Giovanazzi, D. O'Dell, and G. Kurizki, Phys. Rev. Lett.10.1103/PhysRevLett.88.130402 88, 130402 (2002) discussed a “supersolid” phase for a self-bound condensate, in the presence of an additional laser-induced interaction potential.