OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 9 — Sep. 1, 2006
  • pp: 1888–1893

Bose–Hubbard model on a ring: analytical results in a strong interaction limit and incommensurate filling

Ying Wu and Xiaoxue Yang  »View Author Affiliations


JOSA B, Vol. 23, Issue 9, pp. 1888-1893 (2006)
http://dx.doi.org/10.1364/JOSAB.23.001888


View Full Text Article

Enhanced HTML    Acrobat PDF (116 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We derive the explicit analytical results of low-lying eigenenergies, eigenstates, momentum distributions, and all the two-order spatial correlation functions for a Bose–Hubbard model on a ring in the strong interaction limit by means of the first-order perturbation theory. We show explicitly that the ground and the low-lying excited states are all quantum entangled states in the incommensurate filling case and that certain correlation functions in some of these states, the ground state in particular, violate the Schwarz inequality, another indication of their nonclassicality.

© 2006 Optical Society of America

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(190.0190) Nonlinear optics : Nonlinear optics
(270.0270) Quantum optics : Quantum optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 28, 2005
Revised Manuscript: March 29, 2006
Manuscript Accepted: April 18, 2006

Citation
Ying Wu and Xiaoxue Yang, "Bose-Hubbard model on a ring: analytical results in a strong interaction limit and incommensurate filling," J. Opt. Soc. Am. B 23, 1888-1893 (2006)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-23-9-1888


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998). [CrossRef]
  2. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989). [CrossRef]
  3. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott-insulator in a gas of ultracold atoms," Nature 413, 39-44 (2002). [CrossRef]
  4. S. R. Clark and D. Jaksch, "Dynamics of the superfluid to Mott-insulator transition in one dimension," Phys. Rev. A 70, 043612/1-13 (2004). [CrossRef]
  5. D. van Oosten, P. van der Straten, and H. T. C. Stoof, "Quantum phases in an optical lattice," Phys. Rev. A 63, 053601/1-12 (2001). [CrossRef]
  6. D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003). [CrossRef]
  7. Y. Wu and X. Yang, "Analytical results for energy spectrum and eigenstates of Bose-Einstein condensate in Mott insulator state," Phys. Rev. A 68, 013608/1-7 (2003). [CrossRef]
  8. A. A. Svidzinsky and S. T. Chui, "Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field," Phys. Rev. A 68, 043612/1-8 (2003). [CrossRef]
  9. S. Tsuchiya, S. Kurihara, and T. Kimura, "Superfluid-Mott insulator transition of spin-1 bosons in an optical lattice," Phys. Rev. A 70, 043628/1-11 (2004). [CrossRef]
  10. S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004). [CrossRef]
  11. K. V. Krutitsky and R. Graham, "Spin-1 bosons with coupled ground states in optical lattice," Phys. Rev. A 70, 063610/1-10 (2004). [CrossRef]
  12. K. V. Krutitsky, M. Timmer, and R. Graham, "First- and second-order superfluid-Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices," Phys. Rev. A 71, 033623/1-4 (2005). [CrossRef]
  13. P. Jain and C. W. Gardiner, "A phase-space method for Bose-Hubbard model: application to mean-field models," J. Phys. B 37, 3649-3680 (2004). [CrossRef]
  14. W. Zwerger, "Mott-Hubbard transition of cold atoms in optical lattices," J. Opt. 5, S9-S16 (2003). [CrossRef]
  15. B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003). [CrossRef]
  16. A. Polkovnikov and D. W. Wang, "Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices," Phys. Rev. Lett. 93, 070401/1-4 (2004). [CrossRef]
  17. T. D. Kühner, S. R. White, and H. Monien, "One-dimensional Bose-Hubbard model with nearest-neighbor interaction," Phys. Rev. B 61, 12474-12489 (2000). [CrossRef]
  18. L. Amico and V. Penna, "Time-dependent mean-field theory of the superfluid-insulator phase transition," Phys. Rev. B 62, 1224-1237 (2000). [CrossRef]
  19. A. Buchleitner and A. Kolovsky, "Interaction-induced decoherence of atomic Bloch oscillations," Phys. Rev. Lett. 91, 253002/1-4 (2003). [CrossRef]
  20. M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005). [CrossRef]
  21. M. Rigol and A. Muramatsu, "Ground-state properties of hard-core bosons confined on one-dimensional optical lattices," Phys. Rev. A 72, 013604/1-13 (2005).
  22. J. Zakrzewski, "Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms," Phys. Rev. A 71, 043601/1-7 (2005). [CrossRef]
  23. C. Menotti, A. Smerzi, and A. Trombettoni, "Superfluid dynamics of a Bose-Einstein condensate in a periodic potential," New J. Phys. 5, 112/1-20 (2003). [CrossRef]
  24. D. C. Roberts and K. Burnett, "Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice," Phys. Rev. Lett. 90, 150401/1-4 (2003). [CrossRef]
  25. V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, "Revealing the superfluid-Mott-insulator transition in an optical lattice," Phys. Rev. A 66, 031601(R)/l-4 (2002). [CrossRef]
  26. G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).
  27. L. Amico and V. Penna, "Dynamical mean field theory of the Bose-Hubbard model," Phys. Rev. Lett. 80, 2189-2192 (1998). [CrossRef]
  28. L. Tonks, "The complete equation of state of one, two and three-dimensional gases of hard elastic spheres," Phys. Rev. 50, 955-963 (1936). [CrossRef]
  29. M. D. Girardeau, "Relationship between systems of impenetrable bosons and fermions in one dimension," J. Math. Phys. 1, 516-523 (1960). [CrossRef]
  30. E. H. Lieb and W. Liniger, "Exact analysis of an interacting Bose gas. I. The general solution and the ground state," Phys. Rev. 130, 1605-1616 (1963). [CrossRef]
  31. E. H. Lieb, "Exact analysis of an interacting Bose gas. II. The excitation spectrum," Phys. Rev. 130, 1616-1624 (1963). [CrossRef]
  32. M. D. Girardeau and E. M. Wright, "Breakdown of time-dependent mean field theory for a one-dimensional condensate of impenetrable bosons," Phys. Rev. Lett. 84, 5239-5243 (2000). [CrossRef] [PubMed]
  33. M. D. Girardeau, E. M. Wright, and J. M. Triscari, "Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap," Phys. Rev. A 63, 033601/1-6 (2001). [CrossRef]
  34. R. Bhat, L. D. Carr, and M. J. Holland, "Bose-Einstein condensates in rotating lattices," Phys. Rev. Lett. 96, 060405/1-4 (2006). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited