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The European Physical Journal D

, Volume 42, Issue 2, pp 309–316 | Cite as

Studies of bosons in optical lattices in a harmonic potential

  • R. RamakumarEmail author
  • A. N. Das
  • S. Sil
Laser Cooling and Quantum Gas

Abstract.

We present a theoretical study of Bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and evolution to the bulk limit of the condensate fraction and the specific heat. Some preliminary results on the specific heat of fermions in optical lattices are also presented. The results obtained are contextualized within the current experimental and theoretical scenario.

PACS.

03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations 03.75.Nt Other Bose-Einstein condensation phenomena 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties 

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References

  1. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002) CrossRefADSGoogle Scholar
  2. T. Stöferle, H. Moritz, C. Schori, M. Köhl, T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004) CrossRefADSGoogle Scholar
  3. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004) CrossRefADSGoogle Scholar
  4. M. Köhl, H. Moritz, T. Stöferle, C. Schori, T. Esslinger, J. Low Temp. Phys. 138, 635 (2005) CrossRefGoogle Scholar
  5. D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998) CrossRefADSGoogle Scholar
  6. D. Van Oosten, P. van der Straten, H.T.C. Stoof, Phys. Rev. A 63, 054601 (2001) CrossRefGoogle Scholar
  7. W. Zwerger, J. Opt. B: Quantum Semiclass. Opt. 5, S9 (2003) Google Scholar
  8. A.M. Rey, K. Burnett, R. Roth, M. Edwards, C.J. Williams, C.W. Clark, J. Phys. B: At. Mol. Opt. Phys. 36, 825 (2003) CrossRefADSGoogle Scholar
  9. G. Pupillo, E. Tiesinga, C.J. Williams, Phys. Rev. A 68, 063604 (2003) CrossRefADSGoogle Scholar
  10. S. Wessel, F. Alet, M. Troyer, G. Batrouni, Phys. Rev. A 70, 053615 (2004) CrossRefADSGoogle Scholar
  11. H. Kleinert, S. Schmidt, A. Pelster, Phys. Rev. Lett. 93, 160402 (2004) CrossRefADSGoogle Scholar
  12. A.F. Ho, M.A. Cazalilla, T. Giamarchi, Phys. Rev. Lett. 92, 130405 (2004) CrossRefADSGoogle Scholar
  13. L. Pollet, S. Rombouts, K. Heyde, J. Dukelsky, Phys. Rev. A 69, 043601 (2004) CrossRefADSGoogle Scholar
  14. L. Santos, M.A. Baranov, J.I. Cirac, H.U. Everts, H. Fehrmann, M. Lewenstein, Phys. Rev. Lett. 93, 030601 (2004) CrossRefADSGoogle Scholar
  15. K. Sengupta, N. Dupuis, Phys. Rev. A 71, 033629 (2005) CrossRefADSGoogle Scholar
  16. D. Heidarian, K. Damle, Phys. Rev. Lett. 95, 127206 (2005) CrossRefADSGoogle Scholar
  17. R.V. Pai, R. Pandit, Phys. Rev. B 71, 104508 (2005) CrossRefADSGoogle Scholar
  18. V.W. Scarola, S. Das Sarma, Phys. Rev. Lett. 95, 033003 (2005) CrossRefADSGoogle Scholar
  19. D.B.M. Dickerscheid, D. van Oosten, P.J.H. Denteneer, H.T.C. Stoof, Phys. Rev. A 68, 043623 (2003) CrossRefADSGoogle Scholar
  20. S.M. Giampaolo, F. Illuminati, G. Mazzarella, S. De Siena, Phys. Rev. A 70, 061601 (2004) CrossRefADSGoogle Scholar
  21. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Weiman, E.A. Cornell, Science 269, 198 (1995) CrossRefADSGoogle Scholar
  22. K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995) CrossRefADSGoogle Scholar
  23. C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995) CrossRefADSGoogle Scholar
  24. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999) CrossRefADSGoogle Scholar
  25. A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001) CrossRefADSGoogle Scholar
  26. J.R. Anglin, W. Ketterle, Nature 416, 211 (2002) CrossRefADSGoogle Scholar
  27. C.J. Pethick, H. Smith, Bose-Einstein condensation in dilute gases (Cambridge University Press, Cambridge, England, 2002) Google Scholar
  28. J. Kinast, A. Turlapov, J.E. Thomas, Q. Chen, J. Stajic, K. Levin, Science 307, 1296 (2005) CrossRefADSGoogle Scholar
  29. A.M. Rey, G. Pupillo, C.W. Clark, C.J. Williams, Phys. Rev. A 72, 033616 (2005) CrossRefADSGoogle Scholar
  30. V. Bagnato, D. Kleppner, Phys. Rev. A 44, 7439 (1991) CrossRefADSGoogle Scholar
  31. W. Ketterle, N.J. van Druten, Phys. Rev. A 54, 656 (1996) CrossRefADSGoogle Scholar
  32. C. Schori, T. Stöferle, H. Moritz, M. Köhl, T. Esslinger, Phys. Rev. Lett. 93, 240402 (2004) CrossRefADSGoogle Scholar
  33. M. Köhl, H. Moritz, T. Stöferle, K. Günter, T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005) CrossRefGoogle Scholar
  34. M. Köhl, Phys. Rev. A 73, 031601 (2006) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Physics and AstrophysicsUniversity of DelhiDelhiIndia
  2. 2.Condensed Matter Physics Group, Saha Institute of Nuclear PhysicsKolkataIndia
  3. 3.Department of PhysicsSantiniketanIndia

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