The European Physical Journal D

, Volume 50, Issue 1, pp 61–66 | Cite as

How the effective boson-boson interaction works in Bose-Fermi mixtures in periodic geometries

  • G. MazzarellaEmail author
Laser Cooling and Quantum Gas


We study mixtures of spinless bosons and not spin-polarized fermions loaded in two dimensional optical lattices. We approach the problem of the ground state stability within the framework of the linear response theory; by the mean of an iterative procedure, we are able to obtain a relation for the dependence of boson-boson effective interaction on the absolute temperature of the sample. Proceeding from such a formula, we write down analytical expressions for supersolid (SS) and phase separation (PS) transition temperatures, and plot the phase diagrams.


37.10.Jk Atoms in optical lattices 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. D. Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998)Google Scholar
  2. M. Greiner et al., Nature 415, 39 (2002)Google Scholar
  3. M. Houbiers et al., Phys. Rev. A 56, 4864 (1997)Google Scholar
  4. H. Heiselberg et al., Phys. Rev. Lett. 85, 2418 (2000)Google Scholar
  5. A. Albus, F. Illuminati, J. Eisert, Phys. Rev. A 68, 023606 (2003)Google Scholar
  6. F. Illuminati, A. Albus, Phys. Rev. Lett. 93, 090406 (2004)Google Scholar
  7. L. Salasnich, F. Toigo, Phys. Rev. A 75, 013623 (2007)Google Scholar
  8. A.G. Truscott et al., Science 291, 2570 (2001); F. Schreck et al., Phys. Rev. Lett. 87, 080403 (2001); Z. Hadzibabic et al., Phys. Rev. Lett. 88, 160401 (2002)Google Scholar
  9. G. Roati et al., Phys. Rev. Lett. 89, 150403 (2002)Google Scholar
  10. K. Mølmer, Phys. Rev. Lett. 80, 1804 (1998)Google Scholar
  11. M. Amoruso et al., Eur. Phys. J. D 4, 261 (1998)Google Scholar
  12. M.W. Meisel, Physica 178, 121 (1992)Google Scholar
  13. G.A. Lengua et al., J. Low. Temp. Phys. 79, 251 (1990)Google Scholar
  14. A. van Otterlo et al., Phys. Rev. B 52, 16176 (1995)Google Scholar
  15. H.P. Büchler, G. Blatter, Phys. Rev. Lett. 91, 130404 (2003)Google Scholar
  16. N.W. Ashcroft, N.D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976)Google Scholar
  17. H.P. Büchler, G. Blatter, Phys. Rev. A 69, 063603 (2003)Google Scholar
  18. O. Penrose, L. Onsager, Phys. Rev. 104, 576 (1956)Google Scholar
  19. A.F. Andreev, I.M. Lifshitz, Sov. Phys. JETP 29, 1107 (1967)Google Scholar
  20. A.J. Leggett, Phys. Rev. Lett. 25, 1543 (1970)Google Scholar
  21. F. Herbert et al., Phys. Rev. B 65, 014513 (2001); E. Frey, L. Balents, Phys. Rev. B 55, 1050 (1997); K. Gòral et al., Phys. Rev. Lett. 88, 170406 (2002)Google Scholar
  22. D. Pines, P. Nozieres, Theory of Quantum Liquids (The Perseus Books Group, 1970)Google Scholar
  23. G.F. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, 2005)Google Scholar
  24. G. Grüner, Density Waves in Solids (Perseus Publishing, Cambridge, Massachusetts, 2000)Google Scholar
  25. L. Van Hove, Phys Rev. 89, 1198 (1953)Google Scholar
  26. J.E. Hirsch, D.J. Scalapino, Phys. Rev. Lett. 56, 2732 (1986)Google Scholar
  27. L. Viverit et al., Phys. Rev. A 61, 053605 (2000)Google Scholar
  28. A.L. Fetter, J.D. Walecka, Quantum Many Particle Systems (Westview Press, Boulder, 1998)Google Scholar
  29. P.S. Jessen, I.H. Deutsch, Adv. At. Mol. Opt. Phys. 37, 95 (1996)Google Scholar
  30. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1972)Google Scholar
  31. A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover Publications, New-York, 1963)Google Scholar
  32. L. Salasnich, G. Mazzarella, F. Toigo, in preparation (2008)Google Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Dipartimento di Fisica “G. Galilei”Università degli Studi di PadovaPadovaItaly

Personalised recommendations