Studies of bosons in optical lattices in a harmonic potential
The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics - Tập 42 - Trang 309-316 - 2007
Tóm tắt
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.
Tài liệu tham khảo
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)
T. Stöferle, H. Moritz, C. Schori, M. Köhl, T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004)
B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004)
M. Köhl, H. Moritz, T. Stöferle, C. Schori, T. Esslinger, J. Low Temp. Phys. 138, 635 (2005)
D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)
D. Van Oosten, P. van der Straten, H.T.C. Stoof, Phys. Rev. A 63, 054601 (2001)
W. Zwerger, J. Opt. B: Quantum Semiclass. Opt. 5, S9 (2003)
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)
G. Pupillo, E. Tiesinga, C.J. Williams, Phys. Rev. A 68, 063604 (2003)
S. Wessel, F. Alet, M. Troyer, G. Batrouni, Phys. Rev. A 70, 053615 (2004)
H. Kleinert, S. Schmidt, A. Pelster, Phys. Rev. Lett. 93, 160402 (2004)
A.F. Ho, M.A. Cazalilla, T. Giamarchi, Phys. Rev. Lett. 92, 130405 (2004)
L. Pollet, S. Rombouts, K. Heyde, J. Dukelsky, Phys. Rev. A 69, 043601 (2004)
L. Santos, M.A. Baranov, J.I. Cirac, H.U. Everts, H. Fehrmann, M. Lewenstein, Phys. Rev. Lett. 93, 030601 (2004)
K. Sengupta, N. Dupuis, Phys. Rev. A 71, 033629 (2005)
D. Heidarian, K. Damle, Phys. Rev. Lett. 95, 127206 (2005)
R.V. Pai, R. Pandit, Phys. Rev. B 71, 104508 (2005)
V.W. Scarola, S. Das Sarma, Phys. Rev. Lett. 95, 033003 (2005)
D.B.M. Dickerscheid, D. van Oosten, P.J.H. Denteneer, H.T.C. Stoof, Phys. Rev. A 68, 043623 (2003)
S.M. Giampaolo, F. Illuminati, G. Mazzarella, S. De Siena, Phys. Rev. A 70, 061601 (2004)
M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Weiman, E.A. Cornell, Science 269, 198 (1995)
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)
C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995)
F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)
A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)
J.R. Anglin, W. Ketterle, Nature 416, 211 (2002)
C.J. Pethick, H. Smith, Bose-Einstein condensation in dilute gases (Cambridge University Press, Cambridge, England, 2002)
J. Kinast, A. Turlapov, J.E. Thomas, Q. Chen, J. Stajic, K. Levin, Science 307, 1296 (2005)
A.M. Rey, G. Pupillo, C.W. Clark, C.J. Williams, Phys. Rev. A 72, 033616 (2005)
V. Bagnato, D. Kleppner, Phys. Rev. A 44, 7439 (1991)
W. Ketterle, N.J. van Druten, Phys. Rev. A 54, 656 (1996)
C. Schori, T. Stöferle, H. Moritz, M. Köhl, T. Esslinger, Phys. Rev. Lett. 93, 240402 (2004)
M. Köhl, H. Moritz, T. Stöferle, K. Günter, T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005)
M. Köhl, Phys. Rev. A 73, 031601 (2006)