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Q: Quantenoptik
Q 321: Bose-Einstein Kondensation II
Q 321.6: Vortrag
Mittwoch, 6. März 2002, 17:45–18:00, HS 22/B01
BEC in the optical lattice; the 1-dimensional solid approach — •Matt Kalinski1, G Metikas1, E Arimondo2, and W P Schleich1 — 1Abteilung für Quantenphysik, Universität Ulm, Ulm, Germany — 2Dipartimento di Fisica, Università di Pizza, Pisa, Italy
We consider a dilute, weakly interacting Bose-Einstein condensate prepared in a 3-dimensional harmonic trap. The harmonic trap is then switched off and an 1-dimensional optical lattice periodic potential is applied while the condensate is left to expand in the other two dimensions. Within the mean-field framework we have to deal with a Mathieu equation with an extra non-linear term representing the self-interaction of the condensate. Applying perturbation over the weak self-interaction we consider two regimes for the strength of the optical lattice; weak-binding and tight-binding. In each case we find the effective optical lattice which approximates the non-liner term and yields satisfactory agreement with the experimental results. Furthermore, the band structure in the presence of the non-linear term is investigated as well as the interband transition probabilities within the Landau-Zener theory. In addition to these analytical considerations a numerical examination of the non-linear Mathieu equation is performed yielding satisfactory agreement with both the analytical results and the experiment.