Physics – Quantum Physics
Scientific paper
2009-03-18
Physics
Quantum Physics
14 pages, 11 figures; typos and minor errors corrected, five references added, next-to-nearest neighbor hopping included in ex
Scientific paper
10.1103/PhysRevA.80.013404
We calculate numerically the exact energy spectrum of the six dimensional problem of two interacting Bosons in a three-well optical lattice. The particles interact via a full Born-Oppenheimer potential which can be adapted to model the behavior of the s-wave scattering length at Feshbach resonances. By adjusting the parameters of the corresponding Bose-Hubbard (BH) Hamiltonian the deviation between the numerical energy spectrum and the BH spectrum is minimized. This defines the optimal BH parameter set which we compare to the standard parameters of the BH model. The range of validity of the BH model with these parameter sets is examined, and an improved analytical prediction of the interaction parameter is introduced. Furthermore, an extended BH model and implications due to the energy dependence of the scattering length and couplings to higher Bloch bands at a Feshbach resonance are discussed.
Grishkevich Sergey
Saenz Alejandro
Schneider Philipp-Immanuel
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