Inelastic Confinement-Induced Resonances in Low-Dimensional Quantum Systems

A theoretical model is presented describing the confinement-induced resonances observed in the recent loss experiment of Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)]. These resonances originate from possible molecule formation due to the coupling of center-of-mass and relative motion. A corresponding model is verified by ab initio calculations and predicts the resonance positions in 1D as well as in 2D confinement in agreement with the experiment. This resolves the contradiction of the experimental observations to previous theoretical predictions.Comment: 5 pages, 4 figure

Ab-initio determination of Bose-Hubbard parameters for two ultracold atoms in an optical lattice using a three-well potential

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.Comment: 14 pages, 11 figures; typos and minor errors corrected, five references added, next-to-nearest neighbor hopping included in extended Bose-Hubbard mode

Non-perturbative theoretical description of two atoms in an optical lattice with time-dependent perturbations

A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et al. [Phys. Rev. A 84, 062710 (2011)]. It allows presently to treat any time-dependent external perturbation of the lattice potential up to quadratic order. Example calculations of the experimentally relevant cases of an acceleration of the lattice and the turning-on of an additional harmonic confinement are presented.Comment: 8 pages, 6 figure

Feshbach resonances of harmonically trapped atoms

Employing a short-range two-channel description we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a new parameterization of the energy-dependent scattering length which differs from the one previously employed. We validate the model by comparison to full numerical calculations for Li-Rb and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.Comment: 4 pages, 2 figures; revised version with extension to anisotropic traps and new paragraph on trap-induced molecules in excited band