Quasi-Hermitian pseudopotential for higher partial wave scattering

Iris Reichenbach, Andrew Silberfarb, René Stock, Ivan H. Deutsch
2006 Physical Review A. Atomic, Molecular, and Optical Physics  
We formulate a new quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete set of biorthogonal wave functions that can be used as a basis to expand and diagonalize other two-body Hamiltonians. We demonstrate this procedure for the case of ultracold atoms in a polarization-gradient optical lattice, interacting pairwise when two atoms
more » ... re transported together from separated lattice sites. Here the pseudopotential depends explicitly on the trapping potential. Additionally, we calculate the location of trap-induced resonances for higher partial waves, which occur when a molecular eigenstate is shifted to resonance with a trap eigenstate. We verify the accuracy of the pseudopotential approach using a toy model in which a square well acts as the true interaction potential, and see excellent agreement.
doi:10.1103/physreva.74.042724 fatcat:kx3g4dskkjb3diopwsqdk6wofy