2006/05/31 by Iris Reichenbach, Andrew Silberfarb, R. Stock +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Non-Hermitian Physics #Quantum, superfluid, helium dynamics #cond-mat.other #physics.atom-ph #quant-ph
paper · pdf · doi:10.1103/physreva.74.042724
published as Phys. Rev. A 74, 042724 (2006) · 8 pages, 4 figures, accepted by PRA v3: some typos were corrected, published version
openalex publication_date 2006/10/31 · arxiv created 2006/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate a 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 are 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.