A quasi-Hermitian pseudopotential for higher partial wave scattering

Abstract

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 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.

8 pages, 4 figures, accepted by PRA v3: some typos were corrected, published version

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Cited by in corpus (7)

• Few-body physics with ultracold atomic and molecular systems in traps
• Pseudo-potential treatment of two aligned dipoles under external harmonic confinement
• Analytical solutions for two atoms in a harmonic trap: p-wave interactions
• High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap
• Controlled collisions of two ultracold atoms in separate harmonic traps
• Scattering Hypervolume of Spin-Polarized Fermions
• Miscibility of Binary Bose-Einstein Condensates with $p$-wave Interaction