Quasi-one-dimensional scattering in a discrete model

Abstract

We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasi- momenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonance appear due to the non-separability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann- Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.

8 pages, 6 figures

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Repulsively bound atom pairs in an optical lattice
• Controlling a magnetic Feshbach resonance with laser light
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• Confinement induced resonances in anharmonic waveguides
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• Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential

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• Universal properties of Fermi gases in arbitrary dimensions
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• Two-body bound and edge states in the extended SSH Bose-Hubbard model
• An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
• Three-body repulsive forces among identical bosons in one dimension
• Probing the BCS-BEC crossover with persistent currents
• Theory of inelastic confinement-induced resonances due to the coupling of center-of-mass and relative motion
• Momentum-dependent pseudo-spin dimers of coherently coupled bosons in optical lattices
• Escape dynamics of Bose-Hubbard dimer out of a trap
• Universality and tails of long range interactions in one dimension