Scattering of two particles in a 1D lattice

Abstract

This study concerns the two-body scattering of particles in a one-dimensional periodic potential. A convenient ansatz allows for the separation of center-of-mass and relative motion, leading to a discrete Schrödinger equation in the relative motion that resembles a tight-binding model. A lattice Green's function is used to develop the Lippmann-Schwinger equation, and ultimately derive a multi-band scattering K-matrix which is described in detail in the two-band approximation. Two distinct scattering lengths are defined according the limits of zero relative quasi-momentum at the top and bottom edges of the two-body collision band. Scattering resonances occur in the collision band when the energy is coincident with a bound state attached to another higher or lower band. Notably, repulsive on-site interactions in an energetically closed lower band lead to collision resonances in an excited band.

11 pages, 3 figures

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Repulsively bound atom pairs in an optical lattice
• Bose-Fermi Mixtures in a Three-dimensional Optical Lattice
• Two-particle states in the Hubbard model
• Quantum liquid of repulsively bound pairs of particles in a lattice
• Negative quench induced excitation dynamics for ultracold bosons in one-dimensional lattices
• Tunnelling couplings in discrete lattices, single particle band structure and eigenstates of interacting atom pairs
• Two-channel Feshbach physics in a structured continuum
• Lattice Induced Resonances in One Dimensional Bosonic Systems
• Resonant Feshbach scattering of fermions in one-dimensional optical lattices