Lattice Induced Resonances in One Dimensional Bosonic Systems

TL;DR

This paper investigates how lattice-induced resonances affect two-particle spectra and bound state formation in one-dimensional bosonic systems, revealing novel coupling effects and providing an effective Hamiltonian for many-body analysis.

Contribution

It introduces an effective atom-dimer Hamiltonian that accurately models resonant effects and reveals parity-dependent coupling phenomena in 1D bosonic lattices.

Findings

Lattice resonances create bound states above and below the scattering continuum.

The dimer dispersion relation is significantly altered by lattice effects.

Parity of the dimer state influences the atom-dimer coupling mechanism.

Abstract

We study the resonant effects produced when a Feshbach dimer crosses a scattering continuum band of atoms in an optical lattice. We numerically obtain the exact spectrum of two particles in a one-dimensional lattice and develop an effective atom-dimer Hamiltonian that accurately captures resonant effects. The lattice-induced resonances lead to the formation of bound states simultaneously above and below the scattering continuum and significantly modify the curvature of the dimer dispersion relation. The nature of the atom-dimer coupling depends strongly on the parity of the dimer state leading to a novel coupling in the case of negative parity dimers. From the exact solutions we extract the dimer Wannier function from which we quantitatively determine the effective Hamiltonian parameters for a many-body description.