Matter-wave scattering from interacting bosons in an optical lattice

TL;DR

This paper derives an analytical formula for matter-wave scattering from interacting bosons in a 1D optical lattice, revealing a linear decay of inelastic cross section with increasing interaction strength.

Contribution

It introduces a new analytical approach to quantify inelastic scattering in the Bose-Hubbard model using Bogoliubov theory, highlighting interaction effects.

Findings

Inelastic cross section decays linearly with interaction strength.

Decay is independent of particle number, condensate depletion, and system size.

Provides analytical insight into matter-wave scattering in optical lattices.

Abstract

We study the scattering of matter-waves from interacting bosons in a one-dimensional optical lattice, described by the Bose-Hubbard Hamiltonian. We derive analytically a formula for the inelastic cross section as a function of the atomic interaction in the lattice, employing Bogoliubov's formalism for small condensate depletion. A linear decay of the inelastic cross section for weak interaction, independent of number of particles, condensate depletion and system size, is found.