Frustrated collisions and unconventional pairing on a quantum superlattice

TL;DR

This paper analytically solves the scattering and binding of two spin-1/2 fermions on a one-dimensional superlattice, revealing new bound states, continuum states, and frustrated collisions due to the superlattice structure.

Contribution

It provides an exact analytical solution for fermion interactions on a superlattice, including bound states and scattering states with a generalized Bethe ansatz.

Findings

Exact bound states and scattering states identified

Discovery of bound states in the continuum linked to interband transitions

Frustrated collisions occur in certain occupancy conditions

Abstract

We solve the problem of scattering and binding of two spin-1/2 fermions on a one-dimensional superlattice with a period of twice the lattice spacing analytically. We find the exact bound states and the scattering states, consisting of a generalized Bethe ansatz augmented with an extra scattering product due to "asymptotic" degeneracy. If a Bloch band is doubly occupied, the extra wave can be a bound state in the continuum corresponding to a single-particle interband transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision.