Frustrated collisions and unconventional pairing on a quantum superlattice

¹ Institute of Electronic Structure and Laser, FORTH - GR-71110 Heraklion, Crete, Greece, EU
² Institut für Physik, Humboldt-Universität zu Berlin - D-12489 Berlin, Germany, EU

Received: 14 September 2010
Accepted: 20 September 2010

Abstract

We consider the problem of scattering and binding of two interacting spin-(1/2) fermions on a one-dimensional tight-binding superlattice with a period of twice the lattice spacing. We solve the problem analytically for all ranges of parameters of the system. We find that, for the non-trivial case of singlet states, both bound and scattering wave functions consist 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 inter-band transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision.