Frustrated collisions and unconventional pairing on a quantum superlattice

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Published 5 October 2010 • Europhysics Letters Association
, , Citation M. Valiente et al 2010 EPL 92 10001 DOI 10.1209/0295-5075/92/10001

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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

3 Current address: Department of Physics & Astronomy, Aarhus University - DK-8000, Aarhus, Denmark, EU.

Dates

  1. Received 14 September 2010
  2. Accepted 20 September 2010
  3. Published
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0295-5075/92/1/10001

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.

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Accepted by M. Lewenstein

10.1209/0295-5075/92/10001