Anomalous tunneling of bound pairs in crystal lattices

TL;DR

This paper introduces a new method for solving scattering problems involving bound pairs on a lattice, revealing that pairs can tunnel more easily than single particles near certain momenta due to a resonant state.

Contribution

A general and convergent method for calculating scattering and tunneling of bound pairs on lattices, applied to demonstrate anomalously high pair tunneling near specific momenta.

Findings

Pairs tunnel more easily than single particles near momentum .

High transmission coefficient approaching unity at certain momenta.

Existence of a two-body resonant state at the weak link.

Abstract

A novel method of solving scattering problems for bound pairs on a lattice is developed. Two different break ups of the hamiltonian are employed to calculate the full Green operator and the wave function of the scattered pair. The calculation converges exponentially in the number of basis states used to represent the non-translation invariant part of the Green operator. The method is general and applicable to a variety of scattering and tunneling problems. As the first application, the problem of pair tunneling through a weak link on a one-dimensional lattice is solved. It is found that at momenta close to \pi the pair tunnels much easier than one particle, with the transmission coefficient approaching unity. This anomalously high transmission is a consequence of the existence of a two-body resonant state localized at the weak link.