Comment on “Coherent shift of localized bound pairs in the Bose-Hubbard model”

We consider scattering of a single particle from an interaction-bound pair of particles in the one-dimensional Bose-Hubbard model. We show that the transmission probability of the single particle is always significantly smaller than unity. This invalidates the main result of L. Jin et al. [Phys. Rev. A 79, 032108 (2009)], where it is claimed that a single-particle wave packet can pass with unit probability through a bound-particle pair and coherently shift its position by one lattice site.

Figure 1

Transmission probability $T(k)$ of a single particle with relative quasimomentum $k$ through a bound-particle pair, for $U/\kappa =-10$ and total quasimomenta $K=0$ (red solid line) and $\left|K\right|=\pi$ (blue dashed line). Inset: single-particle transmission probability at $k=\pi /2$ (corresponding to maximal transmission for $\left|U\right|\to \infty$) versus interaction strength $\left|U\right|$.