Fractional Excitations in Cold Atomic Gases

Jens Honer(1), J. C. Halimeh(2), U. Schollwöck(2), H.P. Büchler(1)

(1) Institut für theoretische Physik III, Universität Stuttgart,
(2) Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München

In this letter, we analyze the decay of single-article excitations into fractional excitations in a tilted one-dimensional Bose-Hubbard model.
We find that in the limit of large on-site interaction and lattice tilt, the fractional excitations behave like hard core bosons with repulsive nearest-neighbor interaction. An analytical expression for the time evolution of a single-particle excitation is derived, giving rise to a repulsively bound state of fractional excitations above a critical center of mass momentum $2 \pi/3$. DMRG simulations on the original tilted Bose-Hubbard model confirm our results, and allow for probing beyond the effective model including higher-order processes and finite-size effects.