Impurity effects on the quantum coherence of a few-boson system

The impurity effects on the quantum coherence of a few-boson system are studied within the two-site Hubbard model. Periodical collapses and revivals of coherence occur in the presence of either polarized or unpolarized fermionic impurities. The relative strength $U_{BF}/U_{BB}$ of the boson-fermion versus the boson-boson interactions plays a key role in the coherence revivals. As the average filling of the impurity increases, the coherence revivals remain nearly unaffected for $U_{BF}/U_{BB}=z$ ($z\in Z$ is an integer) while the odd revival peaks are damped for $U_{BF}/U_{BB}=z+1/2$, in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.