On-site pairing and microscopic inhomogeneneity in confined lattice fermion systems

In order to explore a universal feature of atomic Fermi gases loaded on optical lattices, we make a systematic study of the particle density profile for one- and two-dimensional attractive Hubbard models with harmonic potential wells. Using the exact diagonalization scheme and the density-matrix renormalization group technique, we show that fine inhomogeneous zigzag patterns universally emerge in the above models. Theoretical and numerical analyses suggest that these structures originate from an effective repulsive interaction between tightly bound pairs and a breakdown of translational invariance. Furthermore, it is emphasized that the pattern obtained numerically in the two-dimensional model is the checkerboard type, which is very similar to results recently observed in a vortex core of high- Tc cuprate superconductor.