  We study ultracold fermionic atoms trapped in a three dimensional optical
lattice by combining the real-space dynamical mean-field approach with
continuous-time quantum Monte Carlo simulations. For a spin-unpolarized system
we show results the density and pair potential profile in the trap for a range
of temperatures. We discuss how a polarized superfluid state is spatially
realized in the spin-polarized system with harmonic confinement at low
temperatures and present the local particle density, local magnetization, and
pair potential.
