  We study the particle-hole symmetry in the Hubbard model using ultracold
fermionic atoms in an optical lattice. We demonstrate the mapping between
charge and spin degrees of freedom and, in particular, show the occurrence of a
state with "incompressible" magnetisation for attractive interactions. Our
results present a novel approach to quantum simulation by giving access to
strongly-correlated phases of matter through an experimental mapping to easier
detectable observables.
