Density correlations in ultracold Fermi systems within the exact Richardson solution

We discuss the occupation number correlations in an ultracold system of interacting fermionic atoms. For a system with a special energy-level distribution, viz. two multiply degenerate levels, explicit expressions for the correlation functions are derived in a canonical approach using the exact ground state wave function of the reduced BCS Hamiltonian. We evaluate the correlators numerically for different interaction strengths and find analytical expressions in some limiting cases. Due to the underlying fermionic nature of the pairs the occupations are predominantly anticorrelated and their statistics is a multinomial distribution.