Density correlations in ultracold Fermi systems within the exact Richardson solution

Abstract

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 wavefunction of the reduced BCS Hamiltonian. We evaluate the correlators numerically for different interaction strength and find analytical expressions in some limiting cases. Due to the underlying fermionic nature of the pairs the occupations are predominantly anti-correlated and their statistics is a multinomial distribution.

8 pages, 7 figures, minor revisions, references added, to be published in PRA

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Cited by in corpus (6)

• Dynamical correlation functions of the mesoscopic pairing model
• Fermion- and Spin-Counting in Strongly Correlated Systems
• Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime
• Fermion- and spin-counting in strongly correlated systems in and out of thermal equilibrium
• Single-particle versus many-body phase coherence in an interacting Fermi gas
• Electron-hole symmetry and solutions of Richardson pairing model