Accuracy of pairing theory for a trapped magnetic dipole fermion gas

Pairing properties of a trapped fermion gas consisting of atoms with magnetic dipole moment are studied using the Hartree-Fock-Bogoliubov theory (HFB) and the results are compared with those obtained from the exact diagonalization approach (EDA). It is shown that HFB underestimates two-body correlations and gives quite different atom-atom correlations than the results in EDA. Extended time-dependent HFB (ETDHFB), which is derived from the truncation of equations of motion for reduced density matrices, is also applied and it is found that the difficulties of HFB can be remedied by ETDHFB.