Pairing fluctuations in trapped Fermi gases

Fluctuations of the amplitude of the order parameter govern the properties of superconducting systems close to the critical transition temperature. In the BCS regime we examine the contribution of these pairing fluctuations to the superfluid order parameter for harmonically confined atomic Fermi gases. In the limit of small systems we obtain an expression for the space dependence of the fluctuations, in good agreement with the results of numerical calculations. In this limit we also predict a parity effect, i.e. that pairing fluctuations should show a maximum or a minimum at the centre of the trap, depending on the value of the last occupied shell being even or odd. We finally propose to detect pairing fluctuations by measuring the density-density correlation function as evaluated after a ballistic expansion of the gas.