Short-range correlations and entropy in ultracold atomic Fermi gases

Zhenhua Yu

Tuesday, September 29, 2009, 1:15 PM
Matfys library

The correlations of atomic Fermi gases at short distances encapsulate essential thermodynamical information. We probe the finite temperature correlation through its relation to the free energy and entropy densities. In the low temperature limit the entropy is dominated by phonon excitations and the correlations increase as $T^4$. In the BEC limit, we calculate a boson model within the Bogoliubov approximation to show explicitly how phonons enhance the fermion correlations. In the high temperature limit, we show from the virial expansion that the correlations decrease as $1/T$. The correlations therefore reach a maximum at a finite temperature. We infer the general structure of the isentropes of the Fermi gas in the $T,-1/k_Fa$ plane, and the temperature dependence of the correlations in the unitary, BEC, and BCS limits. Our results compare well with measurements of the correlations via photoassociation experiments at higher temperatures.