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Short-range correlations and entropy in ultracold atomic Fermi gases

### Zhenhua Yu

**Tuesday, September 29, 2009, 1:15 PM**

Matfys library

**Abstract**:

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.