Bose condensation and the static pair correlation function in4He

J. Mayers

J. Mayers

Markus Holzmann, Yvan Castin

A. S. Jensen, O. Sørensen, D. V. Fedorov +1 more

Paweł Zin, Marek Trippenbach, Mariusz Gajda

The pair-correlation function is one of the basic quantities to characterize the coherence properties of a Bose-Einstein condensate. We calculate this function in the experimentally important case of a zero temperature Bose-Einstein condensate in a metastable triplet helium state using the variational method with a pair-excitation ansatz. We compare our result with a pair-correlation function obtained for the hard-sphere potential with the same scattering length. Both functions are practically indistinguishable for distances greater than the scattering length. At smaller distances, due to interatomic interactions, the helium condensate shows strong correlations.

Alexander Yu. Cherny

Pair wave functions (PWF) which are eigenfunctions of the reduced density 2-matrix are considered for a homogeneous Bose liquid. With the Bogoliubov principle of the correlation weakening it is proved that the distribution of the "dissociated" pair states over momenta is exactly the product of the single-particle distribution functions. Thus, the "dissociated" pair states are naturally classified as condensate-condensate, condensate-supracondensate and supracondensate-supracondensate ones provided the Bose-Einstein condensate exists. The condensate-condensate as well as condensate-supracondensate PWF are expressed in terms of the averages of products of the creation and destruction Bose operators. This leads to the simple interpretation of the anomalous averages as the "scattering parts" of the condensate-condensate and condensate-supracondensate PWF. It is shown that in contrast to the Fermi liquid, the appearance of the anomalous averages for the Bose liquid does not necessarily mean that there exist bound states of pairs of particles. The PWF in the Hartree-Fock-Bogoliubov (HFB) approach are found. Given the density of the condensate is not zero, there are no bound pair states in the HFB scheme. The expansion of the pair correlation function in the set of PWF is very useful in order to take into account both short-range and long-range spatial correlations. Applications (possible and already realized) of the formalism developed are discussed.