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Journal of Experimental and Theoretical Physics

Investigation of the temperature dependence of the density of the Bose condensate in helium-4 in connection with the superfluidity phenomenon

E. V. Dokukin, Zh. A. Kozlov, Vadim A. Parfenov, A. V. Puchkov

Published Dec 1, 1978• 3 citations
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As was shown by Einstein in 1924, Bose-Einstein statistics gives rise to a phase transition in which a macroscopic part of a gaseous state condenses into a phase with ground state properties, offering a unique view on the behavior of matter at zero temperature. From the very start the nature of Bose-Einstein condensation (BEC) has provoked statements concerning its relation with respect to superconductivity in electron gases (Einstein 1925) and the superfluidity of liquid helium (London 1938), but this connection is not easily grasped experimentally. Remarkably, although the concept of BEC appears routinely in very different contexts, ranging from excitons in semiconductors to nuclear matter, it had never been observed in its pure form, i.e., in a gaseous phase, until in 1995 BEC in ultracold Rb vapor was reported by Cornell and Wieman. Bose-Einstein condensation is probably the most exciting phenomenon currently under experimental investigation in ultracold atomic gases. In the tutorial the physics will be addressed which is at the roots of the current interest of BEC in atomic gases.
Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0:77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9, before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. A surface dispersion relation was calculated from imaginary-time density-density correlations. Similar calculations of the superfluid density throughout He-4 droplets doped with linear impurities (HCN)(sub n) are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the first solvation layer. This effective normal fluid exhibits temperature dependence similar to that of a two-dimensional helium system.
Earlier it has been shown that the properties of superfluid helium four have an intimate connection with a non-vanishing coherent pairing as well as the generalized Bose-Einstein condensation. Here, the nature of condensation for an interacting Bose system is re-examined. It is shown that, under conditions of constant temperature and pressure, minimization of the Gibbs free energy leads to a generalized condensation of the type first proposed by Girardeau. Extrapolation of these ideas to quasiparticle models of interacting Bose systems such as helium-II leads to the conclusion that the condensation in momentum space should also be regarded as generalized in the same sense. A bonus of this approach is the disappearance of macroscopic fluctuations in the density encountered in the usual theory of the condensed ideal Bose system.