Bose Condensate in Superfluid 4He and Momentum Distributions by Deep Inelastic Scattering

Abstract

In 1938 London [1,2] offered an explanation of the observation earlier that year of superfluid behavior in liquid 4He when it is cooled below a critical temperature of 2.17 °K. He argued that the superfluid transition was analogous to the Bose condensation of an (ideal) gas of non-interacting atoms obeying the same Bose-Einstein spin-statistics relation as 4He atoms. This relation requires the many-atom wave function to be completely symmetric in the atomic coordinates, resulting in a preference for the atoms to occupy the same single-particle states. For a finite system of atoms the momenta are quantized in spacings proportional to the inverse of the system size. At high temperatures the fraction of atoms occupying any one of the momentum states also scales as the inverse of the size. However, as the temperature is reduced below a critical Bose condensation temperature a significant fraction of the atoms, independent of the system size, begins to occupy the zero-momentum state. The Bose condensate fraction of an ideal gas approaches one at zero temperature. For 4He, by analogy, at high temperatures in the normal fluid the condensate fraction should be zero, but as temperatures are reduced below the superfluid transition temperature the condensate fraction should rise to a non-zero value. The effect of the strong interactions among the (non-ideal) 4He atoms is to deplete the zero temperature condensate fraction from one in an ideal gas to a value much less than one for 4He. While the analogy between superfluidity and Bose condensation is imperfect, the concept of a Bose condensate in the superfluid phase has survived. A variety of increasingly sophisticated many-body calculations have predicted a condensate fraction of about 10 % at zero temperature in superfluid 4He at SVP. Because of the importance of superfluidity and the related phenomenon of superconductivity to condensed matter physics, this simple prediction has motivated a more than twenty year effort involving up to one hundred scientists to measure the Bose condensate fraction in 4He.