The Surface Region of Superfluid $^4$He as a Dilute Bose-Condensed Gas

TL;DR

This paper investigates the surface region of superfluid helium-4, demonstrating that atoms form a dilute Bose-Einstein condensate due to negligible collisions and long-range interactions, and derives a generalized Gross-Pitaevskii equation for this system.

Contribution

It introduces a generalized Gross-Pitaevskii equation for the surface BEC in superfluid helium-4, valid at all temperatures, linking the surface condensate to the bulk properties.

Findings

Numerical evidence supports 100% surface BEC at T=0.

The derived equation describes the inhomogeneous condensate wave function.

Surface BEC amplitude vanishes at the bulk transition temperature.

Abstract

In the low-density surface region of superfluid $^4$He, the atoms are far apart and collisions can be ignored. The only effect of the interactions is from the long-range attractive Hartree potential produced by the distant high-density bulk liquid. As a result, at $T=0$, all the atoms occupy the same single-particle state in the low-density tail. Striking numerical evidence for this 100\% surface BEC was given by Pandharipande and coworkers in 1988. We derive a generalized Gross-Pitaevskii equation for the inhomogeneous condensate wave function $\Phi(z)$ in the low-density region valid at all temperatures. The overall amplitude of $\Phi(z)$ is fixed by the bulk liquid, which ensures that it vanishes everywhere at the bulk transition temperature.