Superfluid helium interferometers

S uperfluid helium is a macroscopic quantum system, as are superconductors, gaseous Bose–Einstein condensates, and the interiors of neutron stars. The common feature of those disparate systems is a complex “order parameter” having magnitude and phase. The order parameter can be a Schrödinger-like wavefunction, or it can be some other function that reflects the system’s physical state. A macroscopic quantum state emerges in a sample of matter when the particles’ thermal de Broglie wavelength approaches the interparticle spacing. The particles then lose their individual identities and merge into a smoothed cloud that behaves as a single correlated quantum state. Matter in such a state differs markedly from a classical collection of distinguishable pointlike particles. For example, the unique quantum properties of superfluid He include zero viscosity, which allows it to flow around a torus indefinitely. Although superfluid He has been known and studied since 1938, there is still no complete microscopic theory that predicts the transition between normal liquid 4He at 2.18 K and the superfluid state at lower temperatures. However, two phenomenological theories explain almost all experiments to date.1 The first model, due to Lev Landau, is essentially thermodynamic. It describes the superfluid as a mixture of two interpenetrating components, one normal and one super, each with its own density (ρn and ρs for the normal and super components, respectively) and its own velocity field (vn and vs). The fluid’s total density is the sum of the densities of the two components, and each velocity field is determined independently by its own hydrodynamics. (The motion of the normal component is governed by the Navier–Stokes equation for viscous flow, and the super component in the absence of a temperature gradient is described by the Euler equation for an ideal inviscid fluid.) A complementary view, provided by Fritz London, Lars Onsager, and Richard Feynman, treats the superfluid as a macroscopic quantum state