16.5.4 Superfluidity

Superfluidity is a macroscopic quantum phenomenon in which a fluid flows with zero viscosity — that is, with absolutely no internal friction or resistance. It is one of the most striking examples of quantum mechanics manifesting at a macroscopic scale.

What is a Superfluid?

A superfluid is a state of matter in which a fluid behaves as if it has zero viscosity, allowing it to flow indefinitely without losing kinetic energy. This occurs when bosonic particles (particles with integer spin) undergo Bose-Einstein Condensation (BEC) — they all collapse into the same quantum ground state and behave as a single quantum entity.

Liquid Helium and the Lambda Point

The most well-studied superfluid is Liquid Helium-4. When cooled, helium-4 undergoes a phase transition at a critical temperature known as the Lambda Point ($\lambda$-point):

$T_{\lambda }=2.17\text{ K}$

The transition is named the lambda point because the shape of the heat capacity curve near this temperature resembles the Greek letter $\lambda$.

Properties of Superfluids

1. Zero Viscosity

Helium II flows through the narrowest capillaries and microscopic pores without any resistance. A normal fluid would be stopped by friction, but a superfluid passes through effortlessly.

2. The Rollin Film Effect

Because of zero viscosity, Helium II spontaneously forms an extremely thin film (approximately 30 nm thick) called the Rollin film. This film:

• Creeps up the walls of any container
• Flows over the rim
• Drips down the outside

This means a superfluid will escape any open container by climbing the walls — a dramatic demonstration of zero viscosity.

3. Infinite Thermal Conductivity

Helium II conducts heat with effectively infinite thermal conductivity. In a normal liquid, heat is transferred by slow molecular collisions. In Helium II, heat propagates as a wave called second sound — an internal convection wave that distributes heat almost instantaneously throughout the fluid.

A visible consequence: when Helium II is heated, it does not boil. Instead of forming bubbles (which require localized hot spots), the heat is distributed so rapidly that the liquid becomes perfectly still as it passes the lambda point.

Connection to Bose-Einstein Condensation

Superfluidity in Helium-4 is understood as a consequence of Bose-Einstein Condensation. Helium-4 atoms are bosons (integer spin). Below the lambda point, a macroscopic fraction of the atoms condense into the lowest quantum energy state, forming a single coherent quantum state. This collective quantum behaviour eliminates viscosity and gives rise to all the exotic properties of Helium II.

Helium-3 (a fermion) can also become superfluid, but only at much lower temperatures (~$2.5\times 10^{-3}\text{ K}$), where pairs of helium-3 atoms form bosonic Cooper-like pairs.

Summary