Superfluidity Simulator: Quantum Vortices in Liquid Helium

simulator advanced ~12 min
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ρs/ρ = 0.82 — mostly superfluid

At 1.5 K, 82% of helium-4 is in the superfluid state. Rotating at 2 rad/s in a 5 mm container, approximately 3 quantized vortices form, each carrying one quantum of circulation.

Formula

ρs/ρ = 1 − (T/Tλ)^5.6
κ = h/m₄ = 9.97 × 10⁻⁸ m²/s
N_vortices ≈ 2m₄ω / h × πR²

Frictionless Flow

In 1937 Pyotr Kapitza in Moscow and John Allen and Don Misener in Cambridge independently discovered that liquid helium-4 below 2.17 K flows without any measurable viscosity. This temperature — the lambda point, named for the shape of the specific heat curve — marks a phase transition into a macroscopic quantum state. Below it, helium atoms undergo Bose-Einstein condensation into a single quantum wavefunction spanning the entire container.

The Two-Fluid Model

Lev Landau proposed that helium II behaves as if it were two interpenetrating fluids: a superfluid component with zero viscosity and zero entropy, and a normal component carrying thermal excitations (phonons and rotons). As temperature drops below Tλ, the superfluid fraction rises from 0% to nearly 100% near absolute zero. This model explains the fountain effect, second sound (temperature waves), and the anomalous thermal conductivity of helium II.

Quantized Vortices

When a superfluid is rotated, it cannot spin like a rigid body because the superfluid velocity field must be curl-free (irrotational). Instead, the rotation is accommodated by discrete vortex lines, each carrying exactly one quantum of circulation κ = h/m₄. These vortices have angstrom-scale cores and arrange themselves in a triangular lattice — directly analogous to magnetic flux vortices in type-II superconductors. This simulation visualizes the vortex lattice and counts vortices as you vary rotation speed.

Beyond Helium-4

Superfluidity appears in other systems: helium-3 becomes superfluid below 2.5 mK through fermionic Cooper pairing (Lee, Osheroff, and Richardson, Nobel Prize 1996), ultracold atomic gases form Bose-Einstein condensates at nanokelvin temperatures, and neutron superfluids flow in the interiors of neutron stars. The study of quantized vortices in these systems connects cryogenics to astrophysics, quantum computing, and fundamental tests of quantum mechanics.

FAQ

What is superfluidity?

Superfluidity is a quantum phase of matter where a liquid flows with zero viscosity. In helium-4, it occurs below the lambda point (2.17 K) due to Bose-Einstein condensation. The superfluid component can flow through nanoscale channels without friction, climb container walls via thin film creep, and sustain persistent currents indefinitely.

What are quantized vortices?

In a rotating superfluid, circulation is quantized in units of κ = h/m₄ ≈ 10⁻⁷ m²/s. Rather than rotating as a rigid body, the superfluid remains irrotational except at discrete vortex cores (about 1 angstrom wide) where the density drops to zero. These vortices arrange in a triangular Abrikosov-like lattice.

What is the two-fluid model?

Landau's two-fluid model treats helium II as a mixture of a superfluid component (zero viscosity, zero entropy) and a normal component (viscous, carries all the entropy). The ratio depends on temperature: at T=0 it is entirely superfluid; at Tλ it is entirely normal. This model explains second sound — temperature waves that propagate through the superfluid.

Why does helium-4 become superfluid but not helium-3?

Helium-4 atoms are bosons (integer spin) and undergo Bose-Einstein condensation at 2.17 K. Helium-3 atoms are fermions (half-integer spin) and must first form Cooper pairs (like electrons in a superconductor) before condensing, which occurs only below 2.5 mK — about 1000 times colder.

Sources

Embed

<iframe src="https://homo-deus.com/lab/cryogenics/superfluidity/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub