Superfluidity

Superfluidity is a property of certain fluids that can sustain flow without the ordinary dissipation associated with viscosity. It is a macroscopic manifestation of quantum mechanics, observed in liquid helium and ultracold atomic gases. Its characteristic features include persistent currents, quantized circulation, and unusual thermal transport. The description “frictionless fluid” requires qualification: nondissipative flow occurs within particular conditions, and superfluid systems can develop resistance through excitations or vortex motion. (rle.mit.edu)

Liquid helium and historical development

The best-known example is helium-4, which undergoes a phase transition into the superfluid phase, called helium II, at approximately 2.17 kelvin under its saturated vapor pressure. The transition is called the lambda transition because the heat capacity has a distinctive, sharply peaked temperature dependence. Above the transition, liquid helium is called helium I. Superfluidity therefore denotes a change within the liquid state, rather than liquefaction itself. (cds.cern.ch)

Pyotr Kapitza established superfluid behavior in helium-4 in the late 1930s. Fritz London connected the phenomenon with Bose–Einstein condensation, while Lev Landau developed a theory of its elementary excitations and flow properties in 1941. Landau received the 1962 Nobel Prize in Physics for pioneering theories of condensed matter, especially liquid helium. These developments helped establish superfluidity as a central subject of condensed matter physics. (nobelprize.org)

The other stable helium isotope, helium-3, becomes superfluid only at temperatures of a few millikelvin or less, depending on pressure. Its superfluid phases were discovered in 1972 by Douglas Osheroff, David Lee, and Robert Richardson, who shared the 1996 physics Nobel Prize for that discovery. Unlike helium-4, helium-3 requires a pairing mechanism to develop its superfluid state. (nobelprize.org)

Quantum coherence and particle statistics

Helium-4 atoms are bosons, whereas helium-3 atoms are fermions. Bosons can occupy the same quantum state, making a Bose–Einstein condensate possible. Fermionic superfluidity instead involves pairing: helium-3 atoms form Cooper pairs, whose collective ordering produces superfluid behavior. This mechanism is related to, but differs in its pairing structure from, conventional BCS theory of superconductivity. (nobelprize.org)

Superfluidity and condensation are closely related but are not interchangeable concepts. Condensation concerns occupation of a quantum state; superfluidity concerns the response of a system to motion and imposed flow. Observing condensation alone consequently does not establish superfluidity. Experiments on atomic gases use additional evidence, especially quantized vortices, to demonstrate it. (rle.mit.edu)

For a simple neutral superfluid, macroscopic quantum coherence can be represented by a complex order parameter with phase $\phi$. The superfluid velocity is related to spatial variation of this phase:

where $m$ is the mass of the condensed atom or pair and $\hbar$ is the reduced Planck constant. Thus flow is connected to the spatial organization of a quantum phase, rather than merely to independent particles moving through a container. (indico.cern.ch)

The two-fluid description

At nonzero temperature, helium II is described by the two-fluid model. Its total mass density is decomposed as

with superfluid and normal densities $\rho_s$ and $\rho_n$. These are interpenetrating dynamical components of one substance, not two chemically distinct liquids. The normal component carries entropy and exhibits viscous behavior; the superfluid component carries no entropy in this description. Their proportions depend on temperature, with the superfluid fraction approaching unity at zero temperature and vanishing at the lambda transition. (cds.cern.ch)

This model explains why different measurements can suggest contradictory viscosities. Flow through a sufficiently narrow channel can be dominated by the superfluid component, while an oscillating object still experiences damping from the normal component. Heat transport can involve counterflow: the normal component moves away from a heat source while the superfluid component moves toward it. (cds.cern.ch)

Two wave modes are also possible. First sound is predominantly an ordinary pressure or density wave. Second sound is predominantly a temperature and entropy wave, associated with opposing motion of the two components. It demonstrates that heat can propagate as a wave rather than solely through diffusive transport. (cds.cern.ch)

Critical velocities and quantized vortices

Landau’s theory relates superfluid flow to the spectrum of quasiparticle excitations. In helium-4 these include long-wavelength phonons and excitations called rotons. Creating excitations can permit a moving fluid to lose energy, so nondissipative flow is restricted by a critical velocity. In practical experiments, vortex formation can cause breakdown at velocities well below the threshold for creating rotons. (nobelprize.org)

For a simple superfluid, circulation around a closed contour is quantized:

where $n$ is an integer. Rotation can therefore produce quantized vortices, each carrying discrete circulation, rather than unrestricted rigid-body rotation. Between vortex cores, the flow is locally irrotational. Vortex generation, interaction, and motion provide routes to dissipative behavior despite the absence of ordinary superfluid viscosity. (indico.cern.ch)

Atomic gases and cryogenic applications

Ultracold gases provide controllable systems for investigating superfluidity. In 2005, researchers observed vortex lattices in a strongly interacting gas of lithium-6 atoms, supplying direct evidence of fermionic superfluidity. A Feshbach resonance allowed interactions to be tuned across the crossover between a condensate of tightly bound molecules and a superfluid of more loosely bound fermion pairs. (rle.mit.edu)

Superconductivity is closely related to superfluidity, but involves electrically charged particles and additional electromagnetic effects. Superfluid helium itself has an important role in cryogenics because of its exceptionally effective heat transport. At CERN, helium at 1.9 K cools the superconducting magnets of the Large Hadron Collider, while second-sound measurements can help locate localized heating in superconducting radio-frequency cavities. (nobelprize.org)