The Liquid That Climbs Out of Its Own Container

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Cool helium to two degrees above absolute zero and it stops behaving like a liquid: it creeps up the wall of its flask as a film thinner than a virus and empties itself over the rim. No pump, no tilt, no leak — and no friction to stop it. The reason is that the atoms have stopped being separate atoms at all.

Picture a small glass vessel. Open at the mouth, no bigger than a thimble. Inside it sits a clear liquid, so clear that when you look at it you cannot be sure whether the vessel is full or empty. The vessel hangs in the middle of an evacuated glass jar, and everything around it is about two degrees above absolute zero. Then you start waiting. After a while a droplet gathers on the outer surface of the vessel, down near its base. Then another. Nobody tilted it, there is no crack in the glass, no hole in the bottom. The liquid climbed its own wall, crossed the rim, ran down the outside and escaped. Lower that same vessel into the liquid while it is empty and the reverse happens: the liquid climbs the wall, pours in, and keeps flowing until the two levels match. No container without a lid can hold it.

This liquid is helium. More precisely, helium below two point one seven kelvin; helium on the far side of the threshold physicists call the lambda point. And the secret behind those droplets is a rule of nature we never meet in everyday life.

The story starts in nineteen oh eight, in the Dutch city of Leiden. After years of work, Heike Kamerlingh Onnes managed to liquefy helium. What he had in his hands boiled at four point two kelvin, was seven times lighter than water, and was very nearly invisible. When he kept cooling it, the oddities began: the helium refused to freeze. Every known substance crystallises if you chill it far enough, yet helium at ordinary pressure stays liquid even if you take it all the way down to absolute zero. But something larger was hiding in those days that nobody had noticed, slipping quietly past the measuring instruments.

In nineteen thirty-two, when the Leiden team measured helium's heat capacity carefully, they found a sharp peak on the graph: at two point one seven kelvin the liquid was turning abruptly into something else entirely. Because the shape of that peak resembled the Greek letter lambda, the threshold came to be called the lambda point. The liquid above it was named helium one, the liquid below it helium two. The same atoms, the same vessel, the same pressure; and yet they behaved like two different substances.

The first visible signature of helium two had been sitting in front of laboratory workers' eyes for years. As you cool boiling liquid helium, exactly at two point one seven kelvin the bubbles stop all at once, and the thrashing liquid goes as still as a pane of glass. The boiling has not ended; the liquid keeps evaporating. It simply no longer makes bubbles, because the way it carries heat to its surface has completely changed.

In the mid nineteen thirties, working in Oxford, Bernard Rollin noticed that heat measurements made with helium two were leaking from a place they had no business leaking from. The walls of the vessel were carrying heat. The only explanation was a thin film of liquid covering every part of the wall, and that film was moving. The film that carries his name today is about thirty nanometres thick; roughly a hundred atoms stacked on top of one another. It climbs the wall, flows at speeds reaching twenty centimetres a second, and at colder temperatures can go as high as thirty-five.

There is a fine point here. A liquid wetting a wall is not in itself extraordinary. Water too creeps a few microns up the side of a glass; the wetness clinging to a teaspoon is the same thing. What is extraordinary is that the film does not stop. In an ordinary liquid a layer that thin is pinned in place by its own internal friction; the moment it tries to flow, it brakes itself. In helium two there is no such brake. The film stuck to the wall sees the smallest difference in level, or in temperature, and begins to flow without losing anything at all, using the rim of the vessel as a siphon.

Two separate groups proved that the friction really had vanished, right at the start of nineteen thirty-eight. In his Moscow laboratory, Pyotr Kapitza pushed helium two through the gap between two polished discs half a micron apart and found that the liquid's resistance to flowing had dropped by a factor of at least several thousand. In those same days, in the English city of Cambridge, John Allen and Don Misener ran the liquid through glass capillaries finer than a human hair and found something even more unsettling: the flow rate barely depended on the applied pressure at all. The harder you push a liquid, the faster it ought to move; helium two did not recognise the rule. In the January issue of a weekly science journal published in London, the two papers appeared side by side. Borrowing from superconductivity, Kapitza named this state superfluidity. Forty years later, in nineteen seventy-eight, part of the Nobel Prize in Physics went to him.

And it did not end there. That same year, Allen and Harry Jones fitted a small glass tube with a narrowing mouth, packed it with fine compressed powder, and then warmed the powder slightly. The helium rushed from the heated side towards the mouth and shot upward like a thin fountain, centimetres high. You heat a liquid, and it sprays upward. Explaining that required rebuilding, from the ground up, the idea of what the liquid was.

The starting point of the new idea was the fact that helium does not freeze. For a solid to form, atoms have to settle into their places. The helium atom is extremely light, and the attraction it forms with its neighbour is incredibly weak. Quantum mechanics, meanwhile, allows no particle to come to a complete stop; even in the coldest state a residual jitter remains, called zero point motion. In helium that leftover motion is stronger than the attraction that would hold the atoms together. The atoms cannot settle, no lattice can be built. If you want to freeze the liquid you have to apply about twenty-five atmospheres of pressure. So when we study helium two, what stands in front of us is a liquid in which the quantum behaviour of the atoms is not an accident but the thing that sets the character of the entire substance.

The second step concerns the identity of helium atoms. The overwhelming majority of naturally occurring helium is helium four: two protons, two neutrons, two electrons. Add up the spins and you get zero, and that makes it a boson. Bosons, unlike fermions, have no rule forbidding them to share the same quantum state; on the contrary, they prefer to pile up. As the temperature falls, the wave-like spread of each atom widens; at a certain point that spread exceeds the distance between atoms, and saying "this atom is here, that one is over there" loses its meaning. This was exactly the result Bose and Einstein calculated in the mid nineteen twenties: in a sufficiently cold collection of bosons, a large fraction collapses into a single quantum state, a single shared wave. In nineteen thirty-eight, Fritz London proposed that this was the root of helium two's strangeness.

We have to be honest here, because popular accounts push the analogy too far. Helium two is not the ideal Bose gas of the textbooks; it is a dense liquid whose atoms interact fiercely with one another. Measurements show that the fraction of atoms actually collapsed into the shared state stays around ten percent. The clean version from the books was only built in the laboratory in nineteen ninety-five, when dilute clouds of atoms were cooled down to nanokelvin. So the mechanism that gives rise to helium two is a relative of quantum condensation, not the same thing; that does not make it any less astonishing, only a harder problem.

The description that finally gathered every experiment under one roof was this: treat helium two as though it behaves like a mixture of two interpenetrating liquids. László Tisza threw the idea out in nineteen thirty-eight, and Lev Landau set it on solid ground in nineteen forty-one. In this description, one part of the liquid is normal: it has viscosity, it carries heat and disorder. The other part is superfluid: it has no friction, it carries no entropy at all, it knows nothing about temperature. As the temperature drops below the lambda point, the superfluid share grows, and approaching absolute zero it covers very nearly all of the liquid.

This is worth stressing: there are not really two separate liquids in the vessel. You cannot separate a glass of helium two into two with a centrifuge. What we call the normal part is the sum of the thermal excitations moving through the liquid; Landau described them as sound vibrations and as short-wavelength swirls he named rotons. As the temperature rises, the number of these excitations grows and the fraction we call normal liquid swells. Elia Andronikashvili measured this directly in nineteen forty-six: he placed a stack of thin discs inside helium two and set them swinging like a torsional pendulum. The discs could only drag the normal part along; from the pendulum's period you could read off how much of the liquid was superfluid at which temperature.

With this description, the fountain becomes intelligible. The pores of the compressed powder are too narrow to let the normal part through, but they are no obstacle at all to the superfluid part. Heating the powder lowers the superfluid fraction in that region, and the liquid starts pulling superfluid in from outside to restore the balance. Because the inflowing liquid brings no entropy with it, pressure builds up, and the only way out is the narrow mouth. Heat flinging a liquid upward is really a temperature difference being converted directly into a pressure difference.

Why the friction falls exactly to zero comes out of the same framework. For a liquid to lose energy to an obstacle, it has to create an excitation inside itself. Landau wrote down the energy-momentum relation of the excitations in helium and drew a simple conclusion: below a certain speed, a flowing superfluid cannot create any excitation at all, because there is no way to conserve energy and momentum at the same time. A flow with no channel for losing energy does not slow down. In practice, something else brakes helium well below that theoretical limit, and that something is the loveliest detail of superfluidity.

A superfluid cannot rotate in any way it likes. The rule Lars Onsager pointed to in nineteen forty-nine and Richard Feynman developed in nineteen fifty-five is this: rotation can only be carried in discrete packets. If you slowly start spinning a bucket of helium two, the liquid does not turn with the bucket; it just sits there. As you increase the rotation speed, at some threshold the first vortex line appears inside the liquid: a core almost a single atom wide, the circulation around it exactly one fixed quantum, a twist running from end to end. Spin it faster and a second vortex is born, then a third, and they push one another apart into a regular lattice. In nineteen seventy-nine, at Berkeley, this vortex lattice was photographed; the mark a quantum rule leaves on a macroscopic object showed up as a set of orderly dots.

The most unexpected prediction of the two-part description had to do with heat. In ordinary matter, heat advances by spreading: a hot region warms its neighbour, that one warms the next, and the temperature distribution blurs and flattens with time. That is not what happens in helium two. Because the normal and superfluid parts can flow in opposite directions, a wave carrying heat can travel through the liquid without any matter moving on balance at all. Raise the temperature at one spot and the hot region does not blur away like a drop of red dye; it moves like sound, it reflects, it interferes, it sets up standing waves.

Theory asked for it, and measurement confirmed it. In nineteen forty-four in Moscow, Vasily Peshkov used a thin electrically heated wire at one end and a very sensitive thermometer at the other to set up standing temperature waves inside helium two, and read off their speed: about twenty metres per second. Roughly a tenth of the speed of ordinary sound in the liquid. This phenomenon, called second sound, falls to zero as you approach the lambda point; once the superfluid part is exhausted, so is the carrier. The same effect was measured in dilute atomic clouds in twenty thirteen; heat travelling as a wave is not a piece of acrobatics peculiar to helium, but a general signature of superfluidity.

This has a direct counterpart in engineering. A liquid that carries heat as a wave has an effective thermal conductivity hundreds of times that of the best metals; on top of that it seeps into every surface by itself, and because it makes no bubbles it does not disrupt the transfer of heat. This is exactly why the superconducting magnets of the Large Hadron Collider, near Geneva, run below the lambda point, at one point nine kelvin; a hundred and twenty tonnes of helium is circulated to keep the facility cold. The coolness of the largest machine in the world leans on the same habit as the liquid that climbs out of its own container.

And what about a liquid that is not made of bosons? Helium's second stable variety, helium three, is one neutron short in its nucleus, so the atom's total spin is a half and it is a fermion. Fermions cannot pile into the same state; before they can build a shared wave they have to pair up two by two and behave like bosons. This is what electrons do in superconducting metals, and for it to happen in helium three takes an unimaginable cold. In nineteen seventy-two, at Cornell University in the United States, Douglas Osheroff, Robert Richardson and David Lee, while actually looking for something else, saw helium three turn superfluid along the melting curve at about two point five millikelvin; that is, a few thousandths of a degree above absolute zero. What is more, there was not one superfluid phase but several: because the paired couples keep their spins and their orbital rotation, this liquid is sensitive to direction and responds to a magnetic field. The three-way discovery took the nineteen ninety-six Nobel Prize in Physics.

Fermions pairing up and turning superfluid carries us far outside the laboratory. The interior of a neutron star is the core of a collapsed star squeezed down to about twenty kilometres across; most of its matter is neutrons, and a neutron is a fermion too. What theorists have been saying since the nineteen sixties is that these neutrons also form pairs and go superfluid. Even at hundreds of millions of degrees, the density is so high that the conditions for pairing are met.

This has an observable consequence, because neutron stars rotate. When a superfluid rotates, it builds quantised vortex lines, just as in the bucket in the laboratory. In a neutron star turning ten times a second, these lines are so dense that hundreds of them fall on every square millimetre of a cross-section. The star's outer crust, meanwhile, is a crystal, and the vortices can snag on the nuclei of that crust and stay pinned. As the star slows down the crust is braked, while the superfluid inside cannot slow along with it because of its pinned vortices, and the speed difference between the two grows. When the difference passes a threshold, the vortices tear loose all together, hand the angular momentum they were holding over to the crust, and the star's rotation rate suddenly jumps. Astronomers call these abrupt speed-ups glitches. The first was seen in nineteen sixty-nine, in the pulsar in the constellation Vela, the Vela pulsar for short; the jump in rotation frequency was of the order of one part in a million. Philip Anderson and Naoki Itoh put forward the idea of vortices tearing loose in nineteen seventy-five, and it still stands as the strongest explanation.

There is a more recent trace as well, and one unafraid of being disputed. The neutron star inside the supernova remnant called Cassiopeia A is only a few hundred years old, which makes it one of the youngest examples humanity has been able to watch. In data gathered over years by NASA's X-ray satellite Chandra, this young star appeared to be cooling unusually fast. In twenty eleven, two separate groups suggested the reason might be that the neutrons in the star's core have begun pairing up only in this recent period; couples forming and breaking constantly sends the production of neutrinos, which carry the heat away, shooting upward. By the calculation, the threshold for neutron pairing is around five hundred million degrees. But the measured cooling rate was pulled downward as the detector calibration was corrected, and the matter has not closed; other mechanisms that could speed up neutrino emission are being proposed too. So this is not a proven result but a strong candidate explanation, and it is right to tell it that way.

The real idea left behind is this. Superfluidity is not a substance but a form of order. That same order shows itself in a thimbleful of helium as a thirty-nanometre film climbing a glass wall, and inside a neutron star as vortices tearing loose from the nuclei they were pinned to. Between the two there is an unimaginable difference in density, but the equations are shared. And that droplet collecting at the bottom of the vessel is tangible proof that quantum mechanics does not stay confined to the small: given the right conditions, the rule that governs a single atom begins to govern the whole of a liquid you can see with your own eyes.

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