Saturday, April 30, 2011

Very Hot, Very Cold - Superfluids Demonstrate the Strangeness of Atoms

When materials find themselves at the extremes of the universe - either very hot or very cold - they act strangely. Superfluids are known to exist at both extremes. In this article I will explore this unique physical state.

A superfluid is a state of matter, like solid, liquid or gas. What makes a superfluid special is that it exhibits a number of bizarre behaviours, which at first glance seem impossible.

Zero Viscosity

First of all, superfluids have no absolutely no viscosity. Viscosity is the resistance of a fluid to flow. It comes from the friction of molecules as they move against each other within the fluid and all fluids except superfluids have at least some resistance to flow. This means all fluids except superfluids have some degree of internal resistance, some level of "thickness." For example, honey is more viscous than water. In honey, layers of molecules oppose movement against each other. This force, called shear stress, opposes the applied force, for example gravity if you are trying to pour some honey into your tea. A superfluid, on the other hand, can stream over a surface in a layer of just a few atoms (30 nm) thick. In fact, it will creep up and over the sides of any container in which it's placed and escape if it isn't enclosed (it has surface tension which makes this action possible). It will also drip through molecule-thin cracks in the container.

Viscosity of Normal Fluids

In some fluids viscosity increases with the rate of shear. These fluids are called dilatants. An interesting example of these fluids is a simple mixture of 1 part cornstarch and 1.5 parts water. Watch this fun video. 

Students who run quickly over the cornstarch mixture do just fine but someone standing still in it quickly sinks.

Unlike cornstarch/water, the viscosity of ketchup decreases when you introduce motion by running a knife into the bottle to start its flow. This fluid's viscosity decreases as shear stress on its molecules increase. Modern paints also have this property so they can be rolled on thinly and evenly but resist running and dripping once applied.

Newtonian fluids have a constant viscosity regardless of the shear stress put on them. Water is a Newtonian fluid. It has the same viscosity no matter how fast you stir it or vigorously you shake it.

In contrast to these fluids, a superfluid has zero viscosity and it acts like this:

This video is a clipping from a BBC one-hour documentary called Absolute Zero. You can watch the entire BBC documentary here.

Infinite Thermal Conductivity

Superfluids are also unique because they have infinite thermal conductivity. This means that any volume of superfluid, no matter how large, will always be precisely the same temperature throughout. All other fluids have at least some resistance to heat. It takes time for heat to transfer from one section to another. The thermal conductivity of a material depends on its structure and composition and this, in turn, is an expression of how the atoms in the structure interact with each other. In glassy and crystalline materials, heat is transported from one part to another through elastic vibrations of the molecular lattice. In metals, heat is transported through freely moving electrons that occupy the outermost orbit around metal atoms, using the same mechanism through which electrical current is transported.

Superfluids transmit heat so fast they create thermal waves. This phenomenon is sometimes (erroneously) called second sound. It's a quantum mechanical phenomenon in which heat transfer occurs by wavelike motion rather than through the mechanics of diffusion. Like a sound wave propagates pressure waves, thermal waves propagate heat through superfluids. What does it mean to have a quantum mechanical property? It means that a volume of sperfluid large enough to see with the naked eye is exhibiting a behaviour that is limited to the realm of single atoms. Single atoms act counter-intuitively, far differently from the larger objects they make up.  How is this possible? You will soon find out.

Very Cold Superfluids

Superfluid Helium-4

Helium-4 is a stable isotope of helium, having a nucleus consisting of 2 protons and 2 neutrons. Liquid helium-4 makes a great superfluid because the bonds between its molecules are very weak compared to other elements. You will see why this is important soon. We will use the Kelvin temperature scale from here on in. Absolute zero is 0 K. This is the lowest theoretical temperature possible, at which all movement, even the movement of elementary particles like electrons, stops. I say "theoretical" because even deep space isn't this cold and scientists as yet have no method to reach absolute zero in a laboratory. At 4.2 K, helium-4 condenses from a gas into a liquid. Below 2.17 K, it enters a superfluid state of almost perfect heat conduction Helium, because of its weak intermolecular bonding, never condenses into a solid even as it approaches absolute zero, unless it is pressurized. In 1938, a group of several researchers discovered this new kind of fluid phase in helium-4. L. D. Landau won the Nobel Prize in Physics in 1962 for his theory of superfluidity based on his research with helium-4.

As the phase change from liquid to superfluid occurs, there is no specific volume change and no latent heat involved - this is yet another unique aspect of this physical state. When ordinary liquids freeze into solids, heat is released. When water freezes into ice cubes it adds some heat to the air inside your freezer. This is water's latent heat of fusion. When the ice later melts in your glass it absorbs the same amount of heat from your liquid drink. A volume change also accompanies a phase change. Water is special because as it freezes, its volume increases. Most liquids freeze into a smaller volume solid. No heat is released or absorbed when a liquid changes into a superliquid and vice versa. And no change in volume occurs.

As a superfluid, helium-4 is in a macroscopic quantum state. This is very unique. Its macroscopic qualities such as thermal conductivity and viscosity, qualities we can observe, are governed by quantum mechanics rather than classical mechanics, as they are in ordinary fluids. Within all matter, atoms jiggle about randomly. This is called Brownian or thermal motion. As heat is applied to the matter, its atoms move about faster and bounce off each other more often and with more force. That is why gases, with more energetic atoms, are less dense than liquids and solids, with slower atoms, can maintain a lattice-like atomic structure. The quantum nature of these atoms is masked by their energetic kinetic behaviour. You cannot observe their quantum nature directly. However, there is so little thermal motion of helium atoms in the superliquid phase that it can no longer mask the underlying quantum nature of its atoms. When in this superfluid state, all the helium atoms, no matter how large the sample, behave as one single entity. They all move together as one particle, somewhat like people in a marching band.

This phenomenon extends to superconductors as well. Certain materials, when they are cold enough, exhibit no electrical resistance. An electrical current can flow through a superconducting wire forever because no current is ever lost to resistance (another form of internal friction, like shear stress in fluids). The atomic structure of superconductors will be compared that of superfluids later in this article.

Superfluids can also quantize vortices. When water goes down a sink drain, it forms a whirlpool, a vortex, with water in the center moving more slowly and water at the edges moving around the fastest. When you spin a superfluid, you get an enormous number of tiny quantized vortices, the number being proportional to h/m where h is Planck's constant  and m is the mass of one atom. These quantum vortices "carry" the angular momentum of the superfluid, and they turn out to be theoretically very similar to flux lines in superconductors, where the flux lines "carry" the magnetic field created by electric current traveling through them. A superfluid placed in a rotating container does not spin uniformly with the container. In fact, it will remain perfectly motionless unless the container spins fast enough to reach what is called critical velocity (each kind of atom has its own critical velocity). When this speed is reached, the superfluid instantaneously starts to spin. A superfluid's spin is quantized. That means it can only spin at certain speeds, and these speeds are determined by the kind of atoms it's made of.

Superfluids exhibit both quantum mechanical behaviours and classic mechanical behaviours at the same time. For example, superfluids can transmit ordinary sound (pressure) waves, a classical phenomenon. The reason for this duality is that superfluids contain of a small percentage of atoms in ordinary (random and variable) quantum states along with atoms that are all confined to one quantum state. The percentage of ordinary randomly quantized atoms approaches zero as absolute zero is approached (absolute zero has never been experimentally observed and you will learn why shortly). This is called the two-fluid model of superfluids. All superfluids, in practice, have at least some proportion of atoms in an ordinary fluid state.

This video demonstrates the fountain effect of superfluid helium.

This effect is a consequence of zero viscosity, as explained in the video. It's an old demonstration from 1963 but the phenomenon is explained very well.

As you watch this video you will learn that superfluids not only possess zero viscosity but they also approach zero entropy. This means that a pure superfluid theoretically possesses the lowest possible energy that a quantum mechanical physical system can have. It is the energy of its ground state. It still possesses some energy, called zero-point energy, because all quantum systems undergo fluctuations in their ground state. A pure superfluid has zero entropy because its energy is below the minimum potential energy required to be able to convert to any other kind of energy such as heat (zero-point energy is the same as the vacuum energy of all energy fields such as the electromagnetic field and the Higgs field.

Bose-Einstein Condensates

Superfluid helium-4 is a Bose-Einstein condensate. This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924-25. The nuclei of helium-4 atoms consist of an even number of neutrons and protons. Each of these particles has a quantum spin of ½. The nucleus as a whole has a whole-integer spin. Bosons are elementary particles that have a whole integer spin and several bosons can occupy the same quantum state at the same time. Examples of bosons are photons, theoretical gravitons, gauge bosons and theoretical Higgs bosons. They are often force carrier particles. Helium-4 nuclei are not true bosons but they can act like bosons if they are cold enough. The wave functions of bosons like to overlap and when the wave functions of helium-4 atoms begin to overlap, they begin to align themselves with one another forming a synchronized wave function. A wave function describes the quantum state of a particle, namely its spin, location and velocity. The individual atoms in this sense lose their individual identity and a Bose-Einstein condensate forms.

Superfluid Helium-3

Helium-3 is stable isotope of helium with a nucleus comprised of 2 protons and 1 neutron. Some molecules are much more difficult to cool into superfluids than others are and helium-3 is one of them. It has to be cooled to 2 mK (0.002 K) before it exhibits any superfluid properties. That's a thousand times colder than Helium-4's lambda point, the temperature at which helium-4 changes from liquid to superfluid.

The helium-3 nucleus is a fermion rather than a boson. That means it contains an odd number of spin ½ particles. As you may have learned in my Our Universe series, fermions are often associated with matter and include elementary particles such as electrons and quarks (quarks are what neutrons and protons are made of). Composite particles such as protons and neutrons, with half-integer spins are also called fermions. Unlike bosons, only one fermion can occupy a particular quantum state at a time.

Cooper Pairs

In order to transition into a superfluid, helium-3 atoms have to pair up so the pairs can act like bosons. That means that it must assemble pairs of atoms into what are called Cooper pairs. Cooper pairs were first theorized in superconductors where two (fermion) electrons pair up to form a boson-like composite, which can then transmit electrical current through the metal without resistance. This is how it works: When they are slowed down, two electrons in a metal, which is an ionic lattice solid, form a Cooper pair and create an ultra low temperature superconductor. As long as the kinetic energy of the atoms in this lattice stays low enough, the Cooper pairs can stay in place and when they do, a phonon arrangement occurs in the lattice. This phonon arrangement means that all the atoms in the lattice vibrate at the same frequency. With this arrangement, the electrons can move in pairs with no electrical resistance.

In a fermion-system superfluid under extreme cold conditions where atoms are greatly slowed down, two (fermion) atoms pair up to form a composite particle that acts like a single particle with a whole-integer spin, a boson in other words. In order to form these pairs the molecules have to be moving very slowly. Helium-3, when organized into Cooper pairs, can then exhibit Bose-Einstein properties and assume a unified quantum state, thereby becoming a superfluid. Helium-3 superfluid is sometimes called a fermion condensate. The 1996 Nobel prize in Physics went to David Lee, Douglas Osheroff and Robert Richardson for discovering the superfluid state in helium-3.

Very Hot Superfluids

The recent discovery of neutron star superfluid really piqued my curiosity. How can this super-dense/super-hot physical state be even remotely related to the cold superfluid state? A neutron star is the remnant of a supernova explosion. It is not quite massive enough to collapse completely into a black hole  as larger stars do when they explode. In fact, the matter inside a neutron star is the densest matter known to exist in the universe. How dense is it? This might give you an idea: A neutron star packs a few hundred thousand grams into each cubic centimeter of matter, that is a density several times higher than the density found inside the heaviest atomic nucleus! (If you are interesting in learning more about these mysterious stars, I have written an article devoted to them on this blog) No laboratory can create matter this dense so it remains up to particle theorists to try to describe this physical state of matter. A number of astronomers have independently determined, based on recent thermal X-ray emission observations from a young neutron star in the Cassiopeia A supernova remnant (this supernova exploded 330 years ago about 11,00 light years away from Earth), that some kind of superfluid must exist inside the star's core. Just after a neutron star is born, in the first several seconds after a supernova explosion, it has a radius of about 50 km and it's very hot, a few trillion degrees K. This is very hot but it's not the hottest theoretically possible temperature. That temperature corresponds to what is called Planck temperature, around 1032 K. Any hotter than this and the laws of physics themselves begin to break down. By comparison, a trillion degrees K is 1012 K. Over a minute or so, the neutron star becomes transparent to the billions of neutrinos inside it. The neutrinos then simply fly right through it and away in all directions, carrying a great deal of energy away with them. As they escape, the baby neutron star rapidly shrinks down to a diameter of about 20 km and its temperature drops below a billion degrees. Its outer layer crystallizes into a special kind of solid crust and after several decades, the interior of the star reaches a uniform hundred million degrees. From this point on it cools very slowly through diffusion from the core to the surface and from there through the release of thermal photons.

Scientists now think that deep inside the core of neutron stars lies a neutron ocean. Just beneath the crust lies a completely ionized lattice of compressed atomic nuclei embedded inside a quantum gas of electrons. This means that the atoms themselves are broken down into a plasma-like state. Beneath this, physicists think there are layers of nuclei, which, as you go deeper, become more and more neutron-rich, until you get to a depth within the star where temperature and pressure are so extreme that neutrons simply drip out of the nuclei. Unbound neutrons in this state cannot be created in any laboratory, so they can only be studied theoretically. There is theoretical evidence that they act like a superfluid. Neutrons are fermions so they cannot create a Boson-Einstein condensate. Because they cannot occupy the same quantum state, and because they exert strong nucleon-nucleon repulsion toward each other over very short distances, they create just enough outward pressure to counteract the enormous gravitational force exerted on them and avoid complete collapse into a black hole. Physicists believe that in the center of the neutron ocean, the pressure becomes high enough to form a fermion condensate much like helium-3 does. The difference, of course, is that helium-3 can only form this condensate at temperatures below a few mK above absolute zero, when its fermion nuclei can slow down enough to form boson-like Copper pairs. Free neutrons carry out this procedure at a temperature of about half a billion degrees. They believe that a hot superfluid can form at these temperatures because the pressure is so incredibly high that neutrons are basically forced together into pairs, creating a boson-like condensate. How much of the star's core is in a superfluid state is still a matter of debate.

The reason physicists predict a superfluid core is that the young neutron star in the Cassiopeia supernova remnant is cooling much faster than can be explained by any other neutron star cooling theory. Neutrons in a superfluid state should theoretically allow neutrinos to escape through tiny channels created by the repeated breaking and formation of neutron pairs. This process should enhance the star's cooling rate for several decades to come. They suspect that the neutron superfluid is just under the critical temperature (lambda point) and that makes it especially effective as a cooling mechanism. They pinpoint the lambda point for free neutrons at about half a billion degrees, and furthermore, they predict that free protons inside the neutron soup are superconducting, possibly forming Cooper pairs of their own.

It is fascinating and counterintuitive to consider that the same physical state can occur at opposite extremes in terms of temperature. The physical states solid > liquid > gas > plasma follow a linear progression as molecules becomes more energetic and jostle around faster and faster. This NOVA website has a fun initiative in which you can play with various interactive experiments, all designed to explore the nature of materials in extreme cold. It seems that extreme pressure and temperature allow for some of the same kinds of processes that occur in extreme cold environments, and that when superfluids are created at either extreme, they act as a single unified macroscopic-scale quantum particles. This gives researchers access to observable quantum dynamic phenomena and they are making the best use they can of this new tool. Superfluid research is a rapidly growing field, as researchers study the properties and behaviours of helium-3/helium-4 mixtures and discover new superfluid materials. Experiments focusing on heat transport, equilibrium dynamics, current vortices and quantum interference are underway at several facilities.

What Happens Past These Extremes?

Absolute Cold

What happens if a material is cooled right down to absolute zero, 0 K or -273.15°C? First of all the laws of thermodynamics do not allow any material to reach absolute zero. At absolute zero that material must still possess at least some quantum mechanical energy, sometimes called vacuum energy. This energy is not available as thermal energy and this is why the material will possess zero entropy as it approaches very close to absolute zero, and it cannot be cooled down further by any external means.

Vaccum energy is the energy that exists even in a perfect vacuum. The uncertainty principle states that virtual particles can and do constantly pop in and out of existence inside a perfect vacuum. This has been proven experimentally with the Casimir effect, for example. The theory is that excitations in fundamental fields such as the electromagnetic field (which necessarily must exist even within a perfect vacuum) correspond to elementary particles such as photons. An electromagnetic photon is a quantized point of the field's vibration (of strings according to the string theory of fundamental fields and particles) inside the vacuum so it will spontaneously appear and disappear in a random fashion inside it. In this vacuum, particle and antiparticles always appear together in pairs and cancel each other out but they may interact with other particles before they so and this leaves a tiny but certain amount of residual energy, vacuum energy. In case you are wondering, electrically neutral particles such as photons are their own antiparticle; the antiparticle of a charged particle is a particle of opposite charge.

As matter approaches absolute zero, all molecular motion ceases and atoms themselves slow down. At room temperature atoms move, on average, about 500 m/s (that's about 1100 mph). This is called Brownian motion. At 200 uK, they move only 0.20 m/s (0.45 mph). At this temperature, most if not all matter would have begun to overlap each other and condense into a Bose-Einstein condensate or fermion condensate where all the atoms in the matter begin to occupy the same quantum state. In absolute zero, all molecular motion and in fact all atomic motion would stop. No one is quite sure what would happen to matter if atoms stopped moving altogether, but according to quantum mechanics, if an atom attained absolute zero, its wave function would extend across the universe, which means the atom would be located nowhere. This is an extension of Heisenberg's uncertainty principle  in which you cannot simultaneously know the speed and position of a subatomic particle. If you can pinpoint the speed, in this case zero, then you cannot know the position or even narrow it down. Another problem with absolute zero is momentum. Momentum is an intrinsic part of what makes a particle a particle. Electrons, for example, have spin. Spin in this sense does not mean rotation, like the Earth's spin. It was simply coined as a word to describe an important part of a particle's quantum state. You can think of it as the "generator" of rotations. It is a type of angular momentum. Each particle has its own spin. An atom's spin is the total angular momentum of each of its particles. This means they have intrinsic angular momentum and electrons would stop being electrons if their motion stopped altogether. Perhaps, and I am only guessing here, if the entire universe actually reached absolute zero, and this is impossible remember) it would be one giant frozen condensate, where every atom would be frozen into the same quantum state. And, in fact, it would no longer be matter at all; the atoms themselves would fail because the subatomic particles, losing their angular momentum, would no longer be particles.

Black Holes and Absolute Hot

If you explore the state of matter inside a neutron star, you are looking at matter very close to complete collapse. The degenerate matter inside these stars consists of atoms broken down into a nucleon soup and finally, deeper inside, a neutron soup where neutrons begin to overlap each other's quantum states as they form a fermion condensate. One might guess that if the degeneracy pressure were overcome, the neutrons would rapidly fall in together and completely overlap each other's quantum state, and this would be the singularity of a black hole. This too is not matter as we know it. Here, trillions upon trillions of atoms all have the same wave function and they are all confined in the same pinpoint of space. At this point, atoms are not atoms anymore. You have pinpointed their location and now their speed is unknowable or perhaps infinite.

In short it appears that matter as an entity is confined within specific energetic parameters. You might even call matter an artifact of the quantization of energy fields ( ) within these energy parameters. Matter did not exist during the first billionth of a second after the Big Bang. Quarks, the building blocks of neutrons and protons, made their appearance only after all the fundamental forces settled out of a roiling energy soup. The universe began from a singularity, a point of infinite energy confined in an infinitely small space. We cannot know what this environment was like because no physical laws we can understand can exist above absolute hot or Planck temperature. All the fundamental forces: gravity, the strong force, the weak force and the electromagnetic force, simply melt together.

A Bose-Einstein Condensate on a Universal Scale?

For some fun reading, I found a thread of people arguing whether the universe evolved from a Bose-Einstein condensate soon after the Big Bang. It's on a body-builder's forum of all places. I also discovered that there is some talk of dark matter being a kind of Bose-Einstein condensate but most theorists prefer the WIMP theory of dark matter. I suspect that we might see more attempts to combine Bose-Einstein condensate theory with cosmology in the future.

Supersolids - A New Field of Research

In 2004, two researchers, Eun-Seong Kim and Moses Chan, found that solid helium-4 does not rotate like a classical solid. This short video demonstrates its behaviour as it spins.

Like superfluids, some of the helium-4 is in a supersolid state so it rotates freely with the oscillator while some of the helium-4 remains in the ordinary solid state and remains fixed in place.

It appears to be matter that retains its solid lattice-like structure but it stops being rigid and flows like a liquid. This phenomenon is still not well understood. This is the theory so far, but I should warn you that it is currently experiencing some road bumps. While Kim and Chan claim to have produced the first supersolid, some physicists - for example John Beamish at the University of Alberta - think they observed a phenomenon called quantum plasticity instead. The atoms in all ordinary solids are structured like lattices, but no lattice is perfect. They always have at least some vacancies where atoms are missing, and it is these vacancies (which are missing neutral atoms and therefore bosons) that can form a Bose-Einstein condensate at a low enough temperature. In a chunk of highly pressurized very cold helium, these vacancies condense into the same quantum state. That means that the vacancies flow without resistance in the solid. The vacancies correspond to a frictionless flow of particles in the opposite direction. If proved to exist, supersolidity will join superfluidity and superconductivity as examples of quantum effects on a macroscopic scale.

The problem with the Kim and Chan experiment is that movement of imperfections in the helium-4 solid crystal could have caused it to soften. This is the general idea behind quantum plasticity, and this could mimic the rotating matter described as supersolid behaviour. Recently, researchers have shown that fluid helium-4 can flow through a chamber filled with solid helium-4, more evidence that it may be a supersolid. Other researchers wonder if the flow was possible only because the helium-4 solid crystal was riddled with defects. At this point the jury is still out about whether true supersolid helium-4 has been discovered or not. And the theory behind supersolidity is still in its infancy. If you wiki "supersolid," you get the Kim and Chan experiment.

I hope you now have a basic sense of how atoms behave in extreme environments. It will be fun to see what happens next as physicists, being the curious creatures they are, continue to push the boundaries of what is possible.


  1. A neutron star has one atom composed of a proton and an electron sharing. Now that is not a quantum dance, at least as far as I can tell from internet reading. And from the amount of data, nobody knows. So, a black hole is a neutron star whose sole particle is a proton/electron sharing becomes a choreographed dance of the quantum world. Additional pressure change the random particle into an organized, synchronized dance indicative of the quantum world. A world in which there is no latent heat, therefore superconducting. Light entering from any point of the 'ring of bright water' surrounding the black hole would transverse the black hole without creating any heat and exit into the 'ring of bright water' on the other side of the hole light years across with out any evidence (heat generated) of its passage. Viola!! Light traverses the black hole unseen!!
    This is the opposite of the latest model where by neutrons compact further into cubes. No need--they become a quantum structure.

  2. This comment has been removed by a blog administrator.

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