Bosons, Lasers and Superfluids

by Nicholas Mee on November 30, 2012

Following the response to my article What on Earth is a Boson? I promised to say a bit more about bosons, so here we are.

Richard Feynman and some of the particle interaction diagrams that he invented.

All particles fall into two distinct categories. They are either fermions or bosons. These two classes of particles behave in very different ways. Bosons love to cluster in the same state as their fellow particles, whereas no two fermions can be in the same state – they obey the exclusion principle. I discussed fermions and their antics in my recent article Fermions, Atoms and Neutron Stars.

A Different Spin

The reason for the different properties of these two classes of particle is well understood. Surprisingly it is simply due to their spin – the rate at which they rotate. Like many quantum properties, spin or angular momentum comes in fixed lumps. In other words particles can only exist in states where they have multiples of a fundamental unit of spin. The smallest amount of spin that a particle can have (other than no spin) is half a unit of spin. Any particle whose spin is a whole number (or integer) i.e. 0, 1, 2 and so on, is a boson. For instance, the Higgs boson has zero spin, whereas photons and gluons have one unit of spin. Any particle whose spin is half-integer i.e. 1/2, 3/2, 5/2 or so on, is a fermion. For instance, the spin of an electron, a quark or a neutrino is 1/2.

Can You Feel the Force?

When bosons are passed between other particles this produces a force. The electromagnetic force is due to the exchange of photons between charged particles such as electrons. This is represented schematically in diagrams known as Feynman diagrams after the great American physicist Richard Feynman, shown above. The simplest Feynman diagram is shown below.

The diagram represents a photon being exchanged between electrons. The wavy line represents the photon and the straight lines with arrows on them represent electrons. Time passes upwards in the diagram. The process shown in the diagram is as follows: two electrons approach each other, they exchange a photon and recede from each other. The exchange of the photon transfers energy and momentum between the two electrons i.e. a force acts between the two electrons – they repel each other. This is how the electromagnetic force is depicted at the level of particle interactions.

Lasers

Photons are the fundamental particles from which light is formed. Being bosons they like to be in the same state as their colleagues and this behaviour is taken advantage of in many modern technologies. You use it every time you play a CD or DVD.

Laser Show
The Australian Pink Floyd

A laser beam is a collection of vast numbers of photons with exactly the same wavelength that are all vibrating together in phase. A typical beam of light is a bit like a choppy sea – there are lots of different waves that partially cancel each other out. In a laser beam all the waves are moving together to produce a single big wave train. All the photons are in the same quantum state. This is why a laser packs much more punch than an ordinary beam of light.

Atoms

Atoms can also be classified as either fermions or bosons. At room temperature this distinction does not matter much. There are vast numbers of different quantum states available to the atoms and most of them are unoccupied, so whether they like to be in the same state as their neighbour or not doesn’t really matter. However, at very low temperatures the situation can be very different and strange quantum effects are possible.

Atoms are formed from a collection of negatively charged electrons bound to a positively charged nucleus. The simplest example is the hydrogen atom, in which the nucleus consists of a single proton, which is orbited by a single electron. The proton and the electron both have spin 1/2 and are therefore fermions. In the hydrogen atom their spins may be oppositely aligned, in which case the total spin of the atom is zero, or they may be aligned in the same direction, in which case the total spin of the atom is one. The hydrogen atom must therefore be a boson. In fact, any atom formed from an even number of protons, neutrons and electrons is a boson, whereas any atom formed of an odd number of component particles is a fermion.

Superfluid Helium

The nucleus of a helium-4 atom contains two protons and two neutrons. The nucleus is orbited by two electrons. The total spin of a helium-4 atom is zero.

The next simplest atom is helium. The nucleus of an atom of helium-3 contains two protons and one neutron, whereas the nucleus of an atom of helium-4 contains two protons and two neutrons. (Helium-3 and helium-4 are known as two different isotopes of helium.) A helium-4 atom is a boson because it is composed of six spin 1/2 particles (the two protons and two neutrons in its nucleus and the two electrons orbiting the nucleus), whereas a helium-3 atom is a fermion because it is composed of five spin 1/2 particle (the two protons and the one neutron in its nucleus and the two orbiting electrons). This subtle difference in their structure leads to dramatically different behaviour at very low temperatures.

When cooled below a temperature of 2.17 degrees above absolute zero helium-4 is transformed into a superfluid – a liquid without any resistance to its flow. A container that holds normal liquid helium perfectly well will suddenly spring numerous leaks when it is cooled below this temperature, as superfluid helium seeps out through ultramicroscopic pores in the container. Superfluid helium has many strange and wonderful properties. However, helium-3 remains a normal liquid at these temperatures.

This surprising behaviour of helium-4 is due to the fact that these atoms are bosons. At the critical temperature all the atoms fall into the same lowest energy state. This means that they behave in a collective way and will all move together in the same way. By contrast the helium-3 atoms are fermions. They obey the exclusion principle and cannot exist in the same state, so helium-3 continues to behave like a normal liquid.

Curiouser and Curiouser

When helium-3 is cooled much further something remarkable happens. At extremely low temperatures of just two and a half thousandths of a degree above absolute zero the helium-3 atoms pair up. Each helium-3 atom has spin 1/2, but the spin of a pair of atoms is aligned in the same direction so that the total spin is 1. The helium-3 pair is therefore a boson. Because these helium-3 pairs are bosons they can all fall into the same lowest energy state. The result is that helium-3 becomes a superfluid. The bonds that hold the helium-3 pairs together are extremely weak and a tiny increase in temperature will shake them apart. This is why helium-3 must be cooled to such ultra-low temperatures before it becomes a superfluid.

In 1996 David Lee, Douglas Osheroff and Robert Coleman Richardson were awarded the Nobel Prize in Physics for the discovery of superfluid helium-3.

Superconductivity

Superfluid helium-3 is certainly curious, but it has no obvious applications. However, it is closely related to another remarkable phenomenon that certainly does have important applications. Many materials lose all electrical resistance at low temperatures. Remarkably once a current has been established in a superconductor it will continue to flow forever. This is known as superconductivity. Just as the atoms in a superfluid will flow without any resistance, so the electrons that form a current in a superconductor will continue to flow without any electrical resistance.

The mechanism by which superconductivity arises is very similar to superfluidity in helium-3. At low temperatures electrons pair up. Electrons are fermions with a spin of 1/2. But in a superconductor they pair up with their spins oppositely aligned to form spin zero states known as Cooper pairs. Because Cooper pairs are bosons, they can all exist in the same state and this is critical to the formation of the superconductor.

The ATLAS detector at CERN during construction. The eight tubes contain superconducting magnets that bend the paths of the charged particles that pass through the detector.

The most important application of superconductivity is in electromagnets. Superconducting magnets were developed at Fermilab for use in particle physics. They now have a wide range of applications and are used in hospitals throughout the world in MRI scanners. The Large Hadron Collider uses superconducting magnets to guide the protons beams around the accelerator. The superconducting magnets operate at a temperature of just two degrees above absolute zero and are cooled in a bath of superfluid helium-4. The particle detectors at the LHC, such as ATLAS shown here, also contain their own sets of superconducting magnets.

More Information

There is much more information about the meaning of Feynman diagrams in my book Higgs Force:
http://quantumwavepublishing.co.uk/higgs-force/

The following link is to a video that illustrates many of the amazing properties of superfluid helium-4:
http://www.alfredleitner.com/superfluid.html

My book Higgs Force contains a lot more information about superconductivity and how it inspired the theory of the Higgs boson:
http://quantumwavepublishing.co.uk/higgs-force/

The layout of the following website is not particularly elegant, but it gives a comprehensive account of many applications of the wonders of superconductivity:
http://www.superconductors.org/Uses.htm

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