All bosons obey Bose-Einstein statistics, whereby all particles can have exactly the same energy levels, they need not, but they can, and when they do the result is called a Bose-Einstein Condensate (BEC).

Helium-4 has an even number of nucleons (four), and the spins of each pair off anti-parallel with each other to produce a nucleus of zero-spin. Any object with integral or zero-spin is a Boson. All Bosons can occupy exactly the same energy level, whereas the opposite is true for the half-integral spin Fermions. Liquid helium-4 (because it has an even number of nucleons) is a Boson liquid below the superfluid critical temperature, obeying Bose-Einstein statistics where all the atoms are in the same ground state energy (which is non-zero) and with all their (atomic) spins parallel. The de-Broglie wavelength (arising from matter waves of the slowly moving atoms) is large and spreads out to encompass the whole mass, at which point all the atoms behave as one, with each atom being indistinguishable from the next. Move one atom and they will all move identically, without friction; it is a superfluid. This is the Bose-Einstein condensate. The thermal conductivity in this superfluid state is extremely high, whilst viscosity is near zero. It also expands on cooling!

Nothing will dissolve in superfluid helium-4, except liquid helium-3, which naturally exists in the ratio 1 : 0.2 ppm. Even this can be removed by using a plug made out of a superleak material, which will allow only the superfluid components to pass. By this means, helium-4 can be purified to extraordinary purity, possibly purer than anything else on Earth. By this means also, further refrigeration can be effected, the non superfluid helium-3 becomes hotter (because it is not superfluid and cannot transport heat rapidly like a superfluid can) whilst the superfluid helium-4 becomes colder. This is the so-called 'dilution refrigerator'.

Helium-3 can also exist in superfluid form; but only below 3 milliKelvin, much lower than for helium-4. Here, because liquid helium-3 is a Fermi liquid with half integral spin, Bose-Einsten condensation can only occur when two atoms of helium-3 pair up to produce a unit having integral spin, but not a spin-zero particle as helium-4, rather a pair with spin-one. Although both are bosons, there is a crucial difference: having spin, it can be aligned by a magnetic field; it is magnetic. In superfluid helium-3 the spins of the nuclei align themselves in one direction, as do the spins of the pairs of atoms, but not necessarily in the same direction as the nuclear spins, so superfluid helium-3, unlike superfluid helium-4, can exist in 3 different phases, and is an anisotropic superfluid, with differing properties in differing directions, for example, the velocity of sound and the superfluid flow velocity are different in differing directions.

In 1995 a 'gaseous' cluster of 1000 atoms of rubidium were cooled in a magnetic trap by laser cooling them to a temperature of a few hundred nanoKelvin and forming a new state of matter. The de-Broglie wavelength (arising from matter waves) of the slowly moving atoms spreads out to encompass the cluster, at which point all the atoms behave as one, and a Bose-Einstein condensate of atoms is formed, where all atoms have identical non-zero ground state energies. The rubidium atoms weakly repel each other maintaining the 'gaseous' state. Previously, this Bosonic state has been observed only in the liquid phase.

In superconductors, the electrons (which are spin-half fermions) pair up in what is known as Cooper pairs, with their spins anti-parallel, such that the total spin of the pair is zero; the pair taken together are now bosonic in character; spin-0 bosons. see Superconductivity [POP]

The electrons in so-called spin-1 superconductors pair up with their spins parallel rather than anti-parallel. The electrons when paired thus become spin-1 bosons. This very rare state is exhibited by the superconducting compound strontium ruthenide, and its very unusual property (for a superconductor) is that it should not have a superconducting critical magnetic field as do spin-0 superconductors. See spin-1 superconductivity [POP]