A short video explaining how a Bose-Einstein Condensate of sodium atoms is created in lab at MIT by Martin Zwierlein. Using highly focused, single frequency lasers it is possible to cool the single sodium atoms, negating their thermal vibrations by inducing electronic transitions which effectively "pushes" them into place. This brings the atoms down to millikelivn temperatures.

However to achieve nanokelvin temperatures, magnetic fields are used to trap the atoms in a well or cup so that the atomic resonance of the atoms begins to match the frequency of the laser light so that , like in a cup of coffee or tea, the hottest atoms are boiled off the surface by "blowing" on the atoms with polarized laser light. This makes the atoms that are in resonance with the light move towards the center, leaving the hotter atoms to boil off. This then shrinks the gas cloud into a supercool sphere.

This arrangement is known as a magneto-optical trap and using it the atoms can be made colder than anywhere else in the universe, cold enough for the subtle effects of quantum mechanics to make the wavefunction of the atoms coherent, just like how a laser makes the photons in a laser medium coherent. The wavefunctions then constructively interfere until the atoms behave as a single quantum object known as a Bose-Einstein Condensate.

In quantum mechanics, a class of particles which have an integer quantum spin are called bosons. For example, photons, gluons, higgs boson etc. Any number of bosons can go to the same quantum state. Thus they obey Bose-Einstein statistics. The wave function associated with bosons is symmetric.

A class of particles which have a half- integer spin are called fermions. Example - proton, neutron, electron, etc. Unlike bosons, only two fermions (at maximum) can go to the same quantum state, as dictated by the Pauli Exclusion Principle. They obey Fermi-Dirac statistics. The wave function associated with fermions is anti-symmetric.

An atom can also be classified as a composite boson or a composite fermion. To find whether an atom is a composite boson or a composite fermion, you need to look at the net spin of the atom due to its constituent particles that make it. For example, consider the simplest of the atoms - Hydrogen. Hydrogen has a proton and an electron. A proton is a half-integer particle and so is an electron. Therefore, the net spin of a normal hydrogen atom is one, which is an integer. Therefore, hydrogen is a composite boson. If we consider a helium-4 atom, there are two protons, two neutrons and two electrons. Each of these particles has a half integer spin. Therefore, the net spin of a normal helium atom is an integer. Hence, helium is also a composite boson.

With Sodium, the number of protons is 11, the number of neutrons is 12, and therefore, the number nucleons is 23 which is an odd number. Since the number of electrons in Sodium atom is 11, this makes the total number of constituent particles 34 which is even and hence Sodium atom is a composite boson.

So by this reasoning, all Sodium-23 (as well as Rubidium-87) atoms are bosons which means that the spin of the atoms is an integer. Bosons obey Bose-Einstein statistics and do not obey the Pauli Exclusion prinipcle and can form non degenerate condensates.

So, because bosons tend to bunch together it is possible for a macroscopic group of N-bosons to form a giant wave function called a Bose-Einstein Condensate.
Therefore, a Bose-Einstein Condensate is essentially a macroscopic occupation of the ground state of a quantum system at thermal equilibrium, and is considered to be a quantum phase transistion just like superfluidity and superconductivity.

This quantum state can be seen in wildly differing physical systems, from liquid helium to electron pairs in superconductors to the laser-cooled atoms in vacuum chambers as shown in the video.
Bose--Einstein condensates composed of a wide range of bosonic atoms and isotopes have been produced.

Related experiments in cooling fermions rather than bosons to extremely low temperatures have created degenerate gases, where the atoms do not congregate in a single state due to the Pauli exclusion principle. To exhibit Bose--Einstein condensation, the fermions must "pair up" to form compound particles (e.g. molecules or Cooper pairs) that are bosons. The first molecular Bose--Einstein condensates were created in November 2003 by the groups of Rudolf Grimm at the University of Innsbruck, Deborah S. Jin at the University of Colorado at Boulder and Wolfgang Ketterle at MIT. Jin quickly went on to create the first fermionic condensate composed of Cooper pairs in a superconductor.