# The Phenomenon of Bose-Einstein Condensation

You may have learned in school that there are three states of matter; solid, liquid, and gas. Some of the more savvy among you may even be privy to a fourth, that being plasma. There are in fact, many more than four states of matter, some of which behave in ways wholly unlike anything we come across in our day to day lives. An example of one of these strange states of matter is a phenomenon known as Bose-Einstein condensation.

Bose-Einstein condensation (from here on referred to as BEC) occurs as particles at very low densities are cooled to temperatures very close to absolute zero, the temperature at which all particle motion stops. At such temperatures, a substantial fraction of the particles in the gas all occupy the same quantum state, the lowest energy state. This allows for some truly strange properties to be observed. BECs are capable of exhibiting superfluidity, they flow with no viscosity. They exhibit coherence, since the system is in one state, and can interfere with other waves.

The idea of a BEC originated with Albert Einstein and Satyendra Nath Bose, for whom it is named. Bose sent a paper to Einstein on the behaviour of photons (the massless particles that make up light), and Einstein expanded this idea to apply to specific massive particles known as bosons. He predicted that at extremely low temperatures, certain particles with integer spin would coalesce into a common quantum state at the lowest available energy level.

BEC comes from a particular branch of physics known as statistical mechanics. Statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large numbers of microscopic particles. The purpose of this is to transform the laws governing the behaviour of individual particles into something that can describe the world around us on a human scale. If you had a box filled with air, not only is it not computationally possible to describe the behaviour of every individual particle in that box, it wouldn’t be that useful to us macroscopically. We don’t need to know the kinetic energy of every one of 10^23 particles, but we might like to know the temperature of the box. This is the power of statistical mechanics. However, statistical mechanics excels not only at transforming the wacky world of quantum mechanics to our classical world, but also taking the wackiness of quantum mechanics and amping it up to eleven, as happens with BECs.

The statistical mechanics that governs systems that form BECs is known as Bose-Einstein statistics. This form of statistics governs particles known as bosons, named for Satyendra Nath Bose. Bosons have particular properties that set them apart from the other main class of particles in statistics known as fermions. In what are known as quantum gases, rather than being able to take any value of energy, only specific values may be taken. These are known as energy levels. In bosonic systems, any number of particles may inhabit a given energy level. As the temperature of these systems goes towards absolute zero, there is obviously less and less energy in the system, which means the particles will inhabit lower and lower energy levels. Eventually, there will be a macroscopic occupation of the energy level with the lowest allowed energy, known as the ground state. The temperature at which this occurs is known as the critical temperature, and once this temperature has been reached, a BEC has been formed.

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