# Bose-Einstein condensate

A Bose-Einstein condensate is a gaseous superfluid phase formed by atoms cooled to temperatures very near to absolute zero. The first such condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder, using a gas of rubidium atoms cooled to 170 nanokelvins (nK). Under such conditions, a large fraction of the atoms collapse into the lowest quantum state, producing a superfluid.

Velocity-distribution data confirming the discovery of a new phase of matter, the Bose-Einstein condensate, out of a gas of rubidium atoms. The artificial colors indicate the number of atoms at each velocity, with red being the fewest and white being the most. The areas appearing white and light blue are at the lowest velocities. Left: just before the appearance of the Bose-Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate. The peak is not infinitely narrow because of the Heisenberg uncertainty principle: since the atoms are trapped in a particular region of space, their velocity distribution necessarily possesses a certain minimum width.

## Theory

The collapse of the atoms into a single quantum state is known as Bose condensation or Bose-Einstein condensation. This phenomenon was predicted in the 1920s by Satyendra Nath Bose and Albert Einstein, based on Bose's work on the statistical mechanics of photons, which was then formalized and generalized by Einstein. The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by the Bose-Einstein statistics, which describes the statistical distribution of certain types of identical particles now known as bosons. Bosonic particles, which include the photon as well as atoms such as helium-4, are allowed to share quantum states with each other. Einstein speculated that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state, resulting in a new form of matter.

The critical temperature (in a uniform three-dimensional gas consisting of particles with no apparent internal degrees of freedom, and with no or uniform external potential) at which this happens can be derived to be:

$T_c=\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\frac{h^2}{2\pi m k_B}$

where:

 Tc is the critical temperature, n the particle density, m the mass per boson, h Planck's constant, kB the Boltzmann constant, and ζ the Riemann zeta function; ζ(3 / 2) ≈ 2.6124.