A Bose-Einstein condensate is a state of matter where bosons cool to near absolute zero and occupy the same quantum state.Imagine a flock of birds that suddenly starts moving as a single whole — each bird repeats the movement of its neighbor, and the flock turns into a giant wave. A Bose-Einstein condensate is a 'flock' of atoms cooled to unimaginably low temperatures, where millions of particles lose their individuality and merge into one quantum droplet. In this state, atoms behave not as a chaotic crowd, but as one super-atom.
The theoretical prediction of BEC dates back to the works of Satyendra Nath Bose (1924) and Albert Einstein (1925). Bose derived a distribution for photons without a classical limit, and Einstein applied this statistics to non-relativistic atoms. He showed that below a certain temperature, the gas should dramatically change its properties due to the accumulation of particles in the lowest energy state. For many decades, the search for the right conditions (necessary to avoid condensation into liquid and solid) yielded no results. The breakthrough came in 1995: the group of Eric Cornell and Carl Wieman from JILA (USA) first cooled a cloud of rubidium-87 atoms to a temperature of 170 nanokelvins and observed the phase transition to BEC, and soon Wolfgang Ketterle from MIT obtained a condensate from sodium atoms. These experiments opened the field of quantum gases and earned the authors the Nobel Prize in Physics in 2001.
A Bose gas at high temperatures is described by Maxwell-Boltzmann statistics. As the temperature decreases, the de Broglie wavelength of the particles increases: λdB ∝ 1/√T. When λdB exceeds the average interparticle distance d (i.e., when nλdB³ ~ 1, more precisely nλdB³ = ζ(3/2) ≈ 2.612), the wave packets of atoms begin to overlap, and one must apply quantum Bose-Einstein statistics. For bosons, unlike fermions, the Pauli principle does not prohibit multiple occupation of a single quantum state; moreover, at low temperatures this becomes energetically favorable. A phase transition occurs, and a macroscopic number of particles accumulates in the ground state. This condensate is described by a single wave function, which satisfies the second law of thermodynamics: the entropy of the system decreases during the transition, but is compensated by heat removal to the external environment. The Gross-Pitaevskii equation incorporates this wave function and accounts for weak interaction between atoms.
The condensate is the coldest substance in the Universe, only a few billionths of a degree above absolute zero. If you place a laser beam into it, light can slow down to the speed of a cyclist (about 60 km/h), or even come to a complete stop, as if frozen inside ice.
| \langle n \rangle | variable | Average occupation number — occupation number |
| \omega | variable | Angular frequency of the bosonic mode — angular frequency radian per second |
| T | variable | Absolute temperature — temperature kelvin |
| \hbar | constant | Reduced Planck constant, relating energy to angular frequency. — reduced planck constant = 1.054571817e-34 joule second |
| k_B | constant | Boltzmann constant, relating temperature to energy. — boltzmann constant = 1.380649e-23 joule per kelvin |
























