Bose-Einstein condensate

Quantum mechanics on a macroscopic scale

Quantum mechanics was developed in the 1920s by a dozen European physicists to describe and understand how atoms come together to form molecules.
Although it describes physical phenomena on the scale of the infinitely small, surprisingly, quantum physics sometimes manifests itself on a macroscopic scale, at very low temperatures. The two emblematic examples are superconductivity and superfluidity.
Superconductivity occurs inside certain materials immersed in a bath of liquid nitrogen close to absolute zero (−273.15°C). Under these circumstances, the absence of electrical resistance and the expulsion of the magnetic field (Meissner effect) makes it possible to levitate a magnet above the superconductor almost eternally. The induced currents can flow without dissipation by Joule effect.
Superfluidity is the state of a fluid which at very low temperature is devoid of any viscosity. Ultracold helium at 2.17 K (lambda point) becomes superfluid and is no longer retained in any container. Helium without any viscosity will flow through the material of the container.
It is therefore at very low temperature that quantum mechanics manifests itself on a macroscopic scale.
The temperature of matter is directly related to the speed of molecular agitation. Thus molecules can be described as corpuscles moving under the effect of heat.
However, when a gas or a fluid is cooled, the speed of its atoms is gradually reduced and the wave nature of matter is favored.
The spatial spreading of the particles is characterized by the thermal wavelength (λ_th) of Louis De Broglie (French mathematician and physicist 1892-1987).
λ_th=h/Mv (h=Planck constant, M=particle mass and v=particle velocity).
When the thermal wavelength is much smaller than the distance between the particles, the gas can be considered as a classical gas consisting of corpuscles.

But when λ_th is greater than the interparticle distance, then quantum effects appear.
When a temperature close to 0 K is reached, all the particles accumulate in the lowest possible fundamental energy state and condense. This is when the Bose-Einstein condensate is formed.
The fact that all the particles are in the ground state is not very surprising because at zero temperature no interaction exists, the kinetic energy is zero. What is amazing is the phase transition that suddenly appears in the Bose-Einstein condensate.
At a sufficiently low temperature, atoms that have an even mass number (deuterium, helium 4, lead 208, etc.) can be considered identical bosons and occupy a single lower energy quantum state. This phenomenon was predicted in 1925 by Albert Einstein.

Image: Bose-Einstein condensation in a gas as a function of temperature.
At room temperature, the wavelength of air molecules (nitrogen, oxygen) is extremely small (about 0.2 angstrom, 1Å=10⁻¹⁰ m).
The thermal wavelength equation tells us that as the speed decreases the wavelength increases and if the wavelength increases the wave packets associated with each particle get bigger and bigger. The volume in the container does not vary, λ_th increases until reaching the distance between particles. At this moment an astonishing phase transition occurs. This phenomenon was predicted in 1925 by Albert Einstein.