Macroscopic quantum phenomena
Macroscopic quantum phenomena refer to processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect and concerted proton tunneling in ice. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein Condensates.
Between 1996 and 2003 four Nobel prizes were given for work related to macroscopic quantum phenomena. Macroscopic quantum phenomena can be observed in superfluid helium and in superconductors, but also in dilute quantum gases and in laser light. Although these media are very different, their behavior is very similar as they all show macroscopic quantum behavior.
Quantum phenomena are generally classified as macroscopic when the quantum states are occupied by a large number of particles (typically Avogadro's number) or the quantum states involved are macroscopic in size (up to km size in superconducting wires).
The concept of macroscopically-occupied quantum states is introduced by Fritz London. In this section it will be explained what it means if the ground state is occupied by a very large number of particles. We start with the wave function of the ground state written as
with Ψ₀ the amplitude and the phase. The wave function is normalized so that
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