Macroscopic quantum phenomena

Macroscopic quantum phenomena are 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 topological order. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein condensates. Between 1996 and 2016 six 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, dressed photons such as polaritons and in laser light. Although these media are very different, they are all similar in that they show macroscopic quantum behavior, and in this respect they all can be referred to as quantum fluids. Quantum phenomena are generally classified as macroscopic when the quantum states are occupied by a large number of particles (of the order of the Avogadro number) or the quantum states involved are macroscopic in size (up to kilometer-sized 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 a single state is occupied by a very large number of particles. We start with the wave function of the state written as with Ψ0 the amplitude and the phase. The wave function is normalized so that The physical interpretation of the quantity depends on the number of particles. Fig. 1 represents a container with a certain number of particles with a small control volume ΔV inside. We check from time to time how many particles are in the control box. We distinguish three cases: There is only one particle. In this case the control volume is empty most of the time. However, there is a certain chance to find the particle in it given by Eq. (). The probability is proportional to ΔV. The factor ΨΨ∗ is called the chance density.