Physics of π-meson condensation and high temperature cuprate superconductors

The idea of condensation of the Goldstone pi-meson field in nuclear matter had been put forward a long time ago. However, it was established that the normal nuclear density is too low, it is not sufficient to condensate pi mesons. This is why the pi condensation has never been observed. Recent experimental and theoretical studies of high-temperature cuprate superconductors have revealed condensation of Goldstone magnons, the effect fully analogous to the pi condensation. The magnon condensation has been observed. It is clear now that quantum fluctuations play a crucial role in the condensation, in particular they drive a quantum phase transition that destroys the condensate at some density of fermions.