BEC of magnons in superfluid3He-Band symmetry breaking fields

Abstract

States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid ${}^{3}$He-$B$ represent the macroscopic examples of the Bose-Einstein condensates of magnons. Once the magnons form one of these states, this many-magnon coherent quantum state is described by a ``single-magnon wave function'' (or an order parameter). A suitable external perturbation may cause the condensate to oscillate around the state of coherent precession, which demonstrates a collective rigidity of the condensate against scattering a single magnon out of it. The states corresponding to a free coherent precession of magnetization are degenerate in the phase of precession, so there exist oscillations around such states with a gapless dispersion relation, known as the Goldstone modes. Here, we present both experimental and theoretical results of the study of the spin density oscillations superposed on a homogeneously precessing domain in superfluid ${}^{3}$He-$B$ in the presence of a high-frequency excitation field ${B}_{\text{rf}}$. We show that the presence of this field lifts the degeneracy of the precessing state with respect to the phase of precession, that is, it violates the symmetry of the magnon condensate, and former Goldstone modes become non-Goldstone ones, as they acquire the energy gap in their spectrum.