Condensation of phonons in an ultracold Bose gas

We consider the generation of longitudinal phonons in an elongated Bose-condensed gas at zero temperature due to parametric resonance as a result of the modulation of the transverse trap frequency. The nonlinear temporal evolution with account of the phonon–phonon interaction leads self-consistently to the formation of the stationary state with the macroscopic occupation of a single phonon quantum state.