Self-consistent field theory of polarised Bose-Einstein condensates: dispersion of collective excitations

We suggest the construction of a set of quantum hydrodynamic equations for Bose-Einstein condensates (BECs), where the atoms have an electric dipole moment. The contribution of dipole-dipole interactions (DDIs) to the Euler equation is obtained. Quantum equations for the evolution of a medium polarisation are derived. A developed mathematical method allows us to study the effect of interactions on the evolution of the polarisation. The developed method can be applied to various physical systems in which dynamics are affected by DDIs. The derivation of the Gross-Pitaevskii equation for polarised particles from quantum hydrodynamics is described. We show that the Gross-Pitaevskii equation applies when all the dipoles have the same orientation which does not change with time. A comparison of the equation for the electric dipole evolution with the equation for the magnetisation evolution is described. Dispersion of collective excitations in the dipolar BEC, either under the influence or not under the influence of an uniform external electric field, is considered using our method. We show that the evolution of the polarisation of the BEC leads to the formation of a novel type of collective excitations. A detailed description of the dispersion of the collective excitations is presented. We also consider the process of wave generation in the polarised BEC by means of a monoenergetic beam of neutral polarised particles. We compute possibilities for the generation of Bogoliubov and polarisation modes by the dipole beam.