Dipole-dipole interaction and polarization mode in BEC

Abstract

We propose the construction of a set of quantum hydrodynamics equations for the Bose-Einstein condensate (BEC) where atoms have electric dipole moment (EDM). The contribution of the dipole-dipole interactions (DDI) to the Euler equation is estimated. Quantum equations for the evolution of medium polarization are constructed for the first time. The mathematical method we developed allows studying the effects of interactions on the evolution of polarization. The developed method may be applied to various physical systems in which dynamics is affected by DDI. A problem of elementary excitations in BEC, either affected or not affected by the uniform external electric field, is addressed using our method. We show that the evolution of polarization in BEC leads to the formation of a novel type of elementary excitations. Also, we consider the process of wave generation in polarized BEC by means of monoenergetic beam of neutral polarized particles. We compute the possibilities of the generation of Bogoliubov's modes and polarization modes by the dipole beam.

Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles

“…Approximate connection of T αβγ (r, t) with the concentration and polarization of particles is presented in work [12].…”

“…In this case if we assume that linear excitations δf are proportional to exp(−ıωt + ıkr) a linearized set of equations (12), ( 13), ( 17), (28) gives us the dispersion equation where…”

“…They deal with quasi-2D and multilayered systems of both charged and neutral polarized particles. There are articles where take into account of the EDM influence on the Bose-Einstein condensate (BEC) [11], [12]. In a particular work a contribution of polarization to the dispersion of Bogoliubov's mode has been analyzed.…”

“…IMM dynamics causes changes in the wave dispersion in magnetized plasma [13][14][15] as well as the existence of novel branches of dispersion in systems of such kind [14]. Interaction between IMM of neutron beam and magnetized plasma leads to the generation of waves in plasma [12], [15]. This effect is due to spin-spin, spincurrent [15] and spin-orbital interactions [16] between IMM of the beam and IMM and currents in plasma.…”

Exact analytical soliton solutions in dipolar Bose-Einstein condensates

“…We present an explicit expression for the potential energy of magnetic dipole interaction, or in other words the energy of the spin-spin interaction, which leads to corresponding Maxwell equations. We derive our model from the first principles (the many-particle Schrodinger equation) using method of the quantum hydrodynamics (QHD) [23]- [29], which has been used for studying of the dipolar BEC [30]- [37]. However, dynamics of dipole direction had been included in previous research, so it was more complicated model hiding some features of the model, which are necessary to understand.…”