Dispersion properties of transverse waves propagating in the electrically polarized BECs

TL;DR

This paper extends quantum hydrodynamics to polarized Bose-Einstein condensates, deriving new equations for polarization dynamics, analyzing electromagnetic and matter wave dispersion, and revealing wave splitting and dipolar effects.

Contribution

It introduces a comprehensive set of quantum hydrodynamic equations for polarized BECs, including polarization evolution, and analyzes the dispersion of coupled electromagnetic and matter waves.

Findings

Electromagnetic wave dispersion splits into two branches.

Four solutions for wave modes: two electromagnetic and two matter waves.

Existence of polarization and dipolar frequency shifts in wave propagation.

Abstract

Further development of the method of quantum hydrodynamics in application for Bose-Einstein condensates (BECs) is presented. To consider evolution of polarization direction along with particles movement we have developed corresponding set of quantum hydrodynamic equations. It includes equations of the polarization evolution and the polarization current evolution along with the continuity equation and the Euler equation (the momentum balance equation). Dispersion properties of the transverse waves including the electromagnetic waves propagating through the BECs are considered. To this end we consider full set of the Maxwell equations for description of electromagnetic field dynamics. This approximation gives us possibility to consider the electromagnetic waves along with the matter waves. We find a splitting of the electromagnetic wave dispersion on two branches. As a result we have four solutions, two for the electromagnetic waves and two for the matter waves, the last two are the concentration-polarization waves appearing as a generalization of the Bogoliubov mode. We also obtain that if the matter wave propagate perpendicular to external electric field when dipolar contribution does not disappear (as it follows from our generalization of the Bogoliubov spectrum). In this case exist a small dipolar frequency shift due to transverse electric field of perturbation.