Non-integral form of the Gross-Pitaevskii equation for polarized molecules

TL;DR

This paper reformulates the Gross-Pitaevskii equation for polarized molecules into a non-integral form coupled with Maxwell equations, enabling analysis of collective excitations and solitons in dipolar Bose-Einstein condensates without instability issues.

Contribution

It introduces a non-integral nonlinear Schrödinger equation coupled with Maxwell equations for polarized BECs, simplifying analysis and highlighting the role of electric dipole moments.

Findings

Dispersion of collective excitations analyzed without dipole moment evolution.

Spectrum shows no instability for repulsive short-range interactions.

Dependence of bright soliton properties on electric dipole moment demonstrated.

Abstract

The Gross-Pitaevskii equation for polarized molecules is an integro-differential equation, consequently it is complicated for solving. We find a possibility to represent it as a non-integral nonlinear Schrodinger equation, but this equation should be coupled with two linear equations describing electric field. These two equations are the Maxwell equations. We recapture the dispersion of collective excitations in the three dimensional electrically polarized BEC with no evolution of the electric dipole moment directions. We trace the contribution of the electric dipole moment. We explicitly consider the contribution of the electric dipole moment in the interaction constant for the short-range interaction. We show that the spectrum of dipolar BEC reveals no instability at repulsive short-range interaction. Nonlinear excitations are also considered. We present dependence of the bright soliton characteristics on the electric dipole moment.