Anomalous Scattering of Low-lying Excitations in a Spin-1 Bose-Einstein Condensate

TL;DR

This paper develops a simple theoretical model for perfect tunneling of low-momentum excitations in a spin-1 Bose-Einstein condensate, revealing universal scattering properties of Nambu-Goldstone modes.

Contribution

It introduces a minimal theory describing perfect tunneling of low-energy excitations in a spin-1 BEC, highlighting universal scattering behaviors of Nambu-Goldstone modes.

Findings

Transmission coefficient T is determined by the order parameter.

Scattering cross section sigma scales as p^4 at low momentum.

Effects of impurity potential vanish in the low-momentum limit.

Abstract

We present the simplest theory of perfect tunneling of an excitation in a Bose-Einstein condensate (BEC) through an impurity potential with an arbitrary shape in the low-momentum limit. That is for the transverse spin wave in the ferromagnetic phase of a spin-1 BEC. This mode obeys a Schr\"odinger-type equation; yet, effects of the potential on its transmission coefficient $T$ and on its scattering cross section $sigma$ vanish in that limit. The order parameter determines $T$, and the momentum $p$-dependence of $sigma$ exhibits a Rayleigh scattering type ($sigma propto p^{4}$). These properties are common between two types of Nambu-Goldstone modes: this spin wave and the Bogoliubov mode.