Tunneling properties of Bogoliubov mode and spin wave modes in supercurrent states of a spin-1 ferromagnetic spinor Bose-Einstein condensate

TL;DR

This paper studies how different collective excitations in a spin-1 ferromagnetic Bose-Einstein condensate tunnel through barriers, revealing conditions for perfect transmission and the effects of symmetry-breaking potentials.

Contribution

It demonstrates the conditions under which Bogoliubov and spin wave modes exhibit perfect tunneling in supercurrent states, extending understanding of anomalous tunneling phenomena in spinor BECs.

Findings

Bogoliubov mode shows anomalous tunneling with perfect transmission at low energy.

Transverse spin wave transmits perfectly only when its momentum matches the supercurrent momentum.

Quadrupolar mode does not exhibit perfect transmission.

Abstract

We investigate tunneling properties of collective excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). In addition to the Bogoliubov mode, this superfluid phase has two spin excitations, namely, the gapless transverse spin wave and the quadrupolar mode with a finite excitation gap. In the mean-field theory at T=0, we examine how these collective modes tunnel through a barrier potential that couples to the local density of particles. In the presence of supercurrent with a finite momentum $q$, while the Bogoliubov mode shows the so-called anomalous tunneling behavior (which is characterized by perfect transmission) in the low energy limit, the transverse spin-wave transmits perfectly only when the momentum $k$ of this mode coincides with $\pm q$. At $k=\pm q$, the wave function of this spin wave has the same form as the condensate wave function in the current carrying state, so that the mechanism of this perfect transmission is found to be the same as tunneling of supercurrent. Using this fact, the perfect transmission of the spin wave is proved for a generic barrier potential. We show that such perfect transmission does not occur in the quadrupolar mode. Further, we consider the effects of potentials breaking U(1) and spin rotation symmetries on the transmission properties of excitations. Our results would be useful for understanding excitation properties of spinor BECs, as well as the anomalous tunneling phenomenon in Bose superfluids.