Anomalous tunneling of collective excitations and effects of superflow in the polar phase of a spin-1 spinor Bose-Einstein condensate

We investigate tunneling properties of collective modes in the polar phase of a spin-1 spinor Bose-Einstein condensate (BEC). This spinor BEC state has two kinds of gapless modes (i.e., Bogoliubov and spin-wave). Within the framework of mean-field theory at T=0, we show that these Goldstone modes exhibit perfect transmission in the low-energy limit. Their anomalous tunneling behavior still holds in the presence of superflow, except in the critical current state. In the critical current state, while the tunneling of Bogoliubov mode is accompanied by finite reflection, the spin wave still exhibits perfect transmission, unless the strengths of spin-dependent and spin-independent interactions take the same value. We discuss the relation between perfect transmission of a spin wave and underlying superfluidity through a comparison of wave functions of the spin wave and the condensate.