Supercurrent behavior of low-energy Bogoliubov phonons and the anomalous tunneling effect in a Bose-Einstein condensate

Abstract

We investigate tunneling properties of Bogoliubov mode in a Bose-Einstein condensate. Using an exactly solvable model with a $\ensuremath{\delta}$-functional barrier, we show that each component in the two-component wave function $(u,v)$ of low-energy Bogoliubov phonon has the same form as the condensate wave function in the supercurrent state. As a result, the currents ${J}_{u}$ and ${J}_{v}$ associated with $u$ and $v$, respectively, have the same tunneling properties as those of supercurrent carried by condensate. Thus, the tunneling of low-energy Bogoliubov phonon described by the tunneling of these two currents shows perfect transmission. We also show that the supercurrent behaviors of Bogoliubov phonon still exist in the presence of supercurrent carried by condensate, except in the critical supercurrent state. In the critical current state, the perfect transmission is absent, because ${J}_{u}$ or ${J}_{v}$ exceeds their upper limit given by the critical value of the supercurrent associated with the condensate. Our results consistently explain the recently proposed two tunneling phenomena associated with Bogoliubov phonon, namely, the anomalous tunneling effect (perfect transmission in the low-energy limit) and the breakdown of the perfect transmission in the critical supercurrent state.