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We investigate tunneling properties of Bogoliubov mode in a Bose-Einsteincondensate. Using an exactly solvable model with a delta-functional barrier, weshow that each component in the two-component wavefunction (u,v) of low-energyBogoliubov phonon has the same form as the condensate wavefunction in thesupercurrent state. As a result, the currents J_u and J_v associated with u andv, respectively, have the same tunneling properties as those of supercurrentcarried by condensate. Thus, the tunneling of low-energy Bogoliubov phonondescribed by the tunneling of these two currents shows perfect transmission. Wealso show that the supercurrent behaviors of Bogoliubov phonon still exist inthe presence of supercurrent carried by condensate, except in the criticalsupercurrent state. In the critical current state, the perfect transmission isabsent, because J_u or J_v exceeds their upper limit given by the criticalvalue of the supercurrent associated with the condensate. Our resultsconsistently explain the recently proposed two tunneling phenomena associatedwith Bogoliubov phonon, namely, the anomalous tunneling effect (perfecttransmission in the low-energy limit) and the breakdown of the perfecttransmission in the critical supercurrent state.

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