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

TL;DR

This paper analyzes the tunneling behavior of low-energy Bogoliubov phonons in a Bose-Einstein condensate, revealing perfect transmission in non-critical supercurrent states and explaining anomalous tunneling phenomena.

Contribution

It provides an exactly solvable model showing the connection between Bogoliubov phonon tunneling and supercurrent states, including the breakdown of perfect transmission at critical currents.

Findings

Perfect transmission of Bogoliubov phonons in non-critical supercurrent states

Breakdown of perfect transmission at the critical supercurrent state

Explanation of anomalous tunneling phenomena in BECs

Abstract

We investigate tunneling properties of Bogoliubov mode in a Bose-Einstein condensate. Using an exactly solvable model with a delta-functional barrier, we show that each component in the two-component wavefunction (u,v) of low-energy Bogoliubov phonon has the same form as the condensate wavefunction 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.