Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current

TL;DR

This paper derives an exact solution for low-energy Bogoliubov excitations in Bose-Einstein condensates with arbitrary barriers, revealing partial transmission and the absence of anomalous tunneling at critical currents due to density fluctuation effects.

Contribution

It provides an explicit analytical expression for transmission coefficients and clarifies the mechanism behind the absence of perfect tunneling at critical currents.

Findings

Partial transmission of excitations at low energy

Wavefunctions differ from condensate wavefunction

Density fluctuations inhibit perfect tunneling

Abstract

We derive the exact solution of low energy limit of Bogoliubov equations for excitations of Bose-Einstein condensate in the presence of arbitrary potential barrier and maximum current of condensate. Using this solution, we give the explicit expression for the transmission coefficient against the potential barrier, which shows partial transmission in the low energy limit. The wavefunctions of excitations in the low energy limit do not coincide with that of the condensate. The absence of the perfect transmission in the critical current state originates from local enhancement of density fluctuations around the potential barrier.