Perfect transmission and perfect reflection of Bogoliubov quasiparticles in a dynamically unstable Bose-Einstein condensate

TL;DR

This paper explores the tunneling behavior of quasiparticles in dynamically unstable Bose-Einstein condensates, revealing conditions for perfect transmission and reflection linked to the modes' stability properties.

Contribution

It demonstrates that perfect transmission occurs for NG modes even in unstable BECs and identifies perfect reflection as a generic feature of unstable modes, expanding understanding of quasiparticle tunneling.

Findings

Perfect transmission occurs for NG modes in unstable BECs.

Perfect reflection happens at maximum imaginary eigenvalue.

Reflection involves destructive interference of quasiparticle waves.

Abstract

The Nambu-Goldstone (NG) mode in a Bose-Einstein condensate (BEC) transmits a potential barrier with probability 1 in the zero-energy limit, which is known as the anomalous tunneling. In this paper, we investigate the tunneling properties of quasiparticles in a dynamically unstable BEC. We prepare a multi-component BEC (binary and spin-1 BEC) in a dynamically unstable state and solve the tunneling problem of the spin-wave excitation from the condensate. We find that the perfect transmission occurs even when the BEC is dynamically unstable if the spin-wave is the NG mode. Here, the mode that exhibits the perfect transmission is the dynamically unstable spin-wave mode, which is a pure-imaginary-eigenvalue solution of the Bogoliubov-de Gennes equation. Hence, we should take the zero-energy limit along not the real axis but the imaginary axis. We also demonstrate the existence of the perfect reflection of a dynamically unstable mode at the point where the imaginary part of the eigenvalue takes its maximum. In this case, the incident and reflected waves destructively interfere, and the amplitude of the quasiparticle wave function is strongly suppressed. We numerically confirm that the perfect reflection is a generic nature of dynamically unstable modes and not related to the NG mode.