Reflection and Refraction of Bose-condensate Excitations

TL;DR

This paper studies how low-energy excitations in Bose-Einstein condensates transmit or reflect at potential barriers, revealing conditions for perfect transmission and total internal reflection, and relating these phenomena to electromagnetic laws and impedance matching.

Contribution

It provides a detailed analysis of Bose-condensate excitation transmission, connecting it to electromagnetic Brewster's law and impedance matching, and compares it with Tomonaga-Luttinger liquids results.

Findings

Perfect transmission occurs at a specific incident angle analogous to Brewster's law.

Total internal reflection occurs at large incident angles in the low energy limit.

Anomalous tunneling is explained via impedance matching.

Abstract

We investigate the transmission and reflection of Bose-condensate excitations in the low energy limit across a potential barrier separating two condensates with different densities. The Bogoliubov excitation in the low energy limit has the incident angle where the perfect transmission occurs. This condition corresponds to the Brewster's law for the electromagnetic wave. The total internal reflection of the Bogoliubov excitation is found to occur at a large incident angle in the low energy limit. The anomalous tunneling named by Kagan et al. [Yu. Kagan et al., Phys. Rev. Lett., 90, 130402 (2003)] can be understood in terms of the impedance matching. In the case of the normal incidence, comparison with the results in Tomonaga-Luttinger liquids is made.