Bogoliubov Excitations in a Kronig-Penney Potential

TL;DR

This paper analytically derives the excitation spectrum of a Bose-Einstein condensate in a 1D periodic potential using the Kronig-Penney model, revealing gapless, linear low-energy excitations due to anomalous tunneling.

Contribution

It provides an analytical solution for the Bogoliubov excitation spectrum in a Kronig-Penney potential, highlighting the role of anomalous tunneling in low-energy excitations.

Findings

Excitation spectrum is gapless and linear at low energies.

Analytical band structure obtained for arbitrary lattice depths.

Low-energy excitations exhibit anomalous tunneling behavior.

Abstract

With use of the Kronig-Penney model, we study the excitation spectrum of a Bose-Einstein condensate in a one-dimensional periodic potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum for arbitrary values of the lattice depth. We find that the excitation spectrum is gapless and linear at low energies, and that it is due to the {\it anomalous tunneling} of low energy excitations, predicted by Kagan {\it et al.}.