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 anomalous tunneling of low-energy excitations, predicted by Kagan et al.

arXiv:cond-mat/0506266Physical Review ANov 10, 200516 citations

Elementary Excitations of Condensates in a Kronig-Penney Potential

Ippei Danshita, Shinichiro Kurihara, S. Tsuchiya

We investigate the excitation spectrum of a Bose‐Einstein condensate in a Kronig‐Penney potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum. We find that the excitation spectrum is gapless and linear at low energies. This property is found to be attributed to the anomalous tunneling behavior of low energy excitations, which has been predicted by Kagan et al.

AIP conference proceedingsJan 1, 20060 citations

Bulletin of the American Physical Society

Bogoliubov Excitations and Superfluidity in a Kronig-Penney Potential

Ippei Danshita, Susumu Kurihara, Shunji Tsuchiya

Published Mar 15, 2006• 1 citation

OpenAlex

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q

and the dynamical instability is caused by the excitations with $q=\ensuremath{\pi}∕a$ at their onsets, where

q

is the quasimomentum of excitation and

a

is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.