Eigenmodal Analysis of Anderson Localization: Applications to Photonic Lattices and Bose-Einstein Condensates

TL;DR

This paper develops eigenmodal analysis methods to study Anderson localization in photonic lattices and Bose-Einstein condensates, revealing localization phenomena and proposing improved lattice potentials for BEC trapping.

Contribution

Enhanced eigenmodal analysis techniques are applied to optical and BEC systems, enabling detailed study of Anderson localization effects and edge localization in complex potentials.

Findings

Edge localization of high-order Tamm-modes in 2-D BECs

Validation of analysis methods through comparison with measurements

Proposal of 3-D lattice potentials to mitigate diffusive effects

Abstract

We present the eigenmodal analysis techniques enhanced towards calculations of optical and non-interacting Bose-Einstein condensate (BEC) modes formed by random potentials and localized by Anderson effect. The results are compared with the published measurements and verified additionally by the convergence criterion. In 2-D BECs captured in circular areas, the randomness shows edge localization of the high-order Tamm-modes. To avoid strong diffusive effect, which is typical for BECs trapped by speckle potentials, a 3-D-lattice potential with increased step magnitudes is proposed, and the BECs in these lattices are simulated and plotted.