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arXiv · 2002.08877

Detecting a logarithmic nonlinearity in the Schr\"odinger equation using Bose-Einstein condensates

Sascha Vowe·Claus Lämmerzahl·Markus Krutzik
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Abstract

We study the effect of a logarithmic nonlinearity in the Schr\"odinger equation (SE) on the dynamics of a freely expanding Bose-Einstein condensate (BEC). The logarithmic nonlinearity was one of the first proposed nonlinear extensions to the SE which emphasized the conservation of important physical properties of the linear theory, e.g.: the separability of noninteracting states. Using this separability, we incorporate it into the description of a BEC obeying a logarithmic Gross-Pittaevskii equation. We investigate the dynamics of such BECs using variational and numerical methods and find that, using experimental techniques like delta kick collimation, experiments with extended free-fall times as available on microgravity platforms could be able to lower the bound on the strength of the logarithmic nonlinearity by at least one order of magnitude.

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Sascha Vowe, Claus Lämmerzahl, Markus Krutzik. 2020-02-20. Detecting a logarithmic nonlinearity in the Schr\"odinger equation using Bose-Einstein condensates. https://doi.org/10.1103/physreva.101.043617

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