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

• URL: http://arxiv.org/abs/2002.08877v2
• Date: Thu, 26 Mar 2020 10:07:19 GMT
• Title: Detecting a logarithmic nonlinearity in the Schr\"odinger equation using Bose-Einstein condensates
• Authors: Sascha Vowe, Claus L\"ammerzahl and Markus Krutzik
• Abstract summary: We study the effect of a logarithmic nonlinearity in the Schr"odinger equation (SE) on the dynamics of a Bose-Einstein condensate (BEC) We find that 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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