Detecting a logarithmic nonlinearity in the Schrödinger equation using Bose-Einstein condensates

Sascha Vowe, Claus Lämmerzahl, Markus Krutzik

备注：: 6 pages, 4 figures
发表信息：: Phys. Rev. A 101, 043617 (2020)
DOI：: 10.1103/PhysRevA.101.043617

英文摘要：

We study the effect of a logarithmic nonlinearity in the Schrödinger 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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