Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates

Keisuke Fujii; Sarah L. Görlitz; Nikolas Liebster; Marius Sparn; Elinor Kath; Helmut Strobel; Markus K. Oberthaler; Tilman Enss

doi:10.1103/physreva.109.l051301

arXiv · 2309.03829

Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates

Keisuke Fujii·Sarah L. Görlitz·Nikolas Liebster·Marius Sparn·Elinor Kath·Helmut Strobel·Markus K. Oberthaler·Tilman Enss

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Abstract

We investigate pattern formation in two-dimensional Bose-Einstein condensates (BECs) caused by periodic driving of the interatomic interaction. We show that this modulation generically leads to a stable square grid density pattern, due to nonlinear effects beyond the initial Faraday instability. We take the amplitudes of two waves parametrizing the two-dimensional density pattern as order parameters in pattern formation. For these amplitudes, we derive a set of coupled time evolution equations from the Gross--Pitaevskii (GP) equation with a time-periodic interaction. We identify the fixed points of the time evolution and show by stability analysis that the inhomogeneous density exhibits a square grid pattern, which can be understood as a manifestation of a stable fixed point. Our stability analysis establishes the pattern in BECs as a nonequilibrium steady state.

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Keisuke Fujii, Sarah L. Görlitz, Nikolas Liebster, Marius Sparn, Elinor Kath, Helmut Strobel, Markus K. Oberthaler, Tilman Enss. 2023-09-07. Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates. https://doi.org/10.1103/physreva.109.l051301

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