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 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.

K. Fujii, S. L. Görlitz, N. Liebster, M. Sparn, E. Kath, H. Strobel, M. K. Oberthaler, T. Enss,
„Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-
Einstein condensates“, Phys. Rev. A 109, L051301 (2024).


Related to Project C02, C03, A04