We investigate pattern formation in two-dimensional Bose-Einstein condensates (BECs) caused by temporal periodic modulation of the interatomic interaction. Temporal modulation of the interaction causes the so-called Faraday instability in the condensate, which we show generically leads to a stable square grid density pattern. We take the amplitudes in each of the two directions spanning the two-dimensional density pattern as order parameters in pattern formation and derive a set of simultaneous time evolution equations for those order parameters 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 as a stable fixed point.
K. Fujii, S. L. Görlitz, N. Liebster, M. Sparn, E. Kath, H. Strobel, M. K. Oberthaler, T. Enss, “Square Pattern Formation as Stable Fixed Point in Driven Two-Dimensional Bose-Einstein Condensates”, Sept. 7, 2023, arXiv:2309.03829 (2023).
Related to Project A04, C02, C03