Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates
arXiv:2309.03829 · doi:10.1103/PhysRevA.109.L051301
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.
arXiv comment7 pages, 3 figures. Supplemental material: 9 pages
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