Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates
arxiv(2023)
摘要
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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