Abstract
A quantum simulator environment is considered in Bose-Einstein condensate under bichromatic optical lattice, manifesting rogue waves. We report an exact analytical model to produce rogue wave excitations, the dynamics of which is investigated by solving the corresponding scalar Gross-Pitaevskii equation. A qualitative understanding of the formation mechanism at various trap parameters is provided by assuming the rogue wave excitation as a mixture of bright and dark solitary waves, which offers a novel illustration of the previous conjecture for rogue waves in Bose-Einstein condensate. We identify the lattice parameters for controlling the spatio-temporal variations of the condensate density. An Anderson-like localization is identified where the condensate is seen to preserve the rogue wave nature at the central frustrated site for larger lattice frustration.
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