Quantum simulation and Anderson localization in vector rogue waves of Bose-Einstein condensate

We report the existence of vector rogue waves in a coupled Bose-Einstein condensate, trapped in a bichromatic optical lattice, which is an appropriate platform for quantum simulation. Such two-component Bose-Einstein condensate plays a vital role to beget hybrid mixtures and structural transition of nonlinear excitations like rogue waves and solitons. An efficient manipulation of rogue waves is embraced, where we identify the slowing down and stopping of dark rogue wave by lattice engineering. This may nurture quantum memory application and transform the rogue wave mixture immiscible. The existence of Anderson localized rogue wave at the central frustrated lattice site is confirmed by showing the exponential nature and localization length of the condensate. A merging of a dual Anderson rogue waves is manifested in their coherent control. Numerical stability analysis is also carried out for a wide range of trap parameters for experimental viability.