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A solvable model of a periodically-driven trapped mixture of Bose-Einsteincondensates, consisting of $N_1$ interacting bosons of mass $m_1$ driven by aforce of amplitude $f_{L,1}$ and $N_2$ interacting bosons of mass $m_2$ drivenby a force of amplitude $f_{L,2}$, is presented. The model generalizes theharmonic-interaction model for mixtures to the time-dependent domain. Theresulting many-particle ground Floquet wavefunction and quasienergy, as well asthe time-dependent densities and reduced density matrices, are prescribedexplicitly and analyzed at the many-body and mean-field levels of theory forfinite systems and at the limit of an infinite number of particles. We provethat the time-dependent densities per particle are given at the limit of aninfinite number of particles by their respective mean-field quantities, andthat the time-dependent reduced one-particle and two-particle density matricesper particle of the driven mixture are $100\%$ condensed. Interestingly, thequasienergy per particle {\it does not} coincide with the mean-field value atthis limit, unless the relative center-of-mass coordinate of the twoBose-Einstein condensates is not activated by the driving forces $f_{L,1}$ and$f_{L,2}$. As an application, we investigate the imprinting of angular momentumand its fluctuations when steering a Bose-Einstein condensate by an interactingbosonic impurity, and the resulting modes of rotations. Whereas the expectationvalues per particle of the angular-momentum operator for the many-body andmean-field solutions coincide at the limit of an infinite number of particles,the respective fluctuations can differ substantially. The results are analyzedin terms of the transformation properties of the angular-momentum operatorunder translations and boosts and the interactions between the particles.Implications are briefly discussed.

entropy

Solvable model of a generic driven mixture of trapped Bose-Einstein  condensates and properties of a many-boson Floquet state at the limit of an  infinite number of particles