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In this paper, we investigate the manipulation of quasi-1D Bose gases thatare trapped in a highly elongated potential by optimal control methods. Theeffective meanfield dynamics of the gas can be described by a one-dimensionalnon-polynomial Schr\"odinger equation. We extend the indirect optimal controlmethod for the Gross-Pitaevskii equation by Winckel and Borzi (2008) to obtainnecessary optimality conditions for state and energy cost functionals. Thisapproach is then applied to optimally compress a quasi-1D Bose gase in an(optical) box potential, i.e., to find a so-called short-cut to adiabaticity,by solving the optimality conditions numerically. The behavior of the proposedmethod is finally analyzed and compared to simple direct optimizationstrategies using reduced basis functions. Simulations results demonstrate thefeasibility of the proposed approach.

Optimal control of quasi-1D Bose gases in optical box potentials