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

作     者：A. Deutschmann-Olek K. Schrom N. Würkner J. Schmiedmayer S. Erne A. Kugi 

作者机构：Complex Dynamical Systems Group Automation and Control Institute TU Wien Vienna Austria Vienna Center for Quantum Science and Technology Atominstitut TU Wien Vienna Austria Center for Vision Automation & Control Austrian Institute of Technology Vienna Austria 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2023年第56卷第2期

页      面：1339-1344页

主　　题：Optimal control partial differential equations non-polynomial Schrödinger equation Bose gases ultra cold atoms 

摘      要：In this paper, we investigate the manipulation of quasi-1D Bose gases that are trapped in a highly elongated potential by optimal control methods. The effective mean-field dynamics of the gas can be described by a one-dimensional non-polynomial Schrödinger equation. We extend the indirect optimal control method for the Gross-Pitaevskii equation by Winckel and Borzì (2008) to obtain necessary optimality conditions for state and energy cost functionals. This approach 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 proposed method is finally analyzed and compared to simple direct optimization strategies using reduced basis functions. Simulations results demonstrate the feasibility of the proposed approach.