Identification and optimal control strategies for the transversal splitting of ultra--cold Bose gases

Splitting a Bose–Einstein condensate (BEC) is a key operation in fundamental physics experiments and emerging quantum technologies, where precise preparation of well–defined initial states requires fast yet coherent control of the condensate’s nonlinear dynamics. This work formulates the BEC splitting process as an optimal feedforward control problem based on a physically interpretable, reduced–order model identified from limited experimental data. We introduce a systematic calibration strategy that combines optimal experiment selection and constrained nonlinear parameter estimation, enabling accurate system identification with minimal experimental overhead. Using this calibrated model, we compute energy–optimal trajectories via indirect optimal control to realize shortcuts to adiabaticity (STAs), achieving rapid transitions to the ground state of a double–well potential while suppressing excitations. Experiments confirm that the proposed control framework yields high–fidelity state transfers across multiple configurations, demonstrating its robustness and scalability for quantum control applications.