Shaking the condensates: Optimal number squeezing in the dynamic splitting of a Bose–Einstein condensate

We apply optimal control theory to the dynamic splitting process of a Bose–Einstein condensate (BEC). Number squeezing of two spatially separated BECs is important for interferometry applications and inhibits phase diffusion due to the nonlinear atom–atom interactions. We show how optimal number squeezing can be obtained on time scales much shorter compared to adiabatic splitting. The non-adiabatic time evolution of the condensates is controlled via the trap geometry, thus making our control schemes directly applicable to experiments. We find that the optimal solution for the trap is oscillatory, where a counterintuitive shaking during the ramp produces highly squeezed states. The underlying process can be identified as a parametric amplification.