Time-optimal force sensing with ultracold atoms
We develop a time-optimal approach to force sensing using a Bose-Einstein condensate in a shaken optical lattice. Optimal control protocols are derived from a Fisher information framework and yield optimal dynamics that spontaneously organize in intereferometer-like structures, where multiple interferences combine to maximize sensitivity. We analyse how measurement precision scales with control time and how the finite momentum dispersion of the condensate changes the optimal dynamics, observing an abrupt change of conformation from single- to double-folded interference structures for robust controls. The protocols are implemented experimentally for cold atoms subjected to inertial and magnetic forces, demonstrating high sensitivity and robustness. Our approach establishes a general route to time-optimal quantum sensing beyond standard interferometric architectures, applcable across all quantum platforms.