Smooth bang-bang shortcuts to adiabaticity for atomic transport in a moving harmonic trap

Abstract

Bang-bang optimization, as a shortcut to adiabaticity, provides a simple but fast protocol allowing highfidelity shuttling of cold atoms or trapped ions, with the wide applications in interferometry, metrology, and quantum information processing. Such time-optimal control with at least two discontinuous switches requires the sudden jumps, which costs extra efforts and harms the overall performance as well. To circumvent these problems, we investigate the smooth bang-bang protocols with near-minimal time for fast atomic transport in a moving harmonic trap. Smoothing is accomplished by the Pontryagins maximal principle with the constraint that limits the first and second derivatives of control input. Moreover, the multiple shooting method is numerically presented for a smoothing procedure for the minimal-time optimization with the same constraints. By numerical examples and comparisons, we conclude that the smooth control input is capable of eliminating the energy excitation and sloshing amplitude at the cost of a slight increase in minimal time. Our smooth bang-bang protocols presented here are more practical and feasible in the relevant experiments, and can be easily extended to other classical and quantum systems where the shortcuts to adiabaticity are requested and implemented.