In the first method, this is achieved by the addition of a spectral component at the trapping frequency, while in the second we use a polynomial trajectory of an order high enough to account for the new boundary conditions. We develop two complementary methods that solve this boundary conditions problem by adding more degrees of freedom to the trajectory parameter space. Our experimental results demonstrate that, as a result, previously suggested trajectories are likely to fall short of the expectation. We show that the common boundary conditions on the atomic position, which are imposed to find the driving trajectory, lead to highly non-practical boundary conditions for the optical trap. Fast optical transfer of atoms between different locations is an important application of shortcuts to adiabaticity. Shortcuts to adiabaticity are techniques allowing rapid variation of the system Hamiltonian without inducing excess heating.
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