  Shortcuts to adiabaticity (STA) have been successfully applied both
theoretically and experimentally to a wide variety of quantum control tasks. In
previous work the authors have developed an analytic extension to shortcuts to
adiabaticity, called enhanced shortcuts to adiabaticity (eSTA), that extends
STA methods to systems where STA cannot be applied directly [Phys. Rev.
Research 2, 023360 (2020)]. Here we generalize this approach and construct an
alternative eSTA method that takes advantage of higher order terms. We apply
this eSTA method to the expansion of both a Gaussian trap and accordion lattice
potential, demonstrating the improved fidelity and robustness of eSTA.
