  Atom matterwave interferometry requires mirror and beamsplitter pulses that
are robust to inhomogeneities in field intensity, magnetic environment, atom
velocity and Zeeman sub-state. Pulse shapes determined using quantum control
methods offer significantly improved interferometer performance by allowing
broader atom distributions, larger interferometer areas and higher contrast. We
have applied gradient ascent pulse engineering (GRAPE) to optimise the design
of phase-modulated mirror pulses for a Mach-Zehnder light-pulse atom
interferometer, with the aim of increasing fringe contrast when averaged over
atoms with an experimentally relevant range of velocities, beam intensities,
and Zeeman states. Pulses were found to be highly robust to variations in
detuning and coupling strength, and offer a clear improvement in robustness
over the best established composite pulses. The peak mirror fidelity in a cloud
of $\sim 80\ \mu$K ${}^{85}$Rb atoms is predicted to be improved by a factor of
2 compared with standard rectangular $\pi$ pulses.
