The growing successes in performing quantum control experiments motivated thedevelopment of control landscape analysis as a basis to explain thesefindings.When a quantum system is controlled by an electromagnetic field, theobservable as a functional of the control field forms a landscape. Theoreticalanalyses have revealed many properties of control landscapes, especiallyregarding their slopes, curvatures, and topologies. A full experimentalassessment of the landscape predictions is important for future considerationof controlling quantum phenomena. Nuclear magnetic resonance (NMR) is exploitedhere as an ideal laboratory setting for quantitative testing of the landscapeprinciples. The experiments are performed on a simple two-level proton systemin a H$_2$O-D$_2$O sample. We report a variety of NMR experiments roving overthe control landscape based on estimation of the gradient and Hessian,including ascent or descent of the landscape, level set exploration, and anassessment of the theoretical predictions on the structure of the Hessian. Theexperimental results are fully consistent with the theoretical predictions. Theprocedures employed in this study provide the basis for future multispincontrol landscape exploration where additional features are predicted to exist.
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