The precise engineering of quantum states, a basic prerequisite
for technologies such as quantum-enhanced sensing or quantum computing,
becomes more challenging with increasing dimension of the system
Hilbert space. Standard preparation techniques then require a large
number of operations or slow adiabatic evolution and give access
to only a limited set of states.
Here, we use quantum optimal control theory to overcome this problem
and derive shaped radio-frequency pulses to experimentally navigate
the Stark manifold of a Rydberg atom. We demonstrate that optimal control,
beyond improving the fidelity of an existing protocol, also enables us
to accurately generate a nonclassical superposition state that cannot
be prepared with reasonable fidelity using standard techniques.
Optimal control thus substantially enlarges the range of accessible states.
Our joint experimental and theoretical work establishes quantum
optimal control as a key tool for quantum engineering in complex
Hilbert spaces.