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.