  In quantum information science, the external control of qubits must be
balanced with the extreme isolation of the qubits from the environment. Atomic
qubit systems typically mitigate this balance through the use of gated laser
fields that can create superpositions and entanglement between qubits. Here we
propose the use of high-order optical Stark shifts from optical fields to
manipulate the splitting of atomic qubits that are insensitive to other types
of fields. We demonstrate a fourth-order AC Stark shift in a trapped atomic ion
system that does not require extra laser power beyond that needed for other
control fields. We individually address a chain of tightly-spaced trapped ions
and show how these controlled shifts can produce an arbitrary product state of
ten ions as well as generate site-specific magnetic field terms in a simulated
spin Hamiltonian.
