  We propose a scheme to generate spin cat states, i.e., superpositions of
maximally separated quasiclassical states on a single high-dimensional nuclear
spin in a solid-state device. We exploit a strong quadrupolar nonlinearity to
drive the nucleus significantly faster than usual gate sequences, achieving
collapses and revivals two orders of magnitude faster than the dephasing
timescale. Furthermore, these states are engineered without entanglement with
an ancilla, hence, are robust against error propagation. With our multitone
control, we can realize arbitrary high-spin rotations within an experimentally
feasible regime, as well as transform a spin coherent state to a spin cat state
using only phase modulation, opening the possibility of storing and
manipulating high-fidelity cat states.
