  We study single- and multi-quantum transitions of the nuclear spins of
ionized arsenic donors in silicon and find quadrupolar effects on the coherence
times, which we link to fluctuating electrical field gradients present after
the application of light and bias voltage pulses. To determine the coherence
times of superpositions of all orders in the 4-dimensional Hilbert space, we
use a phase-cycling technique and find that, when electrical effects were
allowed to decay, these times scale as expected for a field-like decoherence
mechanism such as the interaction with surrounding $^{29}$Si nuclear spins.
