  The 19F spins in a crystal of fluorapatite have often been used to
experimentally approximate a one-dimensional spin system. Under suitable
multi-pulse control, the nuclear spin dynamics may be modeled to first
approximation by a double-quantum one-dimensional Hamiltonian, which is
analytically solvable for nearest-neighbor couplings. Here, we use solid-state
nuclear magnetic resonance techniques to investigate the multiple quantum
coherence dynamics of fluorapatite, with an emphasis on understanding the
region of validity for such a simplified picture. Using experimental,
numerical, and analytical methods, we explore the effects of long-range
intra-chain couplings, cross-chain couplings, as well as couplings to a spin
environment, all of which tend to damp the oscillations of the multiple quantum
coherence signal at sufficiently long times. Our analysis characterizes the
extent to which fluorapatite can faithfully simulate a one-dimensional quantum
wire.
