  We experimentally characterize the non-equilibrium, room-temperature
magnetization dynamics of a spin chain evolving under an effective
double-quantum Hamiltonian. We show that the Liouville space operators
corresponding to the magnetization and the two-spin correlations evolve 90
degrees out of phase with each other, and drive the transport dynamics. For a
nearest-neighbor-coupled N-spin chain, the dynamics are found to be restricted
to a Liouville operator space whose dimension scales only as N^2, leading to a
slow growth of multi-spin correlations. Even though long-range couplings are
present in the real system, we find excellent agreement between the analytical
predictions and our experimental results, confirming that leakage out of the
restricted Liouville space is slow on the timescales investigated. Our results
indicate that the group velocity of the magnetization is 6.04 +/- 0.38 um/s,
corresponding to a coherent transport over N ~ 26 spins on the experimental
timescale. As the double-quantum Hamiltonian is related to the standard
one-dimensional XX Hamiltonian by a similarity transform, our results can be
directly extended to XX quantum spin chains, which have been extensively
studied in the context of both quantum magnetism and quantum information
processing.
