  The interplay between disorder and transport is a problem central to the
understanding of a broad range of physical processes, most notably the ability
of a system to reach thermal equilibrium. Disorder and many body interactions
are known to compete, with the dominance of one or the other giving rise to
fundamentally different dynamical phases. Here we investigate the spin
diffusion dynamics of 13C in diamond, which we dynamically polarize at room
temperature via optical spin pumping of engineered color centers. We focus on
low-abundance, strongly hyperfine-coupled nuclei, whose role in the
polarization transport we expose through the integrated impact of variable
radio-frequency excitation on the observable bulk 13C magnetic resonance
signal. Unexpectedly, we find good thermal contact throughout the nuclear spin
bath, virtually independent of the hyperfine coupling strength, which we
attribute to effective carbon-carbon interactions mediated by the electronic
spin ensemble. In particular, observations across the full range of hyperfine
couplings indicate the nuclear spin diffusion constant takes values up to two
orders of magnitude greater than that expected from homo-nuclear spin
couplings. Our results open intriguing opportunities to study the onset of
thermalization in a system by controlling the internal interactions within the
bath.
