Understanding the dynamics of randomly positioned dipolar spin ensembles

Dipolar spin ensembles with random spin positions are attracting much attention because they help us to understand decoherence as it occurs in solid-state quantum bits in contact with spin baths. Also, these ensembles are systems which may show many-body localization, at least in the sense of very slow spin dynamics. We present measurements of the autocorrelations of spins on diamond surfaces at infinite temperature in a doubly rotating frame which eliminates local disorder. Strikingly, the timescales in the longitudinal and the transversal channel differ by more than one order of magnitude, which is a factor much greater than one would have expected from simulations of spins on lattices. A previously developed dynamic mean-field theory for spins (spinDMFT) fails to explain this phenomenon. Thus, we improve it by extending it to clusters (CspinDMFT). This theory does capture the striking mismatch up to two orders of magnitude for random ensembles. Without positional disorder, however, the mismatch is only moderate with a factor below 4. The pivotal role of positional disorder suggests that the strong mismatch is linked to precursors of many-body localization.