  The problem of how single "central" spins interact with a nuclear spin bath
is essential for understanding decoherence and relaxation in many quantum
systems, yet is highly nontrivial owing to the many-body couplings involved.
Different models yield widely varying timescales and dynamical responses
(exponential, power-law, Gaussian, etc). Here we detect the small random
fluctuations of central spins in thermal equilibrium (holes in singly-charged
(In,Ga)As quantum dots) to reveal the timescales and functional form of
bath-induced spin relaxation. This spin noise indicates long (400 ns) spin
correlation times at zero magnetic field, that increase to $\sim$5 $\mu$s as
hole-nuclear coupling is suppressed with small (100 G) applied fields.
Concomitantly, the noise lineshape evolves from Lorentzian to power-law,
indicating a crossover from exponential to inverse-log dynamics.

Mesoscale and Nanoscale Physics;Materials Science