One of the key challenges in spectroscopy is inhomogeneous broadening that masks the homogeneous spectral lineshape and the underlying coherent dynamics. A variety of techniques including four-wave mixing and spectral hole-burning are used in optical spectroscopy while in nuclear magnetic resonance (NMR) spin-echo is the most common way to counteract inhomogeneity. However, the high-power pulses used in spin-echo and other sequences often create spurious dynamics obscuring the subtle spin correlations that play a crucial role in quantum information applications. Here we develop NMR techniques that allow the correlation times of the fluctuations in a nuclear spin bath of individual quantum dots to be probed. This is achieved with the use of frequency comb excitation which allows the homogeneous NMR lineshapes to be measured avoiding high-power pulses. We find nuclear spin correlation times exceeding 1 s in self-assembled InGaAs quantum dots - four orders of magnitude longer than in strain-free III-V semiconductors. The observed freezing of the nuclear spin fluctuations opens the way for the design of quantum dot spin qubits with a well-understood, highly stable nuclear spin bath.
