  Nuclear magnetic resonance (NMR) has enormous applications. Two-dimensional
NMR is an essential technique to characterize correlations between nuclei and,
hence, molecule structures. Towards the ultimate goal of single-molecule NMR,
dynamical-decoupling- (DD) enhanced diamond quantum sensing enables the
detection of single nuclear spins and nanoscale NMR. However, there is still
the lack of a standard method in DD-based quantum sensing to characterize
correlations between nuclear spins in single molecules. Here we present a
scheme of two-dimensional DD-based quantum sensing, as a universal method for
correlation spectroscopy of single molecules. We design two-dimensional DD
sequences composed of two sets of periodic DD sequences with different periods,
which can be independently set to match two different transition frequencies
for resonant DD. We find that under the resonant DD condition the sensor
coherence patterns, as functions of the two independent pulse numbers of DD
subsequences, can fully determine different types of correlations between
nuclear spin transitions. This work offers a systematic approach to correlation
spectroscopy for single-molecule NMR.
