  Identifying weakly coupled nuclear spins around single electron spins is a
key step of implementing quantum information processing using coupled
electron-nuclei spin systems or sensing like single spin nuclear magnetic
resonance detection using diamond defect spins. Dynamical decoupling control of
the center electron spin with periodic pulse sequences [e.g., the
Carre-Purcell-Meiboom-Gill (CPMG) sequence] has been successfully used to
identify single nuclear spins and to resolve structure of nuclear spin
clusters. Here, we design a new type of pulse sequences by replacing the
repetition unit (a single $\pi$-pulse) of the CPMG sequence with a group of
nonuniformly-spaced $\pi$-pulses. Using nitrogen-vacancy center system in
diamond, we show that the designed pulse sequence improves the resolution of
nuclear spin noise spectroscopy, and more information about the surrounding
nuclear spins is extracted. The principle of dynamical decoupling design
proposed in this paper is useful in many systems (e.g., defect spin qubit in
solids, trapped ion and superconducting qubit) for high-resolution noise
spectroscopy.
