Dynamical decoupling design for identifying weakly coupled nuclear spins in a bath

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.