Fig. 3: Quantum nonlinear spectroscopy of a nuclear spin and a random-phased AC field.

a 2D spectrum of the third moment \(\widetilde{S}\big({\nu }_{{ij}},{\nu }_{{jk}}\big)\) of an NV center spin coupled to a nuclear spin. b The diagonal (orange symbols) and anti-diagonal (purple symbols) slice of a. c 2D spectrum of the third moment \(\widetilde{S}\big({\nu }_{{ij}},{\nu }_{{jk}}\big)\) of an NV center spin coupled to a random-phased AC field. d The calculated average height (curve) of the eight peaks at (0, ±ν₀), (±ν₀, 0), ±(ν₀, 2ν₀), or ±(2ν₀, ν₀) relative to those at ±(ν₀, −ν₀) as a function of the number of uniformly coupled nuclear spins. The symbols are experimental values (green is from Fig. 3a and blue is from Supplementary Fig. S12, measured with a different number of dynamical decoupling pulses). Error bars are standard deviation.