Sensitive measurement of phase shift of an AC magnetic field by quantum sensing with multiple-pulse decoupling sequences

Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen-vacancy (NV) center in the diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC-field can be generally obtained when the π-pulse period in the sequences matches the half time period of the field and the relative phase difference between the sequences and the field is zero. By contrast, the NV quantum sensor acquires no phase accumulation if the relative phase difference is π / 2. Thus, this phase-accumulation condition does not have any advantage for the magnetometry. However, we revealed that the nonphase-accumulation condition is available for detecting a very small phase shift of an AC-field from its initial phase. Measurements of the real part and the imaginary part of AC impedance require the amplitude and the phase information of an AC-field, and thus, this finding is expected to provide a guide for realizing sensitive measurement of AC impedance in the micrometer and nanometer scales.Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen-vacancy (NV) center in the diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC-field can be generally obtained when the π-pulse period in the sequences matches the half time period of the field and the relative phase difference between the sequences and the field is zero. By contrast, the NV quantum sensor acquires no phase accumulation if the relative phase difference is π / 2. Thus, this phase-accumulation condition does not have any advantage for the magnetometry. However, we revealed that the nonphase-accumulatio...