Nitrogen vacancy centers in diamond as angle-squared sensors

Nitrogen-vacancy (NV) centers are defects in diamonds, which, due to their electronic structure, have been extensively studied as magnetic field sensors. Such field detection applications usually employ the NV centers to detect field components aligned with the direction of the internally-defined spin axis of the NV center. In this work we detect magnetic fields which are slightly misaligned with the NV center axis. In particular, we demonstrate that the NV center can measure the square of the angle between the magnetic field and the NV center axis with high sensitivity which diverges as the external field approaches a value pre-defined by NV center's internal parameters, in agreement with predictions. These results show that NV centers could be used as sensitive transducers for making quantum nondemolition (QND) measurements on systems such as nanomechanical oscillators.