Following the precession of a nuclear spin by weak measurements
Kristian S. Cujia, Jens M. Boss, Jonathan Zopes, Christian L. Degen
Department of Physics, ETH Zurich, Switzerland
Magnetic resonance techniques form a powerful toolset with far reaching applications in areas ranging from physics and chemistry to structural biology and materials research. At the heart of these techniques is the detection of the electromagnetic radiation, in the form of a free induction decay (FID) signal, generated by nuclei precessing around a magnetic field. Conventional approaches rely on inductive detection, while more recent experiments take advantage of atomic spin sensors that measure the nuclear field through dipolar interactions. These approaches typically still require an ensemble of spins (≈106) to generate a sufficiently strong and coherent signal. In this regime, the back-action of the atomic spin sensor on the nuclear spin precession can usually be neglected.
As the nuclear ensembles become smaller, eventually consisting of only few or even a single nuclear spin, the quantum back-action of the sensor on the nuclear spin evolution must be considered.
Motivated by recent advances in continuous sampling of coherent signals using NV centers in diamond [1], we have implemented a weak measurement protocol to detect FID signals from single carbon-13 nuclear spins [2]. We study the effect of the measurement strength φ and sampling frequency fS of a series of weak measurements on the nuclear spin precession. In particular, we find that a periodic sampling of the FID accelerates the decoherence of the nuclear spin, and under certain conditions leads to a “frequency pulling” of the nuclear Larmor frequency. In addition, we were able to track a nuclear spin FID signal beyond the T2 and T1 times of the NV sensor spin, indicating that our strategy may be useful for detecting distant, very weakly coupled nuclei.
[1] Quantum sensing with arbitrary frequency resolution, J. M. Boss, K. S. Cujia, J. Zopes, and C. L. Degen, Science 356, 837 (2017)
[2] K. S. Cujia et al., unpublished.