Spin Squeezing Enhanced Quantum Magnetometry with Nitrogen-Vacancy Center Qutrits

We explore the utility of quantum spin squeezing in quantum magnetometry, focusing on three-level (qutrit) Nitrogen-Vacancy (NV) centers within diamond, utilizing a standard Ramsey interferometry pulse protocol. Our investigation incorporates the effects of dephasing and relaxation on NV centers' dynamics during Ramsey measurements, modeled via the Lindblad quantum master equation. We conduct a comparative analysis between the metrological capabilities of a single NV center and a pair of NV centers, considering Quantum Fisher Information both with and without spin squeezing. The quantum correlations between NV centers are assessed through the evaluation of the Kitagawa-Ueda spin squeezing parameter within a two-level manifold. Additionally, parallel calculations are conducted using a two-level model (qubit) for NV centers. Our findings reveal that leveraging qutrits and spin squeezing yields enhanced magnetometric precision, albeit constrained by dephasing effects. Nevertheless, even in the absence of dynamical decoupling methods to mitigate environmental noise, strategic timing of squeezing and free evolution can sustain the advantages of qutrit-based magnetometry.