Temperature Sensitivity of $^{14}\mathrm{NV}$ and $^{15}\mathrm{NV}$ Ground State Manifolds

Abstract: We measure electron and nuclear spin transition frequencies in the ground state of nitrogen-vacancy (NV) centers in diamond for two nitrogen isotopes ($^{14}\mathrm{NV}$ and $^{15}\mathrm{NV}$) over temperatures ranging from 77 K to 400 K. Measurements are performed using Ramsey interferometry and direct optical readout of the nuclear and electron spins. We extract coupling parameters $Q$ (for $^{14}\mathrm{NV}$), $D$, $A_{||}$, $A_{\perp}$, $\gamma_e/\gamma_n$, and their temperature dependences for both isotopes. The temperature dependences of the nuclear-spin transitions within the $m_s = 0$ spin manifold near room temperature are found to be +0.52(1) ppm/K for $^{14}\mathrm{NV}$ ($|m_I=-1> \leftrightarrow |m_I=+1>$) and -1.1(1) ppm/K for $^{15}\mathrm{NV}$ ($|m_I=-1/2> \leftrightarrow |m_I=+1/2>$). An isotopic shift in the zero-field splitting parameter $D$ between $^{14}\mathrm{NV}$ and $^{15}\mathrm{NV}$ is measured to be $\sim$ 120 kHz. Residual transverse magnetic fields are observed to shift the nuclear spin transition frequencies, especially for $^{15}\mathrm{NV}$. We have precisely determined the set of parameters relevant for the development of nuclear-spin-based diamond quantum sensors with greatly reduced sensitivity to environmental factors.