Temperature Sensitivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msup><mml:mi/><mml:mn>14</mml:mn></mml:msup><mml:mi mathvariant="normal">N</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>V</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msup><mml:mi/><mml:mn>15</mml:mn></mml:msup><mml:mi mathvariant="normal">N</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>V</mml:mi></mml:math> Ground-State Manifolds
Sean Lourette, Andrey Jarmola, Víctor M. Acosta, A. Glen Birdwell, Dmitry Budker, Marcus W. Doherty, Tony Ivanov, Vladimir S. Malinovsky
Abstract
We measure electron- and nuclear-spin transition frequencies in the ground state of nitrogen-vacancy (N-$V$) centers in diamond for two nitrogen isotopes (${}^{14}\mathrm{N}$-$V$ and ${}^{15}\mathrm{N}$-$V$) over temperatures ranging from 77 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 ${}^{14}\mathrm{N}$-$V$), $D$, ${A}_{\ensuremath{\parallel}}$, ${A}_{\ensuremath{\perp}}$, and ${\ensuremath{\gamma}}_{e}/{\ensuremath{\gamma}}_{n}$, 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 ${}^{14}\mathrm{N}$-$V$ ($|{m}_{I}=\ensuremath{-}1⟩\ensuremath{\leftrightarrow}|{m}_{I}=+1⟩$) and $\ensuremath{-}1.1(1)$ ppm/K for ${}^{15}\mathrm{N}$-$V$ ($|{m}_{I}=\ensuremath{-}1/2⟩\ensuremath{\leftrightarrow}|{m}_{I}=+1/2⟩$). An isotopic shift in the zero-field splitting parameter $D$ between ${}^{14}\mathrm{N}$-$V$ and ${}^{15}\mathrm{N}$-$V$ is measured to be $\ensuremath{\sim}120$ kHz. Residual transverse magnetic fields are observed to shift the nuclear-spin transition frequencies, especially for ${}^{15}\mathrm{N}$-$V$. 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.