Temperature drift rate for nuclear terms of the NV-center ground-state Hamiltonian

The nitrogen-vacancy (NV) center in diamond has been found to be a powerful tool for various sensing applications. In particular, in ensemble-based sensors, the main “workhorse” so far has been optically detected electron resonance. Utilization of the nuclear spin has the potential to significantly improve sensitivity in rotation and magnetic field sensors. Ensemble-based sensors consume a substantial amount of power, leading to noticeable heating of the diamond and thus requiring an understanding of temperature-related shifts. In this paper, we provide a detailed study of the temperature shift of the hyperfine components of the NV center.

Figure 1

(a) Experimental setup for nuclear spin spectroscopy of the NV-center ensemble. A FPGA was used to control the pulse sequence. (b) Energy levels of the ground state of an NV center. $D$ stands for the zero-field splitting; $Q$, the hyperfine structure constant for splitting due to ${}^{14}\mathrm{N}$ nuclear spin; and $2{\gamma }_{es}B$, Zeeman splitting between electron spins. The blue solid arrows show the allowed dipole MW transitions to the $m_s=\pm 1$ manifold, and the red circular dashed lines are allowed rf transitions of the nuclear spin in the $m_s=\pm 1$ manifold. (c) Pulse sequence of the experiment.

Figure 2

(a) Two-dimensional (2D) scan of the rf and MW resonances. The light-blue rectangles show the data slice for panel (b), and the green rectangle shows the area discussed in (b) and (c). (b) Average of the cross sections in the 2D plot in panel (a), corresponding to the MW resonances not affected by the rf. The solid line corresponds to the fit with three Lorentzian curves. (c) Hyperfine component amplitude vs RF. The microwave frequency for this plot was fixed at the value indicated by the green dot in (b) (see text for more details). The solid line corresponds to the Lorentzian fit.

Figure 3

(a) Schematic representation of the level structure shift due to temperature. (b) Shift of the NV hyperfine transition lines, with the color coding matching that in (a).

Figure 4

(a) Dependence of electronic change in zero-field splitting (ZFS) on the temperature (with respect to 2800 MHz). (b) Dependence of the $Q,A_{\parallel }$ change on the temperature of the diamond. Clearly, a linear dependence is observed. Changes are depicted with respect to the −4946.0-kHz and −2159.6-kHz rfs.

Figure 5

Temperature dependence of the hyperfine constants obtained with Helmholtz coils used as the source of the magnetic field.

Figure 6

Adjusted nuclear Rabi oscillations. The blue line corresponds to $f_{e-}^{n+}=2.79\mathrm{MHz}$, and the yellow line corresponds to $f_{e-}^{n-}=7.11\mathrm{MHz}$ (the offset of 0.0002 was added for clarity).

Figure 7

Loop diagram of the experiment.

Figure 8

Optically detected magnetic resonance for $B_x$ estimation.

Figure 9

Setup for electron-spin ZFS calibration.

Figure 10

Pulsed ODMR scans with sweeping of the temperature.