Spectroscopic Study of N-$V$ Sensors in Diamond-Based High-Pressure Devices

High-pressure experiments are crucial in modern interdisciplinary research fields such as engineering quantum materials, yet local probing techniques remain restricted due to the tight confinement of the pressure chamber in certain pressure devices. Recently, the negatively charged nitrogen-vacancy (N-$V$) center has emerged as a robust and versatile quantum sensor in pressurized environments. There are two popular ways to implement N-$V$ sensing in a diamond anvil cell (DAC), which is a conventional workhorse in the high-pressure community: create implanted N-$V$ centers (IN-$V\mathrm{s}$) at the diamond anvil tip or immerse N-$V$-enriched nanodiamonds (NDs) in the pressure medium. Nonetheless, there are limited studies on comparing the local stress environments experienced by these sensor types as well as their performances as pressure gauges. In this work, by probing the N-$V$ energy levels with the optically detected magnetic resonance (ODMR) method, we experimentally reveal a dramatic difference in the partially reconstructed stress tensors of IN-$V\mathrm{s}$ and NDs incorporated in the same DAC. Our measurement results agree with computational simulations, concluding that IN-$V\mathrm{s}$ perceive a more nonhydrostatic environment dominated by a uniaxial stress along the DAC axis. This provides insights on the suitable choice of N-$V$ sensors for specific purposes and the stress distribution in a DAC. We further propose some possible methods, such as using NDs and diamond nanopillars, to extend the maximum working pressure of quantum sensing based on ODMR spectroscopy, since the maximum working pressure could be restricted by nonhydrostaticity of the pressure environment. Moreover, we explore more sensing applications of the N-$V$ center by studying how pressure modifies different aspects of the N-$V$ system. We perform a PL study using both IN-$V\mathrm{s}$ and NDs to determine the pressure dependence of the zero-phonon line, which helps developing an all-optical pressure sensing protocol with the N-$V$ center. We also characterize the spin-lattice relaxation ($T_1$) time of IN-$V\mathrm{s}$ under pressure to lay a foundation for robust pulsed measurements with N-$V$ centers in pressurized environments.

Figure 1

(a) A simplified energy-level diagram of the N-$V$ center showing the spin-state-dependent transitions. (b) An illustration of the DAC configuration in our experiment. The MW antenna is fabricated on the implanted diamond anvil culet, while some 140-nm NDs are dropcasted on the other unimplanted anvil culet. (c),(d) ODMR responses of a 140-nm ND (labeled as ND1) and a patch of IN-$V\mathrm{s}$ (labeled as IN-$V1$) to the change in pressure of DAC1, respectively. The decrease in their ODMR contrasts is due to the stress-induced mixing of N-$V$ spin states and the degradation of the MW structure, where the latter factor takes a heavier toll on ND1.

Figure 2

(a),(b) Plots of SD of pressure and average $E^{\mathrm{net}}$ against average pressure for three (five) NDs and six (six) patches of IN-$V\mathrm{s}$ in DAC1 (DAC2), where $E^{\mathrm{net}}$ is the net change in $E$ with respect to the ambient value. The two DACs reveal very similar data trends. The NDs show only a tiny increase in SD while the IN-$V\mathrm{s}$ have no observable SD at all, signifying the pressure homogeneity at the pressure medium interface and approximately $10$ nm deep in the culet. Moreover, the IN-$V\mathrm{s}$ reveal a much greater increase in average $E^{\mathrm{net}}$, implying a more hydrostatic environment around the NDs and a more anisotropic environment around the IN-$V\mathrm{s}$. Here, the markers are joined in a way to indicate the pressure sequences in the experiments, while the purple arrows drawn are to emphasize the significantly different behaviors of NDs and IN-$V\mathrm{s}$ at the highest pressure point achieved. (c),(d) The differences in average $D$, average $P$, and average $E^{\mathrm{net}}$ between the three NDs and the six patches of IN-$V\mathrm{s}$ in DAC1 along the pressure sequence. In general, the NDs experience much stronger hydrostatic pressure compared with the IN-$V\mathrm{s}$. For all subfigures, one of the three NDs in DAC1 is replaced by another ND for the statistics at $p_4$ and $p_6$, due to the occasionally weakened fluorescence of those NDs.

Figure 3

(a) Linear fittings of $E^{\mathrm{net}}$ versus $P$ for ND1 in DAC1 and NDa in DAC2 by putting Eq. (10) into Eq. (9). (b) Linear fittings of average $E^{\mathrm{net}}$ versus average $P$ for the six patches of IN-$V\mathrm{s}$ in DAC1 and DAC2 by substituting Eq. (11) into Eq. (8). The fitted values of $\lambda$ for the IN-$V\mathrm{s}$ are at least an order of magnitude greater than that of the corresponding ND in the same DAC, suggesting a more directional stress environment around the IN-$V\mathrm{s}$ with a dominant uniaxial contribution along the DAC axis. Note that the reduced pressure points are not included in (a),(b) for concentrating on the effects of pressurizing our DACs, and $p_1$ is omitted in the fitting for NDa in DAC2 owing to the instability of the pressure medium during measurements of NDs at this pressure point. (c),(d) IN-$V$ crystal-frame stress-tensor components derived from experimental data (presented with markers) and obtained from computational simulations (presented with lines) against average $P$ measured by the six patches of IN-$V\mathrm{s}$, for DAC1 and DAC2, respectively. The lines are plotted in a way to signify the pressure sequences in the experiments. Both the experiment and simulation results reveal the gradual dominance of the stress component along the DAC axis. The insets illustrate that the average of our derived diagonal stress components indeed gives the average measured pressure. (c),(d) share the same legend.

Figure 4

(a) The 2D axisymmetric model used in our computational simulations, with the blue regions representing the (100)-oriented diamond anvils (the bottom one is the implanted anvil) and the orange-brown region representing the beryllium-copper gasket. An enlargement of the beveled diamond culets is provided, and the orientation of IN-$V$ crystal frame with respect to the DAC model is specified. All the boundaries are properly named for discussing the boundary conditions in our simulations. (b) Color maps visualizing the spatial distributions of the loading stress ${\sigma }_{XX}$, the lateral stresses ${\sigma }_{YY},{\sigma }_{ZZ}$, and the shear stress ${\sigma }_{XY}$ from the simulation at the highest pressure point $p_6$ of DAC1. Compressive stresses are taken to be positive. The distributions of ${\sigma }_{XX}$, ${\sigma }_{YY}$, and ${\sigma }_{ZZ}$ are symmetric in the two anvils but it is not the case for ${\sigma }_{XY}$. Furthermore, ${\sigma }_{XY}$ is considerably smaller than the diagonal stress components.

Figure 5

(a) A sample N-$V$ PL spectrum obtained by the measurement method stated in Sec. 3. In general, there is a narrow ZPL followed by broad phonon sidebands. (b) The ZPL fitting procedures in our data analysis, which concentrates on the portion of the PL spectrum from 615 to 658 nm. First, this piece of data is linearly interpolated and fitted with a quadratic polynomial (upper panel). Then, the fitted polynomial is subtracted from the interpolated data and a Lorentzian peak fitting is performed (lower panel). For both (a),(b), the raw data from IN-$V1$ in DAC1 at $p_2$ is used as an example. (c) Linear fittings of ZPL energy versus ODMR-calibrated local pressure for the IN-$V\mathrm{s}$ and NDs in DAC1 and DAC2. The data points for IN-$V\mathrm{s}$ are averages from the six patches in the corresponding DAC. The five fittings reveal similar pressure dependencies of the ZPL, from 0.56 to 0.59 meV/kbar with errors on the order of 0.01 meV/kbar. Our experimental results agree well with the literature.

Figure 6

(a),(b) Pulse sequences for measuring the relaxation curves of the bright $|0⟩$ state and the dark $|+⟩$ state, respectively. The 520-nm laser is for initialization to the $|0⟩$ state and readout of the final state, while the MW $\pi$ pulse is to flip $|0⟩$ to $|+⟩$. Furthermore, $\tau$ is the free precession time to be varied, and the $\pi$ pulse is half the Rabi period of driving the right-hand ODMR resonance $f_{+}$. (c) Exponential decay fitting of the net relaxation curve obtained by subtracting the $|+⟩$ curve from the $|0⟩$ curve. The fitted decay time is taken as the experimental spin-lattice relaxation time $T_1$. The data from IN-$V\mathrm{I}$ in DAC3 at $p_1$ is used as an example here. (d) $T_1$ time versus ODMR-calibrated local pressure for three patches of IN-$V\mathrm{s}$ in DAC3, with the ambient-condition data from a patch of IN-$V\mathrm{s}$ close to the six tracked patches as a reference. No significant changes in $T_1$ time are observed. Fitting errors of $T_1$ from the fitting software are taken as error bars. (e) The Rabi oscillations at different pressure points before and after tuning the MW power fed into the DAC. (Upper panel) If the input MW power is kept the same in the experiment, the Rabi period changes with the DAC pressure, which is expected due to the varying MW transmission efficiency through the $\mathrm{\Omega }$-shaped antenna when the DAC is pressurized. (Lower panel) After appropriately tuning the input MW power, the Rabi period can be fixed at 582 ns such that the IN-$V\mathrm{s}$ receive the same MW power at all pressure points. Here, the data from IN-$V\mathrm{I}$ in DAC3 is used as an example, and the Rabi oscillation amplitudes are normalized for easier comparison of periods.

Figure 7

(a) The modified 2D axisymmetric DAC model with a diamond nanopillar at the center of the implanted anvil culet. The enlargement is a schematic diagram showing a nanopillar, where $r$ and $h$ are the radius and the height, respectively. (b),(c) Spatial maps of $E^{\mathrm{N}\text{−}V1}$ derived from the simulations using the nanopillar geometry of $r,h=100,1500$ nm and the geometry of $r,h=70,150$ nm, respectively. The two maps share the same color scale. $E^{\mathrm{N}\text{−}V1}$ is found to be negligible within the nanopillar but much larger inside the bulk of the anvil.