GPa Pressure Imaging Using Nanodiamond Quantum Sensors

TL;DR

This work addresses the challenge of mapping local pressure distributions inside a diamond anvil cell (DAC) at high pressures. It uses nitrogen-vacancy centers in nanodiamonds embedded in the DAC chamber to perform wide-field ODMR imaging, extracting axial and transverse pressures $P_Z$ and $P_\perp$ and the anisotropy ratio $\lambda=P_Z/P_\perp$, up to about $20$ GPa. By comparing single-layer and double-layer pressure-transmitting-medium configurations, the authors quantify how PTM geometry controls non-hydrostaticity: a single-layer setup yields pronounced uniaxial stress with $\lambda$ typically in the 1.5–2.0 range, while a double-layer PTM produces a near-hydrostatic distribution with $\lambda$ closer to unity. The results demonstrate the utility of ND-based quantum sensing for high-pressure physics and suggest that this approach can extend to other quantities, such as magnetic fields, enabling comprehensive in situ characterization of materials under extreme conditions.

Abstract

We demonstrate wide-field optical microscopy of the pressure distribution at approximately 20 GPa in a diamond anvil cell (DAC), using nitrogen-vacancy (NV) centers in nanodiamonds (NDs) as quantum sensors. Pressure and non-hydrostaticity maps are obtained by fitting optically detected magnetic resonance (ODMR) spectra with models incorporating hydrostatic and uniaxial stress conditions. Two methods for introducing NDs with a pressure-transmitting medium are compared, revealing that the embedding approach affects the degree of non-hydrostaticity. This ND-based technique offers a powerful imaging platform for probing pressure-induced phenomena and is extendable to other physical quantities such as magnetic fields.

Figures (8)

• Figure 1: (Color online) (a) Structure of an nitrogen-vacancy (NV) center. It consists of a nitrogen (N) atom and a vacancy (V) substituting two adjacent carbon (C) atoms in the diamond lattice. The local coordinate system is defined such that the [111] direction corresponds to $\hat{z}$. (b) Energy-level diagram of the ground state of an NV center and its shift under pressure. (c) Simulated ODMR spectra ($I_{\mathrm{NV}}$) under hydrostatic pressure (ODMR amplitude $C=0.0006$, linewidth $d\nu=12\ \mathrm{MHz}$). (d) Simulated ODMR spectra ($I_{\mathrm{NDs}}$) under uniaxial stress (ODMR amplitude $C=0.02$, linewidth $d\nu=40\ \mathrm{MHz}$). The PL ratio, shown on the vertical axes of (c) and (d), is defined as the ratio of the photoluminescence (PL) intensity with and without microwave irradiation.
• Figure 2: (Color online) (a) Schematic of a ND under uniaxial stress in the DAC sample chamber. The vertical and horizontal components correspond to $P_Z$ and $P_\perp$, respectively, in the LAB frame. (b) Orientation of the NV axis ($\bm{e}_{\mathrm{NV}}$) in the LAB frame, represented using the polar angle $\theta$, azimuthal angle $\phi$, and crystal rotation angle $\psi$. (c) Schematic of a ND under uniaxial stress in the NV frame, where the NV axis is defined as the $z$-axis.
• Figure 3: (Color online) (a) A custom wide-field microscopy system used in this study. (b) A custom designed microstrip-line-based antenna with an aperture. The antenna is fabricated by UV laser machining from one side of a PCB substrate composed of a $0.3\,\mathrm{mm}$-thick FR4 with $18\,\mu\mathrm{m}$-thick copper foil on both sides. This structure enables broadband and spatially uniform microwave magnetic field irradiation into the sample chamber, which is located slightly above the central hole, with the field oriented perpendicular to the direction of the microstrip line. (c) Schematic of the DAC. Pressure is applied by sandwiching a rhenium gasket with a sample hole between the upper and bottom diamond anvils. Microwaves are applied to the DAC sample chamber using the antenna shown in (b). The laboratory coordinate system is taken so that the vertical compression direction corresponds to the $Z$-axis. A small gap is introduced between the gasket and the antenna to prevent degradation of the antenna's performance. (d, e) Cross-sectional schematics of the DAC sample chamber in the single-layer PTM configuration (d) and in the double-layer PTM configuration (e). (f, g) Microscope images of the DAC sample chamber taken from above. The gray outline indicates the sample chamber and the pink circle marks the ruby used for pressure calibration. For future magnetic field evaluation, $4\mathrm{N}$ purity iron is placed in the dashed box region. (f) corresponds to the single-layer PTM configuration, and (g) to the double-layer PTM configuration.
• Figure 4: (Color online) Results from the single-layer PTM experiment. (a, b, c) Spatial distributions of (a) the axial pressure $P_Z$, (b) the transverse pressure $P_\perp$, and (c) the pressure anisotropy ratio $\lambda = P_Z / P_\perp$. The white dashed line indicates the boundary of the sample chamber, the pink circle marks the location of the ruby, the black box indicates the iron sample. The black pixels denote regions with insufficient signal intensity. In (a) and (b), the red solid line corresponds to the pressure value of $20.6\,\mathrm{GPa}$ obtained from the ruby. (d) ODMR spectrum at the location marked by a red cross in (a)--(c). Black points are excluded from the fitting to avoid the influence of ambient pressure components. (e) Histogram of $P_Z$ and $P_\perp$ within the sample chamber. (f) Histogram of the pressure anisotropy ratio $\lambda = P_Z / P_\perp$ within the sample chamber.
• Figure 5: (Color online) Results from the double-layer PTM experiment. (a) Spatial distribution of hydrostatic pressure $P$ inside the sample chamber. The gray outline indicates the boundary of the sample chamber. The pink circle and the black box indicate the positions of the ruby and the iron, respectively. Black pixels represent regions with insufficient signal intensity. (b) Histogram of hydrostatic pressure $P$ within the sample chamber. The red solid line indicates the pressure value obtained from ruby fluorescence ($20.0\,\mathrm{GPa}$). (c) ODMR spectrum acquired from the region marked by the white box in (a).