Recent developments of quantum sensing under pressurized environment using the nitrogen vacancy (NV) center in diamond

High pressure is a clean and systematic tuning parameter without introducing chemical impurities to the material system under investigation. It provides unprecedented opportunities for examining various quantum states that emerge only under extreme conditions. Tuning pressure to explore striking states of physical systems has, therefore, become a central tactic in materials research. For example, it has long been proposed that metallic hydrogen can be realized under ultrahigh pressure.^1,2 Other physical phenomena that can be achieved by applying pressure include surface plasmon resonance³ and glass transitions.⁴ Pressure has emerged as a very effective tool in superconductivity research, especially in the quest of room temperature superconductors.

Superconductors with a remarkably high superconducting transition temperature $Tc$ of 250–260 K has been reported in lanthanum hydride (⁠$LaH10−δ$⁠) at around 200 GPa^5,6 and $Tc$ of 203 K has been reported in sulfur hydride (⁠$H3S$⁠) pressurized to 155  GPa.⁷ $Tc$ of 243 K in yttrium hydrides (⁠$YH9$⁠) at 201 GPa was also reported, and it is predicted that the $Tc$ can be further enhanced in different phases.⁸ In 2020, Snider et al.⁹ found superconductivity in a photochemically transformed carbonaceous sulfur hydride (C–S–H) system. The maximum $Tc$ is found to be $287.7±1.2$ K, achieved at $267±10$ GPa. These exciting discoveries define a new landscape for superconductivity research, requiring sophisticated probes to extract physical information under demanding experimental conditions. For instance, the detection of the Meissner effect, a defining property of a superconductor, is not a trivial measurement under such extreme pressures.

To detect superconductivity under pressure, multi-coil mutual induction, tunnel diode oscillator (TDO), and four-wire method are some of the commonly used techniques. The four-wire method is a standard way to measure electrical resistivity, whereby four gold wires are attached to the sample. On the other hand, the multi-coil mutual induction technique and TDO are contactless methods that are sensitive to the magnetic susceptibility of the sample.^10–14 These techniques have played an important role in the superconductivity research. However, a sensor that can directly measure the expulsion of the magnetic field from superconductors provides the most direct confirmation of the Meissner effect.

Diamond anvil cell (DAC) is a traditional workhorse for high pressure research. With careful design, DAC offers superior optical access to the sample. This offers an opportunity for implementing a method based on the negatively charged nitrogen-vacancy (NV$−$⁠) center in diamond for probing the expulsion of the magnetic field when the sample becomes superconducting. It is widely acknowledged that the four-wire technique under pressure is experimentally demanding. On the other hand, contactless methods based on the pickup coil mentioned above can pick up unwanted signals in the proximity of the sample. Incidentally, the NV$−$-based technique is simpler to prepare—the experimentalist can either implant the NV$−$ on the surface of a diamond anvil or disperse small diamond particles around the sample. Furthermore, these sensors can sense the local magnetic field profile close to the superconductor. Local measurement is particularly important for research works focusing on nanoscale phenomena. Therefore, the NV$−$-based technique might even revolutionize the high pressure research of nanomaterials.

In this review, we first describe the key properties of the NV$−$ center in diamond. We then demonstrate that the NV$−$ center is a versatile sensor workable under pressure, making it a powerful tool to probe pressure-induced phenomena as well as the pressure environment itself. Cutting-edge results in the field and future prospects will be discussed.

The NV$−$ center is a point defect in the diamond lattice. We refer NV always as NV$−$ unless otherwise mentioned. It is composed of a vacancy and an adjacent substitutional nitrogen atom, resulting in a $C3v$ symmetry with respect to the NV axis. Due to an extra electron, the NV center is a spin-1 system with electronic ground states (⁠$|3A⟩$⁠) and excited states (⁠$|3E⟩$⁠), both of which are spin triplets. A metastable state also exists in between. A schematic drawing of its atomic structure and energy levels are shown in Figs. 1(a) and 1(b).

Upon incidence of a green laser beam, the NV center is excited from ground states to excited states under spin conservation. From the excited states, the system could return to the ground states directly while conserving spin, thus emitting red fluorescence that originates from a zero-phonon line (ZPL) at 637 nm. Peculiarly, the excited states could also return to the ground states after making a detour through the metastable state, thereby emitting infrared radiation. If the system does go through the metastable state, it would preferentially return to the $|A,0⟩$ state compared to the $|A,±1⟩$ states. Overall, the excitation-decay cycles under continuous green laser incidence favor a higher population at the $|A,0⟩$ state. As a result, the initialization of the spin system to the $|A,0⟩$ state is easily achieved by using a green laser alone. This spin-state-dependent decay leads to spin-state-dependent fluorescence that allows the optically detected magnetic resonance (ODMR) measurement. The ODMR measurement allows us to experimentally obtain the resonance frequencies of the NV energy level structure. During the excitation–decay cycles, if in addition to the green laser, microwave (MW) signals are simultaneously swept and applied to the system, resonances due to transitions from $|A,0⟩$ to $|A,±1⟩$ could be observed in the fluorescence-frequency spectrum. As shown in Fig. 1(c), the left peak corresponds to $|A,0⟩→|A,−1⟩$ transition and the right peak corresponds to $|A,0⟩→|A,+1⟩$ transition. For more details about the NV center, one could refer to some previous studies.^17–23 

The transition frequencies depend heavily on external parameters. Considering the ground states only, the effective Hamiltonian of the NV center could be modeled by

where $S→$ is the electron spin operator, $D↔$ is the spin–spin coupling tensor, $γe≈2.8$ MHz/G is the electron gyromagnetic ratio, and $B→$ represents the external magnetic field. If one chooses the NV axis to be the z-axis thereby diagonalizing matrix $D$⁠, (1) becomes

The first term is the longitudinal (along NV axis) zero-field splitting (ZFS) term, which splits the $|0⟩$ state from the $|±1⟩$ states. $D$ is a constant and approximately equals $2.87GHz$ at ambient pressure and room temperature. The second term is the transverse ZFS term that further splits the $|+1⟩$ and $|−1⟩$ states. Being sample-dependent, $E$ could range from negligible to several MHz as shown in Fig. 1(c). The last term accounts for Zeeman splitting.

The research works on the NV center in diamond not only provided a deeper understanding of the solid-state defect as a quantum system but also opened up opportunities for quantum information technologies. One can tune the solid-state defect into a desired quantum state for further processing.^24–27 On the other hand, fundamental quantum sensing methods using the NV center are often based on exploiting the change in $D$ and $E$ terms as well as the Zeeman splitting term under various circumstances (altering the temperature and pressure, and/or applying an external magnetic field). Some more advanced techniques can be achieved by considering more interaction terms in (2), like the spin-spin coupling term of an electron and a nuclear spin. Including these coupling effects allows the NV center to, for example, sense nearby spins.^28–38 In this review, we focus on pressure sensing using the NV center in diamond, as well as various sensing protocols under pressure.

In the high-pressure community, searching for a robust sensor is a crucial issue since a pressurized environment is too demanding for most of the common devices. The NV center works as an integrated versatile sensor that can be used to probe different parameters given that a correct protocol is implemented. Previous research works have shown that the NV center can be used to probe the magnetic field,^39–42 electric field,⁴³ and temperature.^15,44–46 With a careful design of experimental setup, one can, in principle, measure various parameters under pressure. One recent example is the combination of NV magnetic microscopy and x-ray diffraction under pressure.⁴⁷ 

DAC is a popular tool in high-pressure experiments. The pressure is produced by compressing two opposing diamond anvils toward the pressure medium confined by a gasket. In order to measure the pressure inside a DAC, a calibrated material is placed inside the pressurized chamber. In particular, ruby (⁠$Al2O3$⁠:Cr) works well under pressure, and it is commonly used among the high pressure community.^48,49 Two resonance lines (⁠$R1,R2$⁠) in the ruby fluorescence spectrum are sensitive to both pressure (3.64 Å/GPa) and temperature (0.068 Å/K).

When applying pressure to tune materials properties, hydrostaticity is an important, yet rarely addressed issue. The pressure distribution can induce significant artifacts or even give different results.^50–54 Nonetheless, detailed mapping of the gradient lacks discussion. One major problem is that the usual sensors are in the bulk size and are not sensitive enough. In contrast, the use of the NV center can be an elegant solution to this problem.

Doherty et al.⁵⁵ were the first to experimentally demonstrate the capability of the NV center to detect pressure. The experimental setup is shown in Fig. 2(a). They put a bulk diamond together with a ruby inside the sample chamber of a DAC. The DAC gasket was filled with NaCl/Ne as the pressure medium. A platinum (Pt) wire was used as an MW antenna for ODMR measurement. To perform a pressure calibration for the NV center, the ZFS $D$ from the diamond’s ODMR spectrum was plotted against the pressure measured by the ruby up to 60 GPa, and they discovered a linear slope of $dD/dP=14.58(6)$ MHz/GPa [Figs. 2(b) and 2(c)]. This calibration enabled the NV center to be employed as a pressure sensor. Moreover, a linear shift in ZPL was presented [Fig. 2(d)]. To explain their findings, they outlined a preliminary theoretical picture. Upon increasing pressure, the unpaired spin density of the NV ground-state level would contract, favoring spin–spin interaction and thus increasing $D$⁠. They further suggested two contributions to the spin density contraction: The compression of the nuclear lattice (i) decreases the distance between atomic orbitals and (ii) deepens the localizing electrostatic potential of the NV center to concentrate the electron density more on the inner neighbor shells of the defect. They mathematically demonstrated this physical picture by using a semi-classical molecular orbital model. Assuming hydrostatic pressure, the shift in $D$ due to the displacement of the atomic orbitals was found to be around 6.2 MHz/GPa. The remaining $∼57.5%$ in the total shift of 14.58(6) MHz/GPa was attributed to contribution (ii) mentioned above. Meanwhile, ODMR pressure sensitivity of a single NV center at room temperature is estimated to be $∼0.6$ GPa/$Hz$⁠, analogous to the estimation of field and thermal sensitivities of NV ODMR.⁵⁶ They further proposed to use NV centers for magnetometry under pressure, which will be shown in Sec. III B to be a breakthrough in high-pressure instrumentation.

Ivády et al.⁵⁷ later did a comprehensive theoretical study to discuss the results of Doherty et al.⁵⁵ and further elucidate the physical origin of the observed NV response to applied pressure. Using ab initio computational methods to simulate a single NV center embedded in a 512-atom diamond supercell, they studied the pressure and temperature dependence of the ground-state ZFS tensor of the NV center. By varying the size of the supercell at a fixed temperature, they investigated the longitudinal ZFS $D$ as a function of external pressure $P$ over a broad pressure range from $−20$ to 210 GPa as shown in Fig. 3(a). $D(P)$ was found to show a linear relation to the first order, with a slope of 10.30 MHz/GPa from 0 to 50 GPa. This was in fair agreement with the measurement of Doherty et al. In the complete simulated solution including higher-order terms, $D(P)$ exhibited a weak non-linearity in the high-pressure range, which was attributed to microscopic effects. Furthermore, Ivády et al. summarized four different sources contributing to the shifting in $D$ under pressure: (i) macroscopic compression of the bulk diamond crystal, (ii) microscopic structural relaxation at the defect site, (iii) change in spin density on neighbor shells of the NV center, and (iv) change in $sp$ hybridization of the dangling bonds. Considering source (i) only, they found that $dD/dP=6.26$ MHz/GPa at $P=0$⁠, which agreed excellently with the semi-classical calculation of Doherty et al. However, different from Doherty et al.’s expectation, Ivády et al. proved rigorously that source (ii), instead of source (iii), should be the main contributor to the observed pressure dependence of $D$⁠. In other words, they revealed that the microscopic structural relaxation at the defect site plays a key role in the pressure-induced shifting of the ZFS $D$⁠. Figure 3(b) compares the experimental result and different theoretical methods.

In addition to the flourishing theoretical understandings, experimentalists have also made great progress since Doherty et al. published their pioneer work.⁵⁵ Steele et al.⁵⁸ refined the MW transmission scheme in a DAC. In the setup of Doherty et al., MW transmission to NV centers in the sample space was achieved by embedding a Pt wire as an MW antenna in a non-metallic gasket. To improve the cell design for high-quality NV sensing, Steele et al. proposed the concept of a designer anvil for MW transmission, where metallic microchannels [concentric tungsten rings] were lithographically deposited on the culet of the diamond anvil as shown in Fig. 3(c). In this way, the gasket was not restricted to be non-metallic, and the MW power could also be lowered to reduce undesired heating effects. Besides, in contrast to the bulk diamond used by Doherty et al., Steele et al. glued some 15-$μ$m diamond particles onto the anvil culet using vacuum grease. With Daphne oil 7373 as the pressure medium, they measured a linear pressure dependence of $D$⁠, $dD/dP=11.72(68)$ MHz/GPa as shown in Fig. 3(d), which was in fair agreement with the data of Doherty et al. This showed the feasibility of their proposed DAC design.

Recently, Ho et al.⁶³ conducted a thorough study on the local pressure environment in anvil cells. Their anvil cells consisted of two moissanite anvils and a metallic beryllium copper (BeCu) gasket confining the pressure medium (Daphne oil 7373). Inside the gasket, a microcoil was mounted for MW transmission; a ruby was placed for pressure calibration; a large quantity of 1-$μ$m diamond particles was drop-casted either on one anvil culet or on a dummy sample. The choice of using smaller diamond particles can minimize the disturbance to the pressure medium and allow the pressure environment to be probed locally. This is one of the best resolutions for mapping the local pressure so far. They built a confocal microscope featuring a computer-controlled Galvo mirror to perform spatially resolved ODMR spectroscopy, see Fig. 4(a). As a result, the pressure inhomogeneity can be probed in detail. Besides the ambient condition, Ho et al. also performed measurements at low temperatures with the help of a Montana cryostation. With this experimental setup, the pressure dependence of $D$ was calibrated with reference to the ruby first. After that, they showed that the pressure gradient was not radially symmetric but rather a linear pattern. Moreover, the cell design and alignment affected the pressure gradient in a way that misalignment would induce more gradient. Then, at each pressure point, they used diamond particles to spatially map the local pressure distribution in the pressure medium for different temperatures (295, 10, and 6 K). The mapping measurements were repeated for a few pressure points. All presented in Fig. 4(b). Interestingly, there was a linear pressure gradient parallel to the line joining two screws of the anvil cell, if the Daphne oil already underwent a pressure-induced solidification at room temperature. Nonetheless, no specific pressure pattern was observed if the Daphne oil was solidified upon cooling. This revealed that the solidification upon cooling was purely random. Furthermore, the rise of pressure in cryogenic condition was due to the thermal contraction of the cell body. Besides, to fully utilize the information from ODMR spectroscopy, the transverse ZFS $E$⁠, the linewidth of ODMR peaks, and the standard deviation (SD) of measured pressures at different locations were taken as three independent indicators to characterize the solidification process. From the critical pressure obtained, the $T$–$P$ phase diagram of Daphne oil 7373 was plotted. Last but not least, they examined the temporal dependence of the average pressure and the local pressure distribution in the medium. From the detected pressure relaxation over time, it was found that it took a day for the pressure medium to stabilize after changing the pressure of the anvil cell.

The works mentioned in Sec. III A employed various types of diamond (with NV centers inside) to achieve their particular sensing goals. In general, there are three types: diamond particles, bulk diamond, and implanted diamond anvil. We shall discuss the major properties of each of these incorporation techniques as well as their pros and cons.

Diamond particles have a wide range of sizes depending on the manufacturing process, typically ranging from 30 nm to 10 $μ$m scale. The microscopic size allows the particles to serve as point sensors, provided that a confocal setup is applicable during the experiment. As the diffraction limit of the confocal microscope is usually much bigger than the particle size, the small size of the particle also gives a better spatial resolution. Meanwhile, a point sensor like this can be immersed into the environment without large perturbation or disruption, giving a more accurate result. Moreover, the variation in size grants us the freedom to tune the spatial sensing resolution. The non-reactive and bio-compatible nature of diamond also permits it to be implemented in a vast range of samples unintrusively. It, therefore, works well for materials such as metals, superconductors, or even biological samples. In this sense, it is an excellent real-time quantum sensor. However, one of the biggest drawbacks is that the orientations of the particles are often ambiguous. Since, unlike bulk diamond and implanted diamond anvil, the absolute orientation of each particle in the laboratory frame is unknown, it is difficult to compare any sensing results along the NV axes of different particles. In the case of sensing magnetic field or stress field, the angle of the NV axis relative to the surroundings or samples is a crucial parameter. For instance, under a uniform magnetic field, individual diamond particles could show different ODMR spectra due to different projections of the field on the NV axes. Careful analysis is usually needed upon receiving signals from different diamond particles.

In contrast to diamond particles, bulk diamond is free of this problem. The orientation of NV centers is well-defined for a bulk crystal since there are only four possible choices of the NV axis in the lab frame. This is why they work so well on magnetometry or other imaging that is derived from it. In particular, bulk diamond gives robust performance at ambient pressure as shown in many recent sensing works.^64–69 Nonetheless, the bulk size of the diamond is problematic in high-pressure experiments. Usually, the sample chamber is too tiny to accommodate such a bulk sensor. On the other hand, a bulk sensor detects macroscopic average responses rather than microscopic local responses. Not to mention, the sensor itself may disrupt the pressure environment.

One elegant approach is implanting NV centers at the diamond anvil culet of a DAC. Since diamond is a component of the DAC, it is natural to insert NV centers in it for sensing. Like the bulk diamond, of course, it has four well-defined NV axes and is a great choice for magnetic field imaging. This approach is very powerful when there is the need for wide field imaging. However, unlike diamond particles or bulk diamond, the NV centers are inside the anvils, so they are mainly receiving a uni-axial pressure from the pressure medium. In the case of diamond particles that are immersed in the medium entirely, the NV centers experience thorough pressure of the chamber. The difference between sensing a uni-axial pressure and the actual pressure in the medium may pose a significant effect on the high-pressure experiment.

After summarizing the NV incorporation techniques, we shall see how some of the recent works employed these techniques on pressure sensing experiments. Briefly speaking, recent works employed implanted diamond anvil and diamond particles to probe magnetic transitions, superconducting transitions, and stress-tensor distribution.

Pressure is one of the most successful tuning parameters in material research. Nevertheless, a high-pressure experiment is not trivial at all to implement. One major challenge is the tiny size of the sample chamber, which imposes a huge restriction on the sample and sensor. In particular, compatible magnetic field sensors with sufficient sensitivity are rare. Moreover, to prevent failure of the high pressure device, access to the sample is highly restricted, thus most of the traditional methods can no longer be applied under pressure. Under these demanding experimental conditions, measurements can be extremely difficult to carry out.

In 2019, three groups independently demonstrated quantum sensing using the NV center under pressure.^70–72 They applied different protocols utilizing the excellent spatial resolution and sensitivity of the NV center to probe properties of different materials under pressure. These provide many possibilities for high-pressure instrumentation and the study of pressure-induced phenomena.

Lesik et al.⁷¹ implanted NV centers at the culet of the DAC anvil and used a camera for wide-field imaging of the NV fluorescence. They successfully probed, under high pressure, the magnetization of iron (Fe) at room temperature and the Meissner effect in magnesium diboride (⁠$MgB2$⁠) at low temperature. First, a Fe bead was placed inside the DAC sample chamber, and wide-field ODMR was performed at 24 GPa and under a constant external magnetic field of $∼11$ mT. For each family of NV centers (the four possible NV orientations in the implanted anvil), they provided a spatial map of the splitting of the corresponding ODMR. This splitting was a combined consequence of the non-hydrostatic strain in the anvil, the applied magnetic field, and the stray magnetic field generated by the Fe bead. Thus, the four maps revealed the inhomogeneity in the induced magnetic field and the anisotropy of the strain field. To proceed further, they isolated the ODMR effect of the sample’s stray field by referencing to a region far away from the bead. This allowed them to map the magnetic field solely attributed to the Fe bead, and they fitted the experimental data with a magnetic dipole model where the sample’s magnetization $M$ was the only fitting parameter. In this way, the magnetization was measured for different pressures $P$⁠, and the $α$–$ϵ$ transition of Fe was observed in the $M$–$P$ plot, shown in Fig. 5(a). Meanwhile, different $M−P$ plots were obtained by increasing and releasing the pressure of the DAC, showing the expected hysteresis of the structural transition. Next, instead of a Fe bead, they confined a $MgB2$ sample in the DAC, pressurized it to 7 GPa, and zero-field-cooled it to 18 K with a cryostat. A series of wide-field ODMR was then performed upon warming up from 18 to $>30$ K and under a constant magnetic field of $∼1.8$ mT, where the field direction was chosen such that the four NV orientations showed identical responses. By plotting the ODMR resonance splitting against temperature, the critical temperature $Tc$ of superconducting phase transition was extracted from where the sample’s diamagnetic response disappeared, see Fig. 5(b). Their results were in good agreement with the previously reported data.⁷³ In summary, their work showcased the adaptability of the NV sensing technique to different experimental conditions under extreme conditions.

In contrast to using implanted NV centers and wide-field imaging, Yip et al.⁷⁰ adopted diamond particles and confocal microscopy to probe the Meissner effect of a superconducting material. The experimental setup is similar to Fig. 4(a). In their experiment, they spread 1 $μ$m diamond particles over a type II iron-based superconductor (⁠$BaFe2(As0.59P0.41)2$⁠) and tracked individual particles using a confocal microscope to perform ODMR measurements correspondingly at different temperatures and pressures, shown in Fig. 6(a). From the Zeeman splitting in the ODMR spectrum, the vector magnetic field projected along an NV axis in the diamond particle could be determined. A significant change in the splitting was expected across the critical temperature $Tc$ [Figs. 6(b)–6(e)]. This allowed them to measure $Tc$ as a function of pressure and a $T$–$P$ phase diagram was constructed [Fig. 6(f)]. They benchmarked this novel technique by cross-checking results from measuring AC susceptibility, which are commonly applied to probe the bulk response.^10,74,75 Since the superconducting phase transition is extremely sensitive to temperature, any slight temperature perturbation due to the heating from the measurement can destroy the superconducting state. Both results agreed well on the value of $Tc$⁠, thereby proving that ODMR measurement did not cause an observable heating effect. On the other hand, the same technique also enabled the sensing of the local magnetic field vector near the superconducting sample across the normal state to Meissner state transition. It was clearly shown that an approximately 90$°$ change of the magnetic field vector occurred right above the superconductor upon cooling below the critical temperature, picturizing the field expulsion from the superconductor [Fig. 6(e)]. Furthermore, at each fixed pressure, they extracted the critical fields $Hc1$ and $Hc2$ from the two turning points in the plot of the measured magnetic field against temperature. Then, they could construct the $H$–$P$ phase diagram [Fig. 6(g)], which is crucial for condensed matter physics. In particular, $Hc1$ is not trivial to be measured, so this work opened up a discussion of the superconducting gap function.

Hsieh et al.⁷² showcased the versatility of the NV center by performing NV sensing of stress and magnetic fields under high pressure. In their experimental protocol, NV centers were implanted at the anvil culet in their miniature DAC, and scanning confocal microscopy was adopted to obtain two-dimensional ODMR maps. Their optical resolution was superior, with a $∼600$ nm laser spot illuminating $∼103$ NV centers at a time. One of their big feature is that they resolved the full stress-tensor across the culet surface, see Fig. 7(a). Similar work was done at ambient pressure by Doherty et al.⁷⁶ Under an external magnetic field perpendicular to one selected NV orientation out of the four, the resonance pairs from the three other NV orientations were strongly split apart by the Zeeman effect, leaving the resonance pair from the chosen orientation at around the middle of the entire ODMR spectrum. The stress information corresponding to this particular NV orientation was then extracted, and the same thing was repeated for all other NV orientations to compute the full stress-tensor. By plotting the variation in stress-tensor components along a straight line across the pressurized region, they revealed the emergence of a pressure gradient after the pressure medium entered the glassy phase. This result is important for the high-pressure community. On the other hand, they probed the pressure-driven $α$–$ϵ$ structural phase transition of Fe. After calibrating the magnetic sensitivity of the implanted NV layer, a polycrystalline Fe pellet was placed inside the DAC sample chamber with a constant external magnetic field being applied to induce magnetization in the pellet. From the 2D ODMR mapping, they reconstructed the full vector dipole field due to the pellet’s magnetization. By increasing the DAC pressure, they successfully imaged the depletion of the dipole field after the Fe pellet underwent $α$–$ϵ$ transition at the critical pressure $P=16.7±0.7$ GPa [Fig. 7(b)]. The hysteresis of this first order transition was also demonstrated through measuring a different critical pressure $P=10.5±0.7$ GPa upon decompression of the DAC. Furthermore, they integrated their optical setup into a cryogenic system and constructed the magnetic $P$–$T$ phase diagram of rare-earth element Gd using the same methodology as the Fe measurement. Last but not least, they demonstrated, under ambient pressure and without external magnetic field, the use of noise spectroscopy to probe the ferromagnetic Curie transition of Gd. From the kink and the subsequent decrease in the plot of the depolarization time $T1$ upon entering the ferromagnetic phase, they found that Curie temperature was $∼10$ K higher than that observed via DC magnetometry. This discrepancy was claimed to be evidence for their noise spectroscopy being more sensitive to surface physics.

These three papers show that the NV center helps us to overcome many prevailing obstacles in magnetometry under high pressure, presenting a great breakthrough in high-pressure instrumentation. The NV-based methodologies for stress-tensor reconstruction, magnetic field imaging, magnetic field vector reconstruction, and critical field extraction provide powerful tools for material research under high pressure.

The above discussion has revealed the increasingly important role of NV technology in high-pressure research. It should be clear that there are much potential and advantages in implementing the NV center as a quantum sensor under extreme conditions. In the past few years, novel sensing techniques using the NV center have been developed. Although most of them were demonstrated at ambient pressure only, we hereby highlight a few noteworthy examples that can as well be applied under high pressure with a careful experimental design.

For the high-pressure community, one of the experimental challenges is to collect fluorescence emitted by NV centers inside a DAC for ODMR measurement, as a low numerical aperture and a long working distance must be ensured in the optics. In 2015, Bourgeois et al.⁷⁷ introduced the photoelectric detection of magnetic resonance (PDMR) that allows an electrical readout for the NV spin states. The experimental setup is summarized in Fig. 8(a). They used bulk diamond as a sample to demonstrate the PDMR measurement on an NV ensemble. Electrodes were deposited on the diamond surface for direct detection of electrical signals, while green laser and MW were applied for NV excitation and spin-state manipulation, respectively. The green laser could excite the electrons of NV centers from the ground states to the excited states, and even further to the conduction band, generating a photocurrent across the electrodes. The photocurrent was measured as a function of MW frequency, and it gave a spectrum strikingly similar to that obtained from a simultaneous ODMR measurement. The similarity was attributed to the very same spin-state-dependent decay of the NV center. The PDMR method was shown to have an advantage over the conventional ODMR method in terms of signal contrast. For PDMR, the contrast increased monotonically with the laser power, unlike ODMR in which the contrast started to decrease if the laser power was too high [Fig. 8(b)]. This prompted an expectation that PDMR can be a good alternative to ODMR in high-pressure experiments, for in many cases, a highly pressurized environment reduces the signal contrast in ODMR measurements, and PDMR can provide an easy solution where simply raising the laser power will do. Later, research papers on enhancing the photoelectric detection⁷⁹ and demonstrating coherence spin control⁸⁰ as well as a review about PDMR⁸¹ were published. Recently, Siyushev et al.⁷⁸ refined the PDMR technique to perform Rabi oscillation on a single-defect level [Fig. 8(c)] and photoelectric imaging of individual NV centers. Furthermore, Gulka et al.⁸² applied PDMR to detect the coupling between a single $14N$ spin and the NV electron. All these works convince us that the PDMR method can potentially overcome the limitations faced when performing ODMR measurement. Hence, PDMR opens up a promising direction for the NV sensing research under high pressure. However, it is worth noting that the PDMR involves multi-photon excitation and ionization, which are based on the level structure of color center in the host band. Since the level structure of the NV center under high pressure is not yet clear, the efficiency of this PDMR is an open question for further investigation.

On the other hand, engineering the electrical feedthrough to the pressurized chamber in a DAC is another difficulty in high-pressure experiments using the conventional NV sensing protocol that requires both laser and MW. Recently, Paone et al.⁸³ proposed an all-optical and MW-free sensing scheme for the NV center and demonstrated it by probing the Meissner effect of a $La2−xSrxCuO4$ (LSCO) thin film with an NV implanted diamond membrane. First, without placing the sample, they measured the NV fluorescence drop as a function of an applied magnetic field at ambient conditions. Under specified conditions, they found that a stronger magnetic field would quench more fluorescence. The data of fluorescence drop vs magnetic field were interpolated to obtain a calibration curve [Figs. 9(a) and 9(b)]. To benchmark their methodology, they carefully investigated the LSCO sample by the mutual inductance method and superconducting quantum interference device (SQUID). Then, under a uniform applied field of 4.2 mT and at a temperature of 4.2 K, they measured the NV fluorescence drop (relative to zero-field value) across the membrane with the presence of the LSCO sample. They subsequently converted the fluorescence drop to magnetic field strength using their calibration curve [Fig. 9(c)]. In this way, they could map the spatial distribution of the Meissner screening from the sample. By fitting the mapping data with Brandt’s model,⁸⁴ they extracted the critical current density $jc$⁠, as shown in Fig. 9(d), and it was in good agreement with their SQUID data and the previously reported result.⁸⁵ This proved the viability of their all-optical and MW-free method, offering a potential way out for the difficulty in inserting an MW antenna into the DAC in high-pressure experiments. Nonetheless, the sensitivity to an off-axis magnetic field may be reduced under certain environments. For instance, the ZFS D is the dominant term under strong uni-axial stress, states mixing could be avoided hence reducing the sensitivity to an off-axis magnetic field.

Although the NV center is a reliable pressure sensor, currently, there is a limitation on the pressure working range. For the measurement protocol using ODMR spectroscopy, the maximum working pressure is $∼60$ GPa.⁵⁵ This is limited by the blue shift of the ZPL toward the green optical excitation wavelength (usually around 532 nm). Exciting the NV center with laser beam of a shorter wavelength can increase the value by a few factors, but the trade-off would be a poorer contrast due to the complex charge state dynamics. In fact, with the interesting energy structure and the charge state dynamics of the NV center, we expect that, in the near future, different protocols or energy levels can be used for pressure sensing. For instance, the temperature dependence of the 1042-nm ZPL has been revealed.⁸⁶ This can potentially be a distinct approach to high pressure measurements.

Another challenge of implementing NV sensing under pressure is the electrical wiring. In most of the experiments, MW excitations are required, but the shielding from the gasket will be detrimental. Doherty et al.⁵⁵ and Hsieh et al.⁷² directly embedded Pt wire/foil as the MW antenna. This approach greatly avoided the shielding effect. Moreover, Steele et al.⁵⁸ deposited microchannels on their designer diamond anvils, while Ho et al.⁶³ and Yip et al.⁷⁰ put a microcoil inside the pressure chamber to minimize eddy current. Interestingly, Lesik et al.⁷¹ made a slit in the gasket with a coil outside the pressure chamber. The slit-gasket not only reduced the eddy current but also worked as a converging lens for the MW. In general, metal gaskets are robust under pressure, but the shielding effect is detrimental to MW transmission. In contrast, non-metal gasket could eliminate shielding effects. The best configuration of gasket and MW antenna is still subject to open studies.

In summary, we have presented the NV center in diamond as a unique quantum system, which allows it to be a versatile sensor withstanding a large pressure range. We have also showed various works on pressure calibration and sensing with NV centers in bulk diamond and in small diamond particles. These techniques are found to be very useful in high pressure experiments, for example, studying detailed pressure distribution inside the medium of DAC and phase transitions of superconducting materials. Finally, we would like to emphasize again that the NV center has proven itself to be a promising and robust system for high-pressure experiments.

K.O.H. acknowledges financial support from the Hong Kong Ph.D. Fellowship Scheme. S.K.G. acknowledges financial support from Hong Kong RGC (Nos. GRF/14300418, GRF/14301316, and A-CUHK402/19). S.Y. acknowledges financial support from Hong Kong RGC (No. GRF/14304419), CUHK Start-up Grant, and the Direct Grants.

The data that support the findings of this study are available from the corresponding author upon reasonable request.