Confined Nano‐NMR Spectroscopy Using NV Centers
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2020-06-15 |
| Journal | Advanced Quantum Technologies |
| Authors | D. Cohen, R Nigmatullin, M Eldar, A. Retzker, D. Cohen |
| Institutions | ARC Centre of Excellence for Engineered Quantum Systems, Macquarie University |
| Citations | 13 |
| Analysis | Full AI Review Included |
6CCVD Technical Documentation: Confined Nano-NMR Spectroscopy using NV Centers
Section titled “6CCVD Technical Documentation: Confined Nano-NMR Spectroscopy using NV Centers”This technical analysis reviews the potential for enhanced nano-Nuclear Magnetic Resonance (nano-NMR) spectroscopy by confining liquid samples onto diamond surfaces containing Nitrogen-Vacancy (NV) centers. The findings confirm that nanoscale confinement fundamentally overcomes the resolution limitations imposed by diffusion, a critical advancement for chemical and pharmaceutical engineering utilizing minute samples.
Executive Summary
Section titled “Executive Summary”The following outline summarizes the core technical achievements and commercial implications of the research into confined nano-NMR spectroscopy:
- Diffusion Mitigation: Sample confinement (in cylindrical, hemispherical, or spherical volumes) is shown to counteract the deleterious effects of diffusion, which typically limits spectral resolution in NV-based nano-NMR.
- Unlimited Resolution Potential: By confining the sample, the magnetic field correlation function C(t) decays to a non-zero, constant asymptotic value $C(t > \tau_V)$, fundamentally removing the resolution ceiling imposed by unconfined diffusion.
- Enhanced Sensitivity: The confinement mechanism allows for interrogation times $T$ significantly longer than the typical diffusion time ($\tau_D$), leading to a projected gain in Fisher Information (sensitivity) that scales as $T^3$.
- Material Foundation: The entire spectroscopy platform relies on high-purity Single Crystal Diamond (SCD) wafers hosting extremely shallow NV centers (simulated depth $d=1$ nm) to maximize coupling with the confined nuclear spins.
- Scalability and Applicability: The technique eliminates the need for highly viscous fluids (e.g., immersion oil) to suppress diffusion, allowing researchers to utilize lower-viscosity fluids (e.g., water) while maintaining high-resolution capability.
- Quantitative Scaling: Analytic models and Molecular Dynamics (MD) simulations confirm that the magnetic field correlation scales approximately with the inverse cube of the NV depth, $B^{2}_{rms} \propto d^{-3}$.
Technical Specifications
Section titled “Technical Specifications”Key quantitative parameters derived from the theoretical models and Molecular Dynamics (MD) simulations are summarized below, highlighting the precise requirements for the diamond substrate and confinement geometry.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV Center Depth (d) | 1 | nm | Standard depth used in numerical calculations (Figs 3, 4) |
| Diffusion Coefficient (D) | 0.5 | nm2/µs | Value used for high-viscosity immersion oil simulation |
| Confinement Radius (R) | 50, 100, 200 | nm | Tested confinement sizes (Cylinder, Hemisphere, Sphere) |
| Confinement Height (L) | 50, 100, 200 | nm | Tested confinement height (Cylinder, L=R) |
| SCD Surface Roughness (Simulated) | Ra $\ll$ R, L | nm | Requirement for specular reflection boundary conditions |
| Correlation Decay Rate (Intermediate Regime) | $\propto t^{-1.5}$ | - | Observed scaling for cylindrical geometry ($\tau_D < t < \tau_V$) |
| Instantaneous Correlation Scaling (B2rms) | $\sim d^{-3}$ | - | Expected analytical scaling for magnetic field correlation |
| Sensitivity Gain Factor ($\frac{I_{C}}{I_{UCL}}$) | $\propto (\frac{T_m}{\tau_D})^2 \times (\frac{d^{3}}{V})^2$ | - | Predicted enhancement factor over unconfined limit |
| Total Measurement Time (T) Scaling | $\propto T^3$ | - | Expected scaling of total Fisher Information in Qdyne measurement |
Key Methodologies
Section titled “Key Methodologies”The core analysis relies on calculating the magnetic field correlation function $C^{(m)}(t) = \langle B(t)B(0) \rangle$ induced by the diffusing nuclear spin ensemble at the NV center position.
- Modeling Geometries: Analytic calculations were performed to determine the magnetic field correlations for nuclei confined within three standard volumes: a cylinder (Radius $R$, Height $L$), a hemisphere (Radius $R$), and a full sphere (Radius $R$).
- Diffusion Propagator Calculation: The diffusion propagator $P(\vec{r}, \vec{r}_0, t)$, which describes the probability of a nucleus moving from $\vec{r}_0$ to $\vec{r}$ over time $t$, was analytically solved for the cylindrical and spherical boundary conditions (Dirichlet/Neumann conditions applied to confinement walls).
- Correlation Function Calculation: The correlation function $C^{(m)}(t)$ was calculated by integrating the dipole-dipole interaction Hamiltonian over the volume using the solved diffusion propagator (Eq. 4).
- Molecular Dynamics (MD) Verification: Analytic predictions were corroborated using MD simulations employing the Velocity-Verlet method.
- Particles (N $\approx$ 22,000 for cylinder, N $\approx$ 28,000 for sphere) interacted via the Lennard-Jones (LJ) potential.
- Confinement achieved using specular reflections (top/bottom) and LJ 9/3 potential (curved walls) for cylinders, or LJ 9/3 across the entire surface for spheres.
- Spectroscopy Protocol Analysis: Two measurement schemes were analyzed: Correlation Spectroscopy and Phase Sensitive Measurement (Qdyne), deriving the resulting Fisher Information $I$ to quantify sensitivity enhancement under confinement.
6CCVD Solutions & Capabilities
Section titled “6CCVD Solutions & Capabilities”6CCVD provides the specialized diamond materials and engineering services required to execute and extend this critical quantum sensing research. Successful implementation of confined nano-NMR requires ultra-high purity diamond with exceptional surface quality—key specialties of 6CCVD.
| Application/Requirement | 6CCVD Solution & Capability | Technical Advantage |
|---|---|---|
| Applicable Materials: NV Host | Single Crystal Diamond (SCD) - Electronic Grade | Provides the required defect-free crystal structure essential for high-coherence NV center operation and long spin coherence times ($T_2$). |
| NV Location Control (Shallow Implantation) | Ultra-Thin SCD Plates (0.1 µm - 50 µm) or Substrates | While the paper requires $d=1$ nm NV depth, 6CCVD supplies the underlying high-purity SCD substrate required for reproducible, high-density shallow NV formation via ion implantation or delta doping. |
| Confinement Structure Fabrication | Custom Laser Cutting and Micromachining | The precise nano-scale geometries ($R=50$ nm to $200$ nm) modeled for confinement can be etched or built upon 6CCVD wafers using our laser cutting and focused ion beam services. We offer custom dimensions up to 125 mm. |
| Surface Quality (Boundary Condition) | SCD Polishing (Ra < 1 nm) | An atomically flat surface is crucial for creating well-defined confinement boundaries and minimizing surface defects that can degrade NV coherence. |
| Device Integration & Contacts | Custom Metalization Services (Ti/Pt/Au, W, Cu) | For integration into microfluidic chips or quantum readout circuits, 6CCVD offers multi-layer metal stack deposition (e.g., Ti/Pt/Au contact pads) directly onto the diamond surface. |
| High-Volume or Sensor Array Integration | Inch-size Polycrystalline Diamond (PCD) | For scaling up applications where optical quality is secondary to thermal management or large sensor arrays, 6CCVD supplies PCD wafers up to 125 mm, polished to Ra < 5 nm. |
Engineering Support: 6CCVD’s in-house PhD engineering team specializes in advanced CVD growth recipes and post-processing techniques (polishing, metalization, and customization). We can assist researchers and technical engineers in selecting the optimal SCD or PCD grade, thickness, and customization services to meet the precise demands of confined nano-NMR and similar quantum sensing projects requiring engineered diamond platforms.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Abstract Nano nuclear magnetic resonance (nano‐NMR) spectroscopy with nitrogen‐vacancy (NV) centers holds the potential to provide high‐resolution spectra of minute samples. This is likely to have important implications for chemistry, medicine, and pharmaceutical engineering. One of the main hurdles facing the technology is that diffusion of unpolarized liquid samples broadens the spectral lines thus limiting resolution. Experiments in the field are therefore impeded by the efforts involved in achieving high polarization of the sample which is a challenging endeavor. Here, a scenario where the liquid is confined to a small volume is examined. It is shown that the confinement “counteracts” the effect of diffusion, thus overcoming a major obstacle to the resolving abilities of the NV‐NMR spectrometer.