Polarizing the electronic and nuclear spin of the NV-center in diamond in arbitrary magnetic fields - analysis of the optical pumping process
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2017-07-25 |
| Journal | New Journal of Physics |
| Authors | Tanmoy Chakraborty, Jingfu Zhang, Dieter Suter |
| Institutions | TU Dortmund University |
| Citations | 35 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: NV Center Spin Polarization in MPCVD Diamond
Section titled âTechnical Documentation & Analysis: NV Center Spin Polarization in MPCVD DiamondâThis document analyzes the research paper âPolarizing the electronic and nuclear spin of the NV-center in diamond in arbitrary magnetic fields: analysis of the optical pumping processâ to provide technical specifications and highlight how 6CCVDâs specialized MPCVD diamond materials and services can support and advance this critical quantum technology research.
Executive Summary
Section titled âExecutive SummaryâThe research successfully demonstrates a robust protocol for initializing the electronic and nuclear spins of a single Nitrogen-Vacancy (NV) center in diamond into a high-purity quantum state, a foundational requirement for solid-state quantum computing.
- Core Achievement: High-purity initialization of the two-qubit system (electronic spin $S=1$ and $^{14}N$ nuclear spin $I=1$) into the target $|0, 0\rangle$ state.
- Material Requirement: The experiment relied on ultra-high purity, $^{12}C$-enriched diamond (99.995% concentration) to achieve a long effective dephasing time ($T_2^* \approx 40$ ”s).
- Methodology: A sequence of 532 nm laser, Microwave (MW), and Radio-Frequency (RF) pulses was employed, utilizing a rate equation model to optimize the optical pumping duration ($\tau_L \approx 0.48$ ”s).
- Purity Result: The final purification step achieved a purity of > 96% within the $m_s=0$ electronic spin subspace.
- Model Validation: The rate equation model successfully determined key pumping parameters (electron spin rate $1/k_s \approx 0.29$ ”s, nuclear spin rate $1/k_l \approx 4.7$ ”s), validating the optimization scheme.
- Flexibility: The technique is applicable across arbitrary magnetic field strengths, unlike methods relying on excited-state level anti-crossing (LAC).
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental setup and results:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Isotopic Purity | 99.995 | % | $^{12}C$ concentration |
| Zero-Field Splitting (D) | 2.87 | GHz | NV Electronic Spin |
| Hyperfine Coupling (A) | -2.16 | MHz | Electronic and $^{14}N$ Nuclear Spin |
| Nuclear Quadrupole Coupling (P) | -4.95 | MHz | $^{14}N$ Nuclear Spin |
| Applied Magnetic Field (B) | 6.1 | mT | Along NV symmetry axis |
| Excitation Wavelength | 532 | nm | CW Diode-pumped solid-state laser |
| Optical Power Density | ~150 | ”W | Focused at the sample |
| Effective Dephasing Time ($T_2^*$) | ~40 | ”s | Measured via Ramsey-type FID |
| Optimal Laser Pulse Duration ($\tau_L$) | ~0.48 | ”s | For maximum $ |
| Electron Spin Pumping Rate (1/ks) | 0.29 ± 0.02 | ”s | Rate equation model fit |
| Nuclear Spin Depolarization Rate (1/kl) | 4.7 ± 0.4 | ”s | Rate equation model fit |
| Final $m_s=0$ Subspace Purity | > 96 | % | After final MW purification pulses |
Key Methodologies
Section titled âKey MethodologiesâThe initialization and measurement protocol relies on precise material control and complex pulse sequences:
- Material Foundation: A high-purity, $^{12}C$-enriched Single Crystal Diamond (SCD) sample was used to minimize magnetic noise and maximize the electronic spin coherence time ($T_2^*$).
- Optical Setup: A home-built confocal microscope utilized a 532 nm CW laser, modulated by an Acousto-Optic Modulator (AOM) with a fast rise time (50 ns) to generate precise optical pulses.
- Spin Control: Microwave (MW) and Radio-Frequency (RF) pulses were generated using Direct Digital Synthesis (DDS) sources, amplified, and delivered to the sample via a Cu wire attached to the surface.
- Initial Polarization: The sequence begins with a long (5 ”s) laser pulse to initialize the electronic spin into the $m_s=0$ state, leaving the nuclear spin depolarized.
- Spin Swap: MW and RF $\pi$-pulses were applied to swap the electronic and nuclear spin polarizations, effectively polarizing the nuclear spin into $m_I=0$.
- Re-polarization and Optimization: A second laser pulse of optimized duration ($\tau_L$) was applied to re-polarize the electronic spin. The duration was determined by fitting experimental Rabi oscillation and FID data to a rate equation model.
- Purification: Selective MW $\pi$-pulses (MW3 and MW4) were used as a final step to transfer residual population out of the unwanted nuclear spin states, maximizing the purity of the target $|0, 0\rangle$ state.
- State Readout: Partial quantum state tomography was performed using Ramsey-type Free Induction Decay (FID) and nuclear spin Rabi oscillations, read out via the final laser pulse.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the critical need for ultra-high quality, isotopically pure diamond substrates for scalable quantum registers. 6CCVD is uniquely positioned to supply the materials and customization required to replicate and extend this work, driving higher purity and longer coherence times.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate or extend the high-purity initialization demonstrated in this paper, researchers require diamond with minimal defects and isotopic noise.
| 6CCVD Material | Specification | Application Relevance |
|---|---|---|
| Optical Grade SCD | Ultra-low Nitrogen (< 1 ppb), Low Strain, High Transmission. | Essential for maximizing optical efficiency and minimizing background fluorescence noise during readout. |
| Isotopically Enriched SCD | > 99.99% $^{12}C$ concentration (or higher, upon request). | Directly addresses the paperâs requirement for a $^{12}C$-enriched sample, crucial for achieving $T_2^*$ times suitable for quantum memory and gate operations. |
| Custom Thickness SCD | 0.1 ”m to 500 ”m layers, Substrates up to 10 mm. | Provides flexibility for integrating NV layers into complex quantum devices, such as solid immersion lenses or micro-cavities. |
Customization Potential
Section titled âCustomization PotentialâThe experimental setup requires precise material handling, optical access, and integration of MW/RF delivery structures. 6CCVD offers comprehensive customization services to meet these needs:
- Precision Polishing: The use of a high Numerical Aperture (NA=1.4) objective demands exceptional surface quality. 6CCVD guarantees Ra < 1 nm polishing on Single Crystal Diamond (SCD) wafers, ensuring minimal optical scattering and optimal focusing for single NV center addressing.
- Custom Dimensions: While the paper implies a small sample, 6CCVD can supply SCD wafers and plates in custom dimensions up to 125 mm (PCD) or standard inch-size SCD wafers, allowing for scaling up device fabrication.
- On-Chip Metalization: The experiment used a simple Cu wire for pulse delivery. For improved pulse fidelity and integration, 6CCVD offers in-house metalization (Au, Pt, Pd, Ti, W, Cu) to fabricate high-frequency coplanar waveguides (CPW) or strip lines directly onto the diamond surface, enabling precise control over MW and RF fields.
Engineering Support
Section titled âEngineering SupportâThe determination of optimal pumping rates ($k_s, k_l$) and the management of depolarization mechanisms (like charge state conversion) are highly dependent on the specific material properties.
- 6CCVDâs in-house PhD team specializes in MPCVD growth optimization for quantum applications. We can assist researchers in material selection and recipe tuning for similar NV initialization and quantum register projects, focusing on minimizing strain and controlling NV density to achieve target $T_2$ and $T_2^*$ coherence times.
- We provide technical consultation to ensure the chosen diamond substrate geometry and surface preparation are optimized for the specific optical and microwave coupling requirements of the experiment.
Call to Action
Section titled âCall to Actionâ6CCVD provides the highest quality, isotopically controlled diamond materials necessary to push the boundaries of solid-state quantum information processing. For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We offer global shipping (DDU default, DDP available) to ensure timely delivery of your critical quantum materials.
View Original Abstract
Initializing a set of qubits to a given quantum state is a basic prerequisite\nfor the physical implementation of quantum-information protocols. Here, we\ndiscuss the polarization of the electronic and nuclear spin in a single\nnitrogen vacancy center in diamond. Our initialization scheme uses a sequence\nof laser, microwave and radio-frequency pulses, and we optimize the pumping\nparameters of the laser pulse. A rate equation model is formulated that\nexplains the effect of the laser pulse on the spin system. We have\nexperimentally determined the population of the relevant spin states as a\nfunction of the duration of the laser pulse by measuring Rabi oscillations and\nRamsey-type free-induction decays. The experimental data have been analyzed to\ndetermine the pumping rates of the rate equation model.\n