Measurement of transverse hyperfine interaction by forbidden transitions

At a Glance

Metadata	Details
Publication Date	2015-07-06
Journal	Physical Review B
Authors	Mo Chen, Masashi Hirose, Paola Cappellaro
Institutions	Massachusetts Institute of Technology
Citations	49
Analysis	Full AI Review Included

6CCVD Technical Documentation: Transverse Hyperfine Interaction in NV Centers

Analyzing: Measurement of transverse hyperfine interaction by forbidden transitions (Chen et al., MIT)

Executive Summary

This research establishes a highly precise methodology for characterizing non-secular components of the Nitrogen-Vacancy (NV) center Hamiltonian in diamond, a critical step toward high-fidelity quantum control.

Core Achievement: Determined the transverse hyperfine coupling ($A_{\perp}$) between the NV electronic spin and the nuclear ¹⁴N spin with unprecedented precision ($A_{\perp} = -2.62 \pm 0.05$ MHz).
Methodology: Exploited nominally forbidden transitions during nuclear Rabi nutation, leveraging second-order effects due to mixing of electronic and nuclear spin states.
Material Requirement: The experiment utilized electronic-grade Single Crystal Diamond (SCD) with ultra-low native ¹⁴N concentration (< 5 ppb), emphasizing the requirement for exceptional material purity and low strain.
Quantum Impact: Observed significant enhancement (factors exceeding 100) of the nuclear Rabi nutation rate when working near the ground state level anti-crossing.
Engineering Implication: The enhanced nutation promises fast manipulation of nuclear spin qubits at MHz rates using only moderate driving strengths, crucial for robust quantum gates.
Broader Applicability: The method is scalable to characterize interaction Hamiltonians in other solid-state electronic-nuclear hybrid systems (e.g., donors in Si or SiC, quantum dots).

Technical Specifications

The following hard parameters define the experimental context and the resulting material physics measurements within the NV-¹⁴N system.

Parameter	Value	Unit	Context
Transverse Hyperfine Coupling (A_&perp;)	-2.62 ± 0.05	MHz	Precision achieved via forbidden transitions measurement.
Longitudinal Hyperfine Coupling (A_\|\|)	-2.162	MHz	Previously established component.
Nuclear Quadrupolar Interaction (Q)	-4.945	MHz	Intrinsic ¹⁴N property.
Zero-Field Splitting (D)	2.87	GHz	Electronic spin (S=1) resonance frequency.
External Magnetic Field (B)	509	G	Optimized field for final $A_{\perp}$ measurement (along [111] axis).
Nuclear Rabi Frequency (Enhanced)	> 1	MHz	Maximum observed frequency at B = 509G, enables fast gates.
Excitation Laser Wavelength	532	nm	Used for initial spin polarization and optical readout.
Material Grade	Electronic Grade SCD	N/A	Requirement for single NV spin control and long coherence times.
Native ¹⁴N Concentration (n_V)	< 5	ppb	Ultra-low concentration in the diamond sample.
Rabi Enhancement Factor	> 100	N/A	Observed near the ground state level anti-crossing (B ≈ 0.1 T).

Key Methodologies

The experiment relies on a hybrid optical and magnetic resonance sequence applied to a single NV center within an electronic-grade SCD substrate.

Material Preparation: Selected an electronic grade diamond (Element 6) with extremely low native nitrogen concentration ($n_V < 5$ ppb) and minimal ¹³C abundance to minimize decoherence sources.
Spin Polarization (Optical):
- Applied 532 nm laser excitation (1 µs pulse) to polarize the NV electronic spin.
- Worked at magnetic fields (300G to 500G) close to the Excited State Level Anti-Crossing (LAC) to enable efficient spin transfer, polarizing the NV-¹⁴N system into the $|0, 1\rangle$ state.
Zeeman State Preparation (Microwave):
- Used a strong microwave (MW) pulse ($t_p \approx 50$ ns) to map the NV spin into the desired Zeeman state prior to nuclear driving.
Nuclear Coherent Driving (RF):
- Applied a Radio Frequency (RF) field, on resonance with the nuclear transition ($|m_s, 1\rangle \leftrightarrow |m_s, 0\rangle$), for variable duration $\tau$.
Nuclear State Readout (MW/Optical):
- Used a MW selective pulse ($t_p \approx 700$ ns) to map the nuclear spin state back onto the NV electronic spin.
- The final state was read out optically via spin-dependent fluorescence emission intensity.
Data Acquisition and Fitting:
- Measured the effective nuclear Rabi frequency ($\Omega_m$) as a function of the normalized RF amplitude ($B_1/B_{1,max}$) in all three electronic manifolds at a fixed magnetic field ($B=509$G).
- Fit the resulting data to the Rabi enhancement formulas (Equations 5-7) to extract the transverse hyperfine coupling, $A_{\perp}$.

6CCVD Solutions & Capabilities

6CCVD provides the specialized MPCVD diamond materials and precision engineering services required to replicate this high-precision quantum control research and scale its applications in quantum sensing and computation.

Applicable Materials

To achieve the long coherence times and low defect concentrations essential for single-spin measurements and precise Hamiltonian characterization, the following materials from the 6CCVD catalog are recommended:

Optical Grade Single Crystal Diamond (SCD):
- Requirement Match: Used for NV center studies, this material offers extremely low intrinsic nitrogen ($n_V$) and high crystalline quality, minimizing strain and maximizing $T_2$ coherence times critical for high-fidelity quantum experiments.
- Availability: 6CCVD supplies SCD materials in thicknesses ranging from 0.1 µm up to 500 µm, tailored for both surface-implanted and bulk NV applications.
High-Purity Polycrystalline Diamond (PCD):
- Extension Potential: For large-area sensing arrays or high-power thermal management integrated with NV systems, 6CCVD offers large format PCD plates up to 125 mm diameter, suitable for deposition of thin SCD films or integration layers.

Customization Potential

The measurement of single NV centers requires precise material handling and integration into highly specialized confocal and magnetic resonance setups. 6CCVD directly supports these needs:

Custom Dimensions and Etching: 6CCVD provides precision laser cutting and shaping services, enabling the creation of small, custom-sized diamond pieces suitable for cryogenic or vacuum chambers. We support the production of waveguides, solid-immersion lenses (SILs), and micro-antennae required for enhanced optical readout (as referenced in the paper, e.g., solid-immersion lenses ³⁸).
High-Precision Polishing: SCD substrates are polished to an exceptional surface roughness ($\text{Ra} < 1$ nm), crucial for minimizing scattering losses during 532 nm laser excitation and maintaining high contrast in the optical readout process.
Custom Metalization: For generating the localized MW and RF fields necessary to drive the electronic and nuclear spins (Equation 3), 6CCVD offers in-house metalization services. We can deposit electrode patterns (e.g., Ti/Pt/Au contact layers) using Au, Pt, Pd, Ti, W, and Cu to customer specifications, ensuring reliable contact and efficient field delivery for Rabi oscillation experiments.

Engineering Support

Precise Hamiltonian characterization and the optimization of quantum gates require expert knowledge linking material properties to quantum performance metrics.

Material Selection Consulting: 6CCVD’s in-house PhD team can assist researchers in selecting the optimal material grade and orientation to maximize $T_2$ coherence times and minimize native defects for similar quantum control and sensing projects.
Defect Engineering: We provide guidance on appropriate NV creation methods (e.g., implantation, annealing protocols) to achieve desired NV density and location while maintaining the ultra-low strain necessary for precise spectroscopic measurements like those described in this paper.
Global Logistics: Utilizing DDU (Delivery Duty Unpaid) default and DDP (Delivery Duty Paid) options, 6CCVD ensures seamless and reliable global shipping of fragile, high-value diamond materials directly to research facilities worldwide.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Precise characterization of a system’s Hamiltonian is crucial to its high-fidelity control that would enable many quantum technologies, ranging from quantum computation to communication and sensing. In particular, non-secular parts of the Hamiltonian are usually more difficult to characterize, even if they can give rise to subtle but non-negligible effects. Here we present a strategy for the precise estimation of the transverse hyperfine coupling between an electronic and a nuclear spin, exploiting effects due to forbidden transitions during the Rabi driving of the nuclear spin. We applied the method to precisely determine the transverse coupling between a Nitrogen-Vacancy center electronic spin and its Nitrogen nuclear spin. In addition, we show how this transverse hyperfine, that has been often neglected in experiments, is crucial to achieving large enhancements of the nuclear Rabi driving.