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Measurement of transverse hyperfine interaction by forbidden transitions

MetadataDetails
Publication Date2015-03-30
JournalDSpace@MIT (Massachusetts Institute of Technology)
AuthorsMo Chen, Masashi Hirose, Paola Cappellaro
Citations6
AnalysisFull AI Review Included

Technical Analysis & Documentation: Transverse Hyperfine Interaction in NV Diamond

Section titled “Technical Analysis & Documentation: Transverse Hyperfine Interaction in NV Diamond”

6CCVD - Experts in High Purity MPCVD Diamond for Quantum Applications


This paper presents a high-precision measurement of the transverse hyperfine interaction ($A_{\perp}$) between the electron spin of a Nitrogen-Vacancy (NV) center and its adjacent $\text{}^{14}$N nuclear spin in high-purity diamond. The key achievements and implications for quantum technology include:

  • Precision Measurement: Determination of the transverse hyperfine coupling constant ($A_{\perp}$) to an accuracy of $\pm 0.05$ MHz, significantly enhancing the precision compared to prior methods.
  • Novel Methodology: Utilized nominally forbidden transitions induced by spin-level mixing to dramatically enhance the nuclear Rabi oscillation frequency.
  • Enhanced Manipulation Speed: The observed enhancement factor, which can exceed 100 near the ground state level anticrossing ($B \approx 0.1$ T), enables nuclear spin manipulation at fast, megahertz (MHz) rates with only moderate radio frequency (RF) driving strengths ($B_1 \approx 3.3$ G).
  • Material Requirements: Success relies on high-quality, electronic-grade single-crystal diamond (SCD) with extremely low concentrations of parasitic nitrogen ($\text{}^{14}$N < 5 ppb) and minimal natural carbon-13 ($\text{}^{13}$C) impurities.
  • Quantum Control Validation: The method confirms that incorporating nonsecular Hamiltonian parts (level mixing) is crucial for achieving faster and more accurate control over electron-nuclear hybrid quantum systems, vital for quantum sensing and computation architectures.

The following table summarizes the key experimental and derived physical parameters extracted from the research paper.

ParameterValueUnitContext
Transverse Hyperfine Coupling ($A_{\perp}$)$-2.62 \pm 0.05$MHzPrimary measured value (high precision)
Magnetic Field ($B_z$) for Measurement509GFixed field used for Rabi frequency sweeps
Magnetic Field ($B_z$) Range300 - 500GRange used for general experimentation
Electron Zeeman Frequency ($\gamma_e$)2.8MHz/GGyromagnetic ratio for NV electron spin
Nuclear Zeeman Frequency ($\gamma_n$)-0.308kHz/GGyromagnetic ratio for $\text{}^{14}$N nuclear spin
Laser Excitation Wavelength532nmUsed for initial NV spin polarization
Laser Excitation Time1”sDuration used to polarize the NV-$\text{}^{14}$N system
Enhanced Rabi Frequency (Max)>1MHzAchieved near $B \approx 0.1$ T anticrossing
$\text{}^{14}$N Concentration in Diamond< 5ppbRequirement for electronic grade diamond sample
Total Precision Uncertainty ($\delta A_{\perp}$)$\sim 50$kHzLimited by experimental stability and photon shot noise

The experiment utilized a sequence of microwave (MW) and radio frequency (RF) pulses combined with optical detection (ODMR) under a home-built confocal microscope. The critical steps for material preparation and measurement protocol are listed below.

  1. Material Selection:

    • Use of electronic grade diamond (Element Six) characterized by ultra-low nitrogen ($\text{}^{14}$N < 5 ppb) and minimal natural $\text{}^{13}$C abundance.
    • A single NV center was selected, confirmed to be free from close-by $\text{}^{13}$C impurities.
  2. External Field Application:

    • A stable magnetic field ($B_z$) was applied along the NV axis ([111] crystal axis) to lift $m_s = \pm 1$ degeneracy.
    • Magnetic fields were held constant close to the Excited State Level Anticrossing (300-500 G) to facilitate nuclear polarization transfer.
  3. Spin Initialization (Polarization):

    • NV-$\text{}^{14}$N system was polarized into the $|0,1\rangle$ state using a 532 nm laser pulse ($\approx 1\ \mu$s duration). This polarization transfer relies on strong hyperfine coupling in the excited state.
  4. Spin Preparation & Coherent Driving:

    • The NV electron spin was prepared in the desired Zeeman state using a strong MW pulse ($t_p \approx 50$ ns).
    • The $\text{}^{14}$N nuclear spin was coherently driven using a variable-amplitude RF field, resonant with the nuclear transition ($\text{|}m_s, 1\rangle \rightarrow \text{|}m_s, 0\rangle$) for a duration $\tau$.
  5. Detection and Readout:

    • A MW selective pulse ($t_p \approx 700$ ns) mapped the nuclear spin state onto the electron spin state ($m_s$).
    • The final electron spin state was detected optically via spin-dependent fluorescence emission intensity (ODMR).
  6. Data Extraction:

    • Measured the effective nuclear Rabi frequency ($\Omega_m$) as a function of normalized RF amplitude ($B_1/\text{|}B_{1, max}\text{|}$) at fixed $B_z = 509$ G.
    • Fit data using the enhancement factors derived from the total NV Hamiltonian (Equations 5-7, accounting for level mixing) to extract the highly precise $A_{\perp}$ value.

Replicating and advancing this seminal quantum research requires precision-engineered diamond materials. 6CCVD, an expert in MPCVD diamond growth, provides the exact specifications necessary for these demanding electron-nuclear hybrid spin systems.

To achieve the ultra-low impurity levels and high crystal quality necessary for NV center quantum coherence, researchers must utilize Optical Grade Single Crystal Diamond (SCD).

6CCVD Material RecommendationSpecificationRelevance to Research
Optical Grade SCDNitrogen ($\text{}^{14}$N) below 5 ppb. Low metallic impurities.Essential for minimizing electronic noise and maximizing coherence time ($T_2$). Replicates the high-quality base material used.
SCD Thickness ControlSCD layers from 0.1 ”m up to 500 ”m.Allows precise fabrication of solid-immersion lenses or integration into high-density photonic circuits (as mentioned in references).
Optimized PolishingSurface roughness Ra < 1 nm (SCD).Crucial for high-fidelity optical readout (e.g., maximizing fluorescence collection via air-diamond interface or integration of coupling optics).

The flexibility of the 6CCVD MPCVD process directly addresses common limitations in quantum material integration:

  • Custom Dimensions: We provide plates and wafers up to 125 mm (PCD/SCD substrates), enabling scalability for large-array quantum device fabrication, far exceeding typical small research samples.
  • Precision Substrates: While this paper focused on a single NV, scaling the technology requires reliable substrates. We offer SCD Substrates up to 10 mm thick for robust handling and thermal management in complex setups.
  • Advanced Metalization Services: Many quantum sensing and control experiments require integrated on-chip microwave and RF antennas for local field delivery. 6CCVD offers in-house metalization capabilities, including Au, Pt, Pd, Ti, W, and Cu, allowing researchers to directly deposit transmission lines and strip lines onto the diamond surface for highly efficient spin control.
  • Laser Cutting and Shaping: We provide custom laser cutting and etching services necessary for creating microstructures (e.g., waveguides, pillars, or focused NV implantation zones) that enhance spin readout efficiency.

The enhanced nuclear Rabi oscillations observed in this work promise fast manipulation of the nuclear spin qubit. 6CCVD’s in-house PhD team specializes in diamond defect engineering and material characterization. We can assist your project in:

  • Material Selection: Guiding the choice between SCD and PCD based on required $\text{}^{14}$N concentration, target $T_1$ and $T_2$ times, and intended NV creation methodology (e.g., implantation/annealing recipes).
  • Surface Preparation: Consulting on necessary polishing grades (Ra < 1 nm) required for optimal optical coupling in similar Quantum Sensing and Nuclear Spin Manipulation projects.
  • Defect Control: Providing detailed specifications for diamond material designed for high-density, addressable NV arrays.

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.