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Quantum Metrology with Strongly Interacting Spin Systems

MetadataDetails
Publication Date2020-07-02
JournalPhysical Review X
AuthorsHengyun Zhou, Joon-Hee Choi, Soonwon Choi, Renate Landig, Alexander M. Douglas
InstitutionsAdvanced Science Research Center, University of Cambridge
Citations99
AnalysisFull AI Review Included

Technical Documentation & Analysis: Quantum Metrology with Strongly Interacting Spin Systems

Section titled “Technical Documentation & Analysis: Quantum Metrology with Strongly Interacting Spin Systems”

This document analyzes the research paper “Quantum Metrology with Strongly Interacting Spin Systems” (arXiv:1907.10066v2) to highlight the critical role of high-quality diamond materials and advanced fabrication in achieving state-of-the-art quantum sensing performance.


The research demonstrates a breakthrough in solid-state quantum metrology by overcoming the sensitivity limit imposed by spin-spin interactions in dense Nitrogen-Vacancy (NV) ensembles in diamond.

  • Interaction Limit Surpassed: A novel robust quantum control sequence (Seq. B), based on Floquet engineering and average Hamiltonian theory, was developed to simultaneously decouple disorder, interactions, and control imperfections.
  • Coherence Enhancement: Sequence B achieved a 5-fold enhancement in spin coherence time ($T_{2}$) compared to the conventional XY-8 dynamical decoupling sequence, extending $T_{2}$ to $7.9$ ”s in a dense ensemble.
  • Sensitivity Record: This robust decoupling resulted in a 40% improvement in volume-normalized AC magnetic field sensitivity ($\eta_{V}$) over XY-8, reaching $8.3(8)$ nT $\cdot$ ”m$^{3/2}/\sqrt{\text{Hz}}$.
  • Material Requirement: The experiment relied on high-density Type-Ib HPHT diamond ($\sim 15$ ppm NV concentration) fabricated into a nanobeam structure to confine the sensing volume ($8.1 \times 10^{-3}$ ”mÂł).
  • Robustness Demonstrated: The Seq. B protocol maintained superior sensitivity even in the presence of systematic rotation angle errors up to $\pm 12%$, confirming its fault-tolerant design.

The following hard data points were extracted from the experimental results and material characterization:

ParameterValueUnitContext
Diamond TypeType-Ib HPHTN/APrecursor material for NV creation.
NV Concentration ($\rho$)$\sim 15$ppmHigh density ensemble used for sensing.
Sensing Volume ($V$)$8.1 \times 10^{-3}$”m³Volume confined by the diamond nanobeam.
On-site Disorder ($W$)$4.0$MHzGaussian standard deviation of NV resonance linewidth.
Dipolar Interaction Strength ($J$)$35$kHzEstimated strength at 11 nm typical separation.
Coherence Time ($T_{2}$) - XY-8$1.6(1)$”sInteraction-limited conventional performance.
Coherence Time ($T_{2}$) - Seq. B$7.9(2)$”sAchieved with robust interaction decoupling.
Volume-Normalized Sensitivity ($\eta_{V}$)$8.3(8)$nT $\cdot$ ”m$^{3/2}/\sqrt{\text{Hz}}$State-of-the-art performance for ensemble sensors.
Pulse Spacing ($\tau$)$25$nsFixed free evolution interval in decoupling sequences.
$\pi$-Pulse Width ($t_{\pi}$)$20$nsDuration of control pulses.
Static Magnetic Field ($B_{0}$)$260$GaussUsed to isolate a single NV group.

The experimental success hinges on precise material engineering and advanced quantum control techniques:

  1. High-Density NV Creation: Type-Ib HPHT diamond was irradiated with high-energy electron beams ($1.4 \times 10^{19}$ cm-2 fluence) and annealed (700 - 800 °C) to achieve a high NV concentration ($\sim 15$ ppm).
  2. Nanobeam Fabrication: The bulk diamond was etched using Faraday cage angled etching to create a 20 ”m-long nanobeam structure. This confined the probing volume and improved control homogeneity.
  3. Microwave Control: Coherent spin dynamics were driven using resonant microwaves synthesized by an Arbitrary Waveform Generator (AWG) at a Rabi frequency ($\Omega$) of 25 MHz, corresponding to a 10 ns $\pi/2$ pulse length.
  4. Robust Sequence Design (Seq. B): A novel pulse sequence was designed using a generalized average Hamiltonian analysis and algebraic rules to ensure fault-tolerance against leading-order imperfections, including rotation angle errors and finite pulse duration effects.
  5. Vectorial Sensing Scheme: The protocol utilized the full vector nature of the effective sensing field ($\vec{B}_{\text{eff}}$) along the [1, 1, 1]-direction, requiring phase-synchronized modulation functions across all three axes for optimal sensitivity.
  6. Optimal Initialization and Readout: Sensitivity was maximized by initializing the spins perpendicular to the effective magnetic field direction ($\vec{B}_{\text{eff}}$) and employing an unconventional readout rotation to maximize contrast.

The demonstrated research requires ultra-high-quality diamond substrates and precision fabrication capabilities—areas where 6CCVD excels. We offer tailored MPCVD diamond solutions necessary to replicate, scale, and advance this quantum metrology platform.

Research Requirement6CCVD Solution & Value Proposition
High NV Density Precursor (15 ppm NV)High-Purity Single Crystal Diamond (SCD) Substrates: We supply SCD material with controlled nitrogen incorporation during MPCVD growth, optimized for high-efficiency NV creation. Our material ensures low background impurity levels critical for long $T_{1}$ and $T_{2}$ times, essential for surpassing the interaction limit.
Nanobeam Fabrication (Etched structure, $8.1 \times 10^{-3}$ ”m³)Custom Dimensions and Laser Processing: 6CCVD provides custom SCD plates and wafers up to 125 mm (PCD). We offer precision laser cutting and shaping services, delivering ideal starting geometries for subsequent nanostructure etching (e.g., nanobeams or photonic crystal cavities).
Ultra-Smooth Surfaces (Required for high-Q nanostructures)Precision Polishing (Ra < 1 nm): Our SCD material is polished to an atomic scale roughness (Ra < 1 nm). Minimizing surface defects is crucial for reducing decoherence and ensuring optimal performance for integrated optical components and nanostructures.
Microwave Delivery Integration (Ω-shaped line)Custom Metalization Services: We offer in-house deposition of standard metals (Au, Pt, Pd, Ti, W, Cu) directly onto diamond surfaces. This capability enables seamless integration of microwave control lines and electrodes required for high-frequency spin manipulation ($\Omega = 25$ MHz).
Scaling and Replication (Need for larger, uniform ensembles)Large-Area Polycrystalline Diamond (PCD): For scaling ensemble magnetometry, our PCD wafers (up to 125 mm diameter) provide large, uniform sensing areas while maintaining the high quality necessary for robust dynamical decoupling sequences like Seq. B.
Future Sensitivity Goals (Projected $\eta_{V} \sim 8$ pT $\cdot$ ”m$^{3/2}/\sqrt{\text{Hz}}$)Engineering Support for Readout Optimization: Achieving projected sensitivity requires improved photon collection efficiency ($C > 5%$). Our in-house PhD team can consult on material selection and surface preparation to facilitate the integration of advanced nanofabrication techniques (e.g., parabolic reflectors) for enhanced readout.

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

View Original Abstract

Quantum metrology makes use of coherent superpositions to detect weak\nsignals. While in principle the sensitivity can be improved by increasing the\ndensity of sensing particles, in practice this improvement is severely hindered\nby interactions between them. Using a dense ensemble of interacting electronic\nspins in diamond, we demonstrate a novel approach to quantum metrology. It is\nbased on a new method of robust quantum control, which allows us to\nsimultaneously eliminate the undesired effects associated with spin-spin\ninteractions, disorder and control imperfections, enabling a five-fold\nenhancement in coherence time compared to conventional control sequences.\nCombined with optimal initialization and readout protocols, this allows us to\nbreak the limit for AC magnetic field sensing imposed by interactions, opening\na promising avenue for the development of solid-state ensemble magnetometers\nwith unprecedented sensitivity.\n