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Robust Detection of High-Frequency Signals at the Nanoscale

MetadataDetails
Publication Date2020-11-20
JournalPhysical Review Applied
AuthorsCarlos Munuera-Javaloy, Yue Ban, Xi Chen, J. Casanova
InstitutionsIkerbasque, University of the Basque Country
Citations12
AnalysisFull AI Review Included

Technical Documentation & Analysis: Robust Nanoscale Quantum Sensing

Section titled “Technical Documentation & Analysis: Robust Nanoscale Quantum Sensing”

This document analyzes the research paper “Robust Detection of High-Frequency Signals at the Nanoscale” and outlines how 6CCVD’s advanced MPCVD diamond materials and engineering services are essential for replicating, extending, and commercializing this robust quantum sensing technology.


The research demonstrates a breakthrough in Nanoscale Nuclear Magnetic Resonance (NMR) by achieving robust detection of high-frequency nuclear spin signals using Nitrogen Vacancy (NV) centers in diamond.

  • Core Value Proposition: Integration of Shortcuts to Adiabaticity (STA) techniques into Dynamical Decoupling (DD) sequences (XY8) yields highly resilient quantum control pulses.
  • Robustness Achieved: The protocol successfully cancels typical control errors, including Rabi frequency deviations (up to 1%) and significant detuning errors ($2\pi \times 1$ MHz), which typically spoil high-field NMR experiments.
  • High-Field Operation: Demonstrated reliable detection of ${}^{13}$C and ${}^{1}$H nuclear spins under strong static magnetic fields ($B_z = 3$ T), a regime where conventional methods fail due to power limitations.
  • Performance Superiority: STA-optimized pulses deliver significantly higher spectral contrast and reliable resonance identification compared to standard top-hat or extended $\pi$ pulses.
  • Material Requirement: The success relies fundamentally on high-quality, low-strain solid-state quantum sensors, specifically NV centers in diamond, highlighting the critical need for Electronic Grade Single Crystal Diamond (SCD).
  • General Applicability: The methodology is transferable to other solid-state sensors, including Silicon Vacancy (SiV), Germanium Vacancy (GeV) centers, and divacancies in Silicon Carbide (SiC).

The following table summarizes the critical experimental parameters and performance metrics achieved using the STA-optimized protocol:

ParameterValueUnitContext
Static Magnetic Field ($B_z$)3TStrong magnetic field regime
Sensor TypeNitrogen Vacancy (NV) CenterN/AQuantum sensor host material: Diamond
Zero-Field Splitting (D)$2\pi \times 2.87$GHzNV electronic spin property
Target Nuclei Detected${}^{13}$C, ${}^{1}$HN/ANanoscale NMR targets
Control SequenceXY8 (102 repetitions)N/ADynamical Decoupling sequence
${}^{13}$C Pulse Duration ($t_{\pi}$)$\approx 0.22$”sSTA-optimized pulse length
${}^{1}$H Pulse Duration ($t_{\pi}$)$\approx 0.17$”sSTA-optimized pulse length
Rabi Frequency Error Tolerance ($\xi_{\Omega}$)$0.5%$ to $1%$N/ARobustness against MW power variations
Detuning Error Tolerance ($\xi_{\delta}$)$2\pi \times 1$MHzRobustness against frequency offsets/strain
${}^{13}$C Total Sequence Time$\approx 0.19$msTotal interrogation time
${}^{1}$H Total Sequence Time$\approx 0.14$msTotal interrogation time
${}^{13}$C Hyperfine Vector (A)$2\pi \times [-4.81, -8.33, -26.74]$KHzCoupling at 1.1 nm distance

The robust detection protocol relies on a sophisticated integration of quantum control techniques and numerical optimization:

  1. Hamiltonian Definition: The system is modeled by the NV center coupled to the target signal (nuclear spin or classical wave) and driven by a Microwave (MW) control field.
  2. Rotating Frame Analysis: The Hamiltonian is simplified using the Rotating Wave Approximation (RWA) and subsequent frame transformations to isolate the control term $H_c$.
  3. STA Parameterization: The NV spin state evolution is parameterized using the Bloch sphere angles ($\theta(t)$, $\beta(t)$, $\gamma(t)$) based on Shortcuts to Adiabaticity (STA) principles.
  4. Coupling Condition: The control fields $\Omega(t)$ (Rabi frequency) and $\delta(t)$ (detuning) are designed to satisfy the maximal NV-target interaction strength, ensuring the coupling integral (Eq. 8) is zero.
  5. Error Cancelation Condition: Perturbation theory is used to calculate the transition probability $P(t_{\pi})$ under imperfect pulses (up to second order in $\xi_{\Omega}$ and $\xi_{\delta}$). The control functions are then optimized to satisfy the error cancelation condition (Eq. 9), eliminating undesired NV transitions.
  6. Pulse Generation: An ansatz inspired by the Blackman function is used for $\theta(t)$, and free parameters ($\eta_{1}$, $\eta_{2}$) are tuned to achieve the required robustness and pulse length ($t_{\pi}$).
  7. Dynamical Decoupling Implementation: The optimized robust $\pi$ pulses are integrated into the standard XY8 DD sequence for numerical simulation and performance validation at $B_z = 3$ T.

The successful implementation of robust nanoscale quantum sensing, as demonstrated in this paper, requires diamond substrates with exceptional purity, low strain, and precise surface engineering—all core competencies of 6CCVD.

Applicable Materials & Requirements6CCVD Solution & CapabilityTechnical Advantage for Quantum Sensing
High Coherence & Low Strain (Essential for minimizing detuning errors $\xi_{\delta}$ and maximizing $T_2$)Electronic Grade Single Crystal Diamond (SCD)Ultra-low defect density (PPB nitrogen level) SCD wafers ensure minimal internal strain, maximizing the quantum coherence time necessary for long DD sequences (0.14 ms to 0.19 ms).
Quantum Defect Hosting (NV, SiV, GeV)Custom Defect Engineering & SubstratesWe supply SCD substrates optimized for post-processing (e.g., ion implantation for shallow NVs) or in-situ growth of SiV/GeV centers via tailored MPCVD recipes, supporting the general applicability of the protocol.
Precise Sensor Depth (Shallow NVs for surface NMR)Custom Thickness Control (0.1 ”m - 500 ”m)SCD layers can be grown to specific thicknesses, enabling precise control over the depth of the quantum sensor relative to the sample surface.
MW Control Integration (Fabricating high-frequency waveguides)In-House Custom Metalization ServicesWe offer deposition of thin films (Au, Pt, Ti, W, Cu) directly onto the diamond surface, critical for fabricating the high-power microwave antennas required to deliver the high-frequency $\Omega(t)$ control pulses.
Surface Quality (Minimizing noise and facilitating implantation)Precision Polishing (Ra < 1 nm for SCD)Our chemical-mechanical polishing achieves atomic-scale smoothness, essential for minimizing surface noise and ensuring uniform implantation for shallow NV centers.
Device Scalability (Ensemble detection, large arrays)Large Format Wafers (Up to 125 mm)We provide inch-size SCD and large-area PCD wafers (up to 125 mm) to support the development of scalable quantum sensor arrays for applications requiring ensemble averaging, such as the ${}^{1}$H cluster detection scenario described.

6CCVD’s in-house PhD team specializes in the material science of quantum defects and high-power microwave applications in diamond. We offer comprehensive consultation on material selection, defect incorporation strategies, and surface preparation necessary to replicate or extend this robust Nanoscale NMR research.

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

View Original Abstract

We present a method relying on shortcuts to adiabaticity to achieve quantum\ndetection of high frequency signals at the nanoscale in a robust manner. More\nspecifically, our protocol delivers tailored amplitudes and frequencies for\ncontrol fields that, firstly, enable the coupling of the sensor with\nhigh-frequency signals and, secondly, minimise errors that would otherwise\nspoil the detection process. To exemplify the method, we particularise to\ndetection of signals emitted by fast-rotating nuclear spins with nitrogen\nvacancy center quantum sensors. However, our protocol is straightforwardly\napplicable to other quantum devices such as silicon vacancy centers, germanium\nvacancy centers, or divacancies in silicon carbide.\n