Quantum sensing with arbitrary frequency resolution

At a Glance

Metadata	Details
Publication Date	2017-05-25
Journal	Science
Authors	J M Boss, K. S. Cujia, J. Zopes, C. L. Degen
Institutions	ETH Zurich
Citations	276
Analysis	Full AI Review Included

Technical Analysis and Commercial Solutions for Ultra-High Resolution Quantum Sensing

Document Reference: arXiv:1706.01754v1 (Boss et al., 2017) Subject: Quantum sensing with arbitrary frequency resolution using NV Centers in Diamond.

Executive Summary

6CCVD analyzes the pioneering work by Boss et al., which demonstrates a quantum sensing technique leveraging NV centers in diamond to achieve frequency resolution limited only by external clock stability and measurement time. This technology has critical implications for high-resolution spectroscopy and quantum metrology, relying fundamentally on advanced Single Crystal Diamond (SCD) material engineering.

Arbitrary Resolution Achieved: Demonstrated magnetic field sensing with an unprecedented frequency resolution of 70 µHz and a precision of 260 nHz, surpassing limitations imposed by the NV center’s intrinsic coherence time.
High Sensitivity: Achieved an exceptional Signal-to-Noise Ratio (SNR) exceeding 10⁴ for a 170 nT oscillating magnetic field measured over a one-hour interval.
Core Methodology: Utilized continuous periodic sampling via a quantum lock-in amplifier (CPMG sequence) combined with Compressive Sampling (CS) to reconstruct wideband spectra up to the MHz range.
Material Platform: The sensor is based on single Nitrogen Vacancy (NV) centers in nanopillar diamond waveguides, fabricated via 5 keV ¹⁵N⁺ implantation and high-temperature annealing (850 °C).
Qubit Architecture: Implemented a two-qubit sensor system, using the NV electronic spin as the probe and a coupled ¹⁵N nuclear spin as a long-lived quantum memory, optimized via repetitive Quantum Non-Demolition (QND) readout.
Commercial Relevance: This research validates the need for ultra-high purity, engineered SCD substrates with superior surface quality and crystal control, core capabilities of 6CCVD’s MPCVD manufacturing process.

Technical Specifications

The following hard performance and operational data were extracted from the study:

Parameter	Value	Unit	Context
Minimum Frequency Resolution	70 µHz	-	Achieved over 4 hours measurement time.
Minimum Frequency Precision	260 nHz	-	Achieved via $T^{-1.5}$ scaling.
Test Signal Amplitude ($B_{ac}$)	170	nT	Detected with SNR > 10⁴ (1 hr interval).
Qubit Operating Frequency	9916	MHz	NV $m_s=0 \leftrightarrow m_s=-1$ transition.
Magnetic Bias Field ($B_{z}$)	456.54 - 546.59	mT	Used for state polarization and alignment.
Optical Excitation Wavelength	532	nm	Green laser for NV initialization/readout.
NV Initialization Laser Pulse	1 - 2	µs	Typical duration for electronic spin initialization.
Repetitive Readout Laser Pulse	600 - 800	ns	Duration per QND cycle.
Optical Contrast ($\epsilon$)	≈ 0.35	-	Max observed contrast.
Optimum Readout Gain ($C_{thresh}$)	27	photons	Achieved at $n=260$ QND measurements.
Ion Implantation Energy	5	keV	Used for near-surface ¹⁵N NV creation.
Annealing Temperature	850	°C	Post-implantation thermal treatment.

Key Methodologies

The experimental achievement of arbitrary frequency resolution relies on precise quantum control sequences and advanced diamond material processing:

Diamond Nanofabrication: NV centers were created near the surface of the diamond, followed by etching into nanopillar waveguides to achieve 10x to 15x enhancement in photon collection efficiency, essential for high SNR.
NV Creation and Control: ¹⁵N⁺ ion implantation (5 keV) and 850 °C annealing were used to form NV centers. The electronic and ¹⁵N nuclear spins were used as probe and memory qubits, respectively.
MW/RF Delivery: Microwave (~10 GHz) and radio-frequency (~2 MHz) pulses were generated using arbitrary waveform generators and delivered to the NV center via a Coplanar Waveguide (CPW) deposited on a quartz cover slip, terminated by a 50 Ω load.
Quantum Lock-in Detection: The signal measurement employed a Carr-Purcell-Meiboom-Gill (CPMG) sequence (K=16 or 32 pulses) applied to the electronic spin, which modulates the qubit phase accumulation based on the instantaneous value of the external AC magnetic field.
Indirect QND Readout: The final electronic spin state was mapped onto the ¹⁵N nuclear memory qubit via c-NOT gates. The nuclear spin state was then read out repetitively (n up to 2,000 times) using QND measurements to achieve high statistical gain ($C$) and optimize the SNR against projection and shot noise.
Continuous Sampling and Drift Correction: Measurements were performed continuously for up to 4 hours. A dedicated short pulse sequence tracked the EPR resonance frequency, allowing real-time adjustment of the MW frequency to compensate for slow magnetic field drifts (< 100 kHz detuning maintained).
Wideband Spectrum Reconstruction: To overcome the sub-Nyquist sampling limitation necessary for high-resolution, the absolute frequency was recovered using Compressive Sampling (CS). This required recording multiple time traces with slightly randomized sampling periods ($t_s$) achieved by adjusting the delay time ($t_{d}$).

6CCVD Solutions & Capabilities

6CCVD provides the high-performance MPCVD diamond materials and engineering services required to replicate, scale, and advance this cutting-edge research in quantum sensing and metrology.

Applicable Materials

Successful replication and scaling of this quantum sensor require materials with extremely high purity, low strain, and controlled surface quality—characteristics guaranteed by 6CCVD’s growth capabilities.

Optical Grade Single Crystal Diamond (SCD): Required for achieving long electronic and nuclear spin coherence times ($T_2, T_2^*$) and high optical throughput. 6CCVD supplies SCD materials optimized for quantum applications with controlled nitrogen/impurity levels, essential for tuning NV density.
High-Quality Polished Substrates: The fabrication of nanopillars (waveguides) and the need for low-loss optical coupling necessitate exceptional surface finish. 6CCVD offers SCD polished to an exceptional roughness specification of Ra < 1 nm, minimizing scattering losses and improving nanofabrication yield.

Customization Potential

The experimental setup required specialized components, including near-surface NV creation and integrated RF elements. 6CCVD’s engineering solutions directly address these needs:

Requirement from Paper	6CCVD Capability	Value Proposition
Nanopillar Etching Base	Custom SCD Wafers (0.1 µm - 500 µm thickness)	Provides precise material dimensions and superior surface quality for repeatable, high-aspect-ratio nanofabrication.
RF/MW Pulse Delivery	Internal Metalization (Ti/Pt/Au/Pd/Cu/W)	Custom design and deposition of Coplanar Waveguides (CPW) or microstrip lines directly onto the SCD or carrier substrates, ensuring low-loss RF delivery up to 10 GHz and beyond.
Sample Size / Integration	Plates/Wafers up to 125 mm (PCD); Substrates up to 10 mm (SCD/PCD)	Enables scaling from single-NV experiments to integrated arrays and commercial devices utilizing large-format diamond substrates.
Precise Sensor Placement	High-Precision Laser Cutting & Shaping	Custom laser cutting services allow researchers to obtain diamond chips and substrates with unique orientations and dimensions necessary for precise alignment in complex cryo-optical systems.

Engineering Support

Reaching the performance metrics demonstrated (70 µHz resolution, SNR > 10⁴) requires meticulous material selection and integration.

MPCVD Expertise: 6CCVD’s in-house PhD team offers consultation on optimizing MPCVD growth parameters (e.g., controlling background nitrogen impurities, achieving specific crystal orientations) to maximize $T_2^*$ for high-resolution magnetic resonance spectroscopy (NMR/ESR) and solid-state quantum simulation projects.
Implantation Support: We can advise on optimal substrate preparation and post-processing treatments (like the 850 °C annealing used here) necessary to maximize the yield and fidelity of near-surface implanted NV centers.
Global Logistics: We ensure reliable global shipping (DDU default, DDP available) for time-critical research projects worldwide.

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

View Original Abstract

Enhancing quantum sensing The quantum properties of the nitrogen vacancy (NV) defect in diamond can be used as an atomic compass needle that is sensitive to tiny variations in magnetic field. Schmitt et al. and Boss et al. successfully enhanced this sensitivity by several orders of magnitude (see the Perspective by Jordan). They applied a sequence of pulses to the NV center, the timing of which was set by and compared with a highly stable oscillator. This allowed them to measure the frequency of an oscillating magnetic field (megahertz bandwidth) with submillihertz resolution. Such enhanced precision measurement could be applied, for example, to improve nuclear magnetic resonance-based imaging protocols of single molecules. Science , this issue p. 832 , p. 837 ; see also p. 802

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Original Source

DOI: https://doi.org/10.1126/science.aam7009