Hybrid quantum magnetic-field sensor with an electron spin and a nuclear spin in diamond

At a Glance

Metadata	Details
Publication Date	2016-11-22
Journal	Physical review. A/Physical review, A
Authors	Yuichiro Matsuzaki, Takaaki Shimo-Oka, Hirotaka Tanaka, Y. Tokura, Kouichi Semba
Institutions	Kyoto University Institute for Chemical Research, Japan Science and Technology Agency
Citations	22
Analysis	Full AI Review Included

Hybrid Quantum Magnetic Field Sensor: Material Analysis & Engineering Solutions

This document analyzes the technical requirements and achievements of the research paper “Hybrid quantum magnetic field sensor with an electron spin and a nuclear spin in diamond” and outlines how 6CCVD’s specialized MPCVD diamond capabilities can facilitate and extend this research.

Executive Summary

The paper proposes an advanced NV-center based magnetometer utilizing a hybrid electron-nuclear spin system to overcome the primary limitation of conventional sensors: the short coherence time ($T_{2e}$) of the electron spin.

Core Achievement: Demonstrated theoretical pathway for constructing a magnetic field sensor with sensitivity enhanced by a factor of $\sqrt{N}$ (where N is the number of transfers) compared to single-electron spin sensors.
Mechanism: The long-lived nuclear spin (coherence time $T_{2n} > 1$ second at RT) acts as a quantum memory, storing phase information acquired repeatedly from the electron spin via hyperfine coupling.
Methodology: Implementation requires precise quantum operations including C-NOT and SWAP gates, facilitated by microwave control and optical readout.
Material Demand: Requires high-purity, stable diamond substrates containing isolated Nitrogen-Vacancy (NV) centers coupled to specific nuclear spins (e.g., ¹³C, ¹⁴N, or ¹⁵N).
Fidelity Requirement: Enhancement is realized only under low-frequency, non-Markovian noise conditions; high-fidelity gates are crucial, requiring error rates ($\epsilon$) below 7.5%, with optimal gain achieved below 0.1%.
6CCVD Value: The success of this hybrid sensor is fundamentally dependent on ultra-high-quality Single Crystal Diamond (SCD) with controlled isotope enrichment, a core specialization of 6CCVD.

Technical Specifications

The following hard data points define the performance metrics and operational parameters of the proposed hybrid sensor scheme:

Parameter	Value	Unit	Context
Electron Spin ($S$)	1	Unitless	NV center triplet ground state (
Nuclear Spin Coherence Time ($T_{2n}$)	> 1	second	Achieved at Room Temperature (RT); utilized for quantum memory
Environment Correlation Time ($\tau_c$)	$\sim 25$	µs	Waiting time ($T_W$) between measurement cycles must be > $\tau_c$
Target Magnetic Field Uncertainty (Conventional)	$\propto 1 / \sqrt{M T_{2e}}$	Quantity	Limited by electron spin dephasing time ($T_{2e}$)
Target Magnetic Field Uncertainty (Hybrid)	$\propto 1 / \sqrt{M N T_{2e}}$	Quantity	Reduced by the number of phase transfers ($N$)
Required Gate Error ($\epsilon$)	< 7.5	%	Minimum threshold to demonstrate sensitivity improvement over conventional sensor
Optimal Gate Error ($\epsilon$)	< 0.1	%	Achieves sensitivity ratio ($r$) of approximately 10x (order of magnitude)
Total Quantum Gates per Cycle	$2N + 1$	Gates	$2N$ C-NOT gates and 1 SWAP gate

Key Methodologies

The following ordered steps outline the quantum recipe required for hybrid field detection, leveraging the inherent properties of the NV center and adjacent nuclear spin.

State Preparation: The electron spin ($|e\rangle$) and nuclear spin ($|n\rangle$) are initialized. The nuclear spin is placed into a superposition state: $\frac{1}{\sqrt{2}}(|0\rangle_n + |1\rangle_n)$.
Entanglement (C-NOT Gate 1): A C-NOT gate is performed (electron is target, nuclear is control) to create an entangled state $\frac{1}{\sqrt{2}}(|0\rangle_e |0\rangle_n + |1\rangle_e |1\rangle_n)$.
Phase Accumulation (Free Evolution): The system evolves under the target magnetic field $B$ for a time $t = k T_{2e}$. The phase $\omega t$ accumulates exclusively on the $|1\rangle_e$ component of the electron spin, as this state is sensitive to the magnetic field.
Phase Transfer (C-NOT Gate 2): A second C-NOT gate is performed. This transfers the phase information accumulated by the short-lived electron spin onto the long-lived nuclear spin, resulting in the separable state $|0\rangle_e \otimes \frac{1}{\sqrt{2}}(|0\rangle_n + e^{-i\omega t} |1\rangle_n)$.
Repetition: Steps 2 through 4 are repeated $N$ times consecutively, leveraging the nuclear spin’s stability to accumulate a total phase $\theta = N \omega T_{2e}$. This constitutes the quantum Zeno effect application, suppressing decoherence propagation.
Readout Preparation: A SWAP gate is executed to transfer the accumulated phase information back from the nuclear spin onto the electron spin.
Detection: Standard optical fluorescence measurement (using laser and photon detector) is performed on the electron spin, which is coupled to the nuclear spin phase, to determine the accumulated phase $\theta$ and, consequently, the magnetic field $\omega$.

6CCVD Solutions & Capabilities

6CCVD provides the foundational high-coherence diamond materials and essential fabrication services required to realize and advance this hybrid quantum sensing architecture.

Requirement/Challenge	6CCVD Material/Capability	Engineering Value Proposition
High Crystal Quality & Long $T_{2e}$	Optical Grade Single Crystal Diamond (SCD) Wafers: Extremely low defect density, grown via proprietary MPCVD processes, ensuring optimal $T_{2}$ performance necessary for effective phase accumulation.	Maximizes the inherent electron spin coherence time ($T_{2e}$), enhancing the initial phase fidelity before transfer to the nuclear spin. Polishing available down to $R_a < 1$ nm.
Nuclear Spin Isolation/Coupling	Isotope-Enriched Diamond Substrates: Custom growth using gas precursors enriched with ¹²C (to minimize background ¹³C) or enriched with ¹⁵N (to maximize target nuclear spin interaction).	Provides precision control over the quantum register environment (NV center + specific nuclear spin), crucial for stabilizing the hyperfine coupling and maximizing $T_{2n}$.
Quantum Gate Implementation	Custom Metalization Services (Ti/Pt/Au, W, Cu): Internal capability to deposit multi-layer thin films necessary for constructing high-frequency microwave transmission lines (striplines/antennas) directly on the diamond surface.	Ensures low-loss delivery of control pulses (C-NOT, SWAP, Rabi oscillations) with the stability and precision required to achieve gate errors $\epsilon < 0.1%$.
Sensor Integration & Miniaturization	Custom Dimensions and Processing: Capability to fabricate wafers up to 125 mm, and to laser cut, thin, or dice substrates down to custom geometries for AFM-tip integration or hybrid chip integration.	Provides flexible dimensions and mechanical stability for advanced quantum platform integration, supporting both bulk and nanophotonic structures.
Material Optimization	In-House PhD Engineering Support: Our team assists in tailoring MPCVD growth recipes (temperature, pressure, gas flows, post-growth annealing) specifically for maximizing NV center yield and optimizing the $NV^-$ charge state stability.	Accelerates R&D cycles and ensures the material specifications meet the stringent coherence and reproducibility standards required for quantum metrology projects.

Engineering Support & Call to Action

The realization of the proposed $\sqrt{N}$ sensitivity enhancement relies critically on the underlying diamond substrate’s quality and the ability to fabricate high-fidelity control gates. 6CCVD is an industry leader in engineering high-purity, isotopically tailored MPCVD diamond solutions for quantum sensing and memory applications. Our technical expertise ensures your research can move beyond theoretical models to high-performance demonstrators.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We offer global DDU shipping (DDP available upon request).

View Original Abstract

Recently, magnetic field sensors based on an electron spin of a nitrogen\nvacancy (NV) center in diamond have been studied both from an experimental and\ntheoretical point of view. This system provides a nanoscale magnetometer, and\nit is possible to detect a precession of a single spin. In this paper, we\npropose a sensor consisting of an electron spin and a nuclear spin in diamond.\nAlthough the electron spin has a reasonable interaction strength with magnetic\nfield, the coherence time of the spin is relatively short. On the other hand,\nthe nuclear spin has a longer life time while the spin has a negligible\ninteraction with magnetic fields. We show that, through the combination of such\ntwo different spins via the hyperfine interaction, it is possible to construct\na magnetic field sensor with the sensitivity far beyond that of previous\nsensors using just a single electron spin.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.94.052330