Probabilistic magnetometry with a two-spin system in diamond

At a Glance

Metadata	Details
Publication Date	2021-04-29
Journal	Quantum Science and Technology
Authors	Raúl Coto, Hossein T. Dinani, Ariel Norambuena, Mo Chen, J. R. Maze
Institutions	Massachusetts Institute of Technology, Universidad Mayor
Citations	5
Analysis	Full AI Review Included

Technical Documentation & Analysis: Probabilistic Magnetometry in Diamond

Reference Paper: Coto et al., “Probabilistic magnetometry with two-spin system in diamond” (arXiv:2003.11925v3)

Executive Summary

This research proposes an advanced quantum metrology protocol utilizing the Nitrogen-Vacancy (NV) center in diamond coupled to a nearby nuclear spin (¹³C or ¹⁵N) to enhance DC magnetic field sensitivity.

Core Achievement: Demonstrated that a probabilistic, post-selection-based two-spin protocol significantly improves magnetic field sensitivity ($\Delta B$) compared to conventional Ramsey spectroscopy, particularly in regimes of short transverse relaxation times ($T_2^* \le 3$ µs).
Sensitivity Improvement: Achieved an estimated sensitivity of 43.5 nTHz^-1/2 at 4 K using a ¹³C meter, and showed a 28% improvement over Ramsey using the native ¹⁵N nuclear spin in the suboptimal $T_2^*$ regime.
Mechanism: The protocol leverages the hyperfine coupling between the NV electronic spin (system) and the nuclear spin (meter) to concentrate valuable sensing information into a single, successful post-selection measurement.
Material Requirement: Success relies critically on high-quality Single Crystal Diamond (SCD) hosting isolated NV centers and controllable nuclear spins (either native ¹⁵N or implanted/native ¹³C).
Application Range: The protocol is suitable for detecting weak magnetic fields in the µT range ($10^{-2}$ G to $10^0$ G) across both cryogenic (4 K) and room temperature environments.
6CCVD Value Proposition: 6CCVD provides the necessary ultra-high purity, isotopically engineered SCD substrates required to maximize $T_2^*$ coherence times and enable precise nuclear spin control for replicating and extending this cutting-edge quantum sensing research.

Technical Specifications

The following table summarizes the key performance metrics and material parameters extracted from the analysis, focusing on the optimal performance regimes.

Parameter	Value	Unit	Context
Cryogenic Sensitivity (¹³C)	43.5	nTHz^-1/2	Optimal $\tau = 1.3$ µs, $T_2^* = 2$ µs, $C=1$
Cryogenic Sensitivity (¹⁵N)	61.5	nTHz^-1/2	Non-ideal scenario ($C=0.707$), $T_2^* = 2$ µs
Room Temp. Sensitivity (¹⁵N)	1.5	µTHz^-1/2	High bias field ($B_z > 2000$ G), $t_p = 5$ ms, $t_r = 8$ ms
Sensitivity Improvement	28	%	Over Ramsey, using ¹⁵N at $T_2^* = 2$ µs
Optimal Interrogation Time ($\tau$)	1.3 to 2.2	µs	Short time regime where post-selection outperforms Ramsey
*Transverse Relaxation Time ($T_2^$)**	2	µs	Assumed for naturally occurring NV centers
Weak Magnetic Field Range ($B$)	10^-2 to 10⁰	G	Range where protocol is suitable
NV Zero-Field Splitting ($D/2\pi$)	2.87	GHz	NV electronic spin parameter
¹³C Hyperfine Coupling ($A_{zz}$)	500	kHz	Weakly coupled nuclear spin
¹⁵N Hyperfine Coupling ($A_{zz}$)	3.03	MHz	Native nuclear spin (stronger coupling, faster gates)

Key Methodologies

The probabilistic magnetometry protocol relies on precise quantum control of a bipartite system (NV electronic spin $S=1$ and nuclear spin $I=1/2$).

System Initialization: The bipartite system (NV + ¹³C/¹⁵N) is initialized to a specific state, typically $| \Psi_i \rangle = |0\rangle | \downarrow \rangle$. Efficient nuclear spin initialization is critical.
Pre-Selection Preparation: The nuclear spin (meter) is prepared in a coherent superposition state using a Radiofrequency (RF) field pulse ($\Omega_c$).
System Rotation: A strong Microwave (MW) pulse rotates the NV electronic spin (system) by an angle $\theta_i$, creating the pre-selected state $| \Psi_{pre} \rangle$.
Free Evolution (Sensing): The system evolves for an interrogation time $\tau$ under the external magnetic field $B$. This imprints the magnetic field information into the relative phase of the electronic spin.
Post-Selection: The NV electronic spin is post-selected onto a target state $| \Psi_f \rangle$. This process transfers the accumulated phase information onto the nuclear spin.
Readout: The nuclear spin state is read out. This step requires efficient single-shot readout, which is achieved either at cryogenic temperatures (4 K) or at room temperature using a high bias magnetic field ($B_z > 2000$ G) and repetitive readout protocols.
Decoherence Mitigation: The interrogation time $\tau$ is limited by the transverse relaxation time $T_2^$ of the NV electronic spin. The protocol demonstrates superior performance in the short $T_2^$ regime, where standard Ramsey sequences fail.

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the advanced diamond materials and fabrication services necessary to replicate and extend this high-sensitivity quantum magnetometry research.

Applicable Materials

The success of this protocol hinges on maximizing the NV electronic spin coherence time ($T_2^*$) and ensuring precise control over the coupled nuclear spins.

Research Requirement	6CCVD Material Solution	Technical Advantage
*High $T_2^$ Coherence**	Ultra-High Purity SCD (Isotopically Engineered)	SCD with < 1% ¹³C concentration minimizes spin bath noise, extending $T_2^*$ far beyond the 2 µs reported for natural abundance diamond. Essential for maximizing interrogation time $\tau$.
Controllable Nuclear Spins	Custom Doped SCD (e.g., ¹⁵N or Low ¹⁴N)	Precise control over nitrogen concentration (for NV creation) and isotopic purity (for ¹⁵N or ¹³C meter spins) is achieved through MPCVD growth and post-processing.
High Fidelity Readout	Optical Grade SCD Wafers	SCD with low strain and high optical transmission ensures efficient laser excitation and fluorescence collection required for high-fidelity single-shot NV readout at 4 K.
BDD Electrodes (Potential Extension)	Boron-Doped Diamond (BDD)	For integration into micro-electronic devices or creating on-chip RF/MW structures, 6CCVD offers BDD films with tunable conductivity.

Customization Potential

The implementation of this protocol requires specialized substrate preparation and integration of control elements. 6CCVD offers comprehensive services to meet these needs:

Custom Dimensions: We supply SCD plates and wafers in custom sizes, suitable for integration into cryogenic or high-vacuum setups, with dimensions up to 125mm (PCD) and SCD thicknesses from 0.1 µm to 500 µm.
Surface Quality: To minimize surface-related decoherence, 6CCVD guarantees ultra-smooth polishing, achieving Ra < 1 nm on Single Crystal Diamond (SCD) surfaces.
Metalization Services: The application of MW and RF pulses (required for spin manipulation and readout) necessitates on-chip control lines. 6CCVD offers in-house metalization capabilities, including Ti/Pt/Au, Pd, W, and Cu stacks, patterned to customer specifications for optimized Rabi frequency delivery.
Substrate Engineering: We provide SCD substrates up to 10 mm thick, ideal for high-power MW delivery and robust experimental setups.

Engineering Support

The successful implementation of probabilistic quantum metrology requires deep expertise in material science and quantum control.

6CCVD’s in-house PhD team specializes in optimizing diamond material properties for quantum applications. We can assist researchers with:

Material Selection: Consulting on the optimal isotopic purity and nitrogen concentration required to achieve target $T_2^*$ and $T_1$ coherence times for similar NV Magnetometry projects.
Decoherence Modeling: Providing guidance on how material defects (P1 centers, strain) impact the Markovian and non-Markovian noise models discussed in the paper (Appendix C).
Fabrication Integration: Supporting the design and fabrication of custom metalization patterns for efficient MW/RF delivery and high-fidelity single-shot readout.

Call to Action: For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).

View Original Abstract

Solid-state magnetometers like the Nitrogen-Vacancy center in diamond have\nbeen of paramount importance for the development of quantum sensing with\nnanoscale spatial resolution. The basic protocol is a Ramsey sequence, that\nimprints an external static magnetic field into phase of the quantum sensor,\nwhich is subsequently readout. In this work we show that the hyperfine coupling\nbetween the Nitrogen-Vacancy and a nearby Carbon-13 can be used to set a\npost-selection protocol that leads to an enhancement of the sensitivity under\nrealistic experimental conditions. We found that for an isotopically purified\nsample the detection of weak magnetic fields in the $\mu$T range can be\nachieved with a sensitivity of few nTHz$^{-1/2}$ at cryogenic temperature ($4$\nK), and $0.1$ $\mu$THz$^{-1/2}$ at room temperature.\n

Tech Support

Original Source

DOI: https://doi.org/10.1088/2058-9565/abfce1

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