Nuclear spin metrology with nitrogen vacancy center in diamond for axion dark matter detection

At a Glance

Metadata	Details
Publication Date	2025-04-29
Journal	Physical review. D/Physical review. D.
Authors	So Chigusa, M. Hazumi, Ernst David Herbschleb, Yuichiro Matsuzaki, Norikazu Mizuochi
Institutions	Lawrence Berkeley National Laboratory, Japan Aerospace Exploration Agency
Citations	2
Analysis	Full AI Review Included

Executive Summary

This research proposes a novel quantum metrology method utilizing the nuclear spin of Nitrogen-Vacancy (NV) centers in diamond to search for axion dark matter (DM).

Core Value Proposition: The method provides complementary sensitivity to axion-neutron (g_ann) and axion-proton (g_app) couplings, which are independent of the axion-electron coupling (g_aee) targeted by conventional electron-spin NV magnetometry.
Sensing Mechanism: Nuclear spin metrology (magnetometry) is employed, leveraging the long coherence time (T_2N) of the ¹⁴N nuclear spin (I=1) within the NV center.
Frequency Range: The Ramsey sequence protocol is sensitive to a broad, low-frequency range, potentially covering axion masses up to m_a/2π ≤ 200 Hz (m_a ≤ 4 x 10^-13 eV).
Sensitivity Scaling: Detection limits scale favorably with the total number of NV centers (N) and total observation time (t_obs), approaching N^-1/2t_obs^-1/2 for coherent signals.
Protocol Flexibility: Both broadband (Ramsey) and narrow-band (Hahn Echo, Dynamic Decoupling) protocols are analyzed, allowing optimization for different axion mass ranges and signal coherence times (τ_a).
Material Requirement: Achieving competitive sensitivity requires large ensembles, with optimistic projections utilizing N = 10²⁰ NV centers over a 1-year observation period.

Technical Specifications

Parameter	Value	Unit	Context
Electron Spin Zero-Field Splitting (Δ₀)	~2π x 2.87	GHz	NV electronic ground state
Nuclear Quadrupole Interaction (Q₀)	~-2π x 4.95	MHz	¹⁴N nuclear spin
Electron Gyromagnetic Ratio (γ_e)	~2π x 28	GHz/T	Standard magnetometry reference
Nuclear Gyromagnetic Ratio (γ_N)	~2π x 3.08	MHz/T	¹⁴N spin reference
Electron T₁ Relaxation (T_1e)	~6	ms	Room temperature
Nuclear T₁ Relaxation (T_1N)	~4	min	Room temperature
Electron T₂ Dephasing (T_2e)**	~1	µs	Room temperature, Ramsey limit
Nuclear T₂ Dephasing (T_2N)**	~7.25	ms	Room temperature, Ramsey limit
Hahn Echo T_2e	~100	µs	Room temperature
Cryogenic T_1e (≤50 K)	~100	s	Potential for enhanced coherence
Axion DM Velocity (v_a)	~10^-3	(unitless)	Virialized DM halo
Axion Coherence Time (τ_a)	~6.6 s x (10^-10 eV / m_a)	s	Time over which axion phase is stable
Target Frequency Range (Ramsey)	≤ 200	Hz	Corresponds to m_a ≤ 4 x 10^-13 eV
Optimistic NV Center Count (N)	10²⁰	(unitless)	Required for competitive limits
Required Diamond Samples (N=10²⁰)	~3 x 10⁹	(unitless)	1 mm side, 70 µm thick, 0.68% yield

Key Methodologies

The NV center metrology relies on precise quantum control sequences applied to the two-qubit system formed by the electron spin (S=1) and the ¹⁴N nuclear spin (I=1).

Spin Initialization:
- The electron spin is initialized to the S^z = 0 state using 532 nm green laser cooling.
- The nuclear spin is polarized (e.g., to the I^z = 0 state) using Controlled-NOT (CNOT) gates, transferring polarization from the electron spin.
DC Magnetometry (Ramsey Sequence):
- Used for detecting signals with angular frequency ε much less than 1/τ (where τ is the free precession time).
- Sequence: R_y^π/2 (rotation) - Free Precession (τ) - R_y^π/2 (rotation).
- Optimization: The free precession time τ is optimally set to τ ~ T_2N*/2 to maximize sensitivity while mitigating dephasing noise.
- Sensitivity: Provides frequency-independent sensitivity for axion masses where the observation time t_obs is less than the axion coherence time τ_a.
AC Magnetometry (Hahn Echo Sequence):
- Used for narrow-band detection of oscillating signals (ε ~ 2π/τ).
- Sequence: R_y^π/2 - Free Precession (τ/2) - R_y^π (pulse) - Free Precession (τ/2) - R_y^π/2.
- Noise Mitigation: The central R_y^π pulse cancels static magnetic noise effects, allowing the use of the longer T_2N coherence time.
- Optimization: Optimal τ is set to τ ~ T_2N/2.
Dynamic Decoupling (DD) Sequence:
- An extension of the Hahn Echo using a large number (N_π) of R_y^π pulses during free precession.
- Function: Further prolongs the effective coherence time T₂ and shifts the sensitivity peak to higher frequencies (N_ππ/τ). Generally less suitable for DM searches due to the unknown signal frequency.
Signal Readout:
- The nuclear spin state is mapped onto the electron spin state using a final CNOT gate.
- The electron spin state is read out via fluorescence measurement (S^z = 0 state yields higher fluorescence than S^z = ±1 states).
- The signal strength F is characterized by the relative phase factor acquired during free precession.

Commercial Applications

The underlying technology—high-fidelity quantum control and metrology using solid-state spin ensembles—is highly relevant to several emerging commercial sectors:

Quantum Sensing and Metrology: Development of ultra-sensitive magnetometers, particularly for low-frequency or DC fields, applicable in geological surveys, medical diagnostics (e.g., low-field MRI), and fundamental physics experiments.
Diamond Material Engineering: Demand for high-purity, high-concentration, and perfectly aligned NV center ensembles drives advancements in Chemical Vapor Deposition (CVD) diamond growth and nitrogen implantation techniques (e.g., ¹⁵N doping for specialized sensing).
Quantum Computing and Information Processing: The NV center serves as a robust solid-state qubit. Research into nuclear spin manipulation and long coherence times directly supports the development of quantum memory and quantum processors.
Nanoscale NMR/MRI: Using NV ensembles to perform Nuclear Magnetic Resonance (NMR) or Magnetic Resonance Imaging (MRI) on extremely small samples (e.g., single proteins or molecules) with high spatial resolution.
Cryogenic Technology: The demonstrated improvement in spin coherence times (T_1e, T_2N) at cryogenic temperatures motivates the integration of NV sensors into advanced low-temperature systems.

View Original Abstract

We present a method to directly detect the axion dark matter using nitrogen vacancy centers in diamonds. In particular, we use metrology leveraging the nuclear spin of nitrogen to detect axion-nucleus couplings. This is achieved through protocols designed for dark matter searches, which introduce a novel approach of quantum sensing techniques based on the nitrogen vacancy center. Although the coupling strength of the magnetic fields with nuclear spins is three orders of magnitude smaller than that with electron spins for conventional magnetometry, the axion interaction strength with nuclear spins is the same order of magnitude as that with electron spins. Furthermore, we can take advantage of the long coherence time by using the nuclear spins for the axion dark matter detection. Our method has the potential to be sensitive to a broad frequency range <a:math xmlns:a=“http://www.w3.org/1998/Math/MathML” display=“inline”><a:mrow><a:mo>≲</a:mo><a:mn>100</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mrow><a:mi>Hz</a:mi></a:mrow></a:mrow></a:math> corresponding to the axion mass <c:math xmlns:c=“http://www.w3.org/1998/Math/MathML” display=“inline”><c:mrow><c:msub><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>a</c:mi></c:mrow></c:msub><c:mo>≲</c:mo><c:mn>4</c:mn><c:mo>×</c:mo><c:msup><c:mrow><c:mn>10</c:mn></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>13</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>eV</c:mi></c:mrow></c:math>. We present the detection limit of our method for both the axion-neutron and the axion-proton couplings and discuss its significance in comparison with other proposed ideas. We also show that the sensitivities of the NV center sensor to various spin species will open up new directions for constructing protocols that can mitigate magnetic noise effects.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevd.111.075028