Cross-relaxation studies with optically detected magnetic resonances in nitrogen-vacancy centers in diamond in external magnetic field

At a Glance

Metadata	Details
Publication Date	2021-04-09
Journal	Physical review. B./Physical review. B
Authors	Reinis Lazda, Laima Busaite, Andris Bērziņš, Jānis Šmits, F. Gahbauer
Institutions	GSI Helmholtz Centre for Heavy Ion Research, Helmholtz Institute Mainz
Citations	13
Analysis	Full AI Review Included

Executive Summary

This research utilizes continuous-wave (CW) Optically Detected Magnetic Resonance (ODMR) to analyze cross-relaxation (CR) dynamics between Nitrogen-Vacancy (NV^-) centers and substitutional nitrogen (P1 centers) in high-nitrogen diamond.

CR Mechanism Confirmation: Cross-relaxation was successfully measured via ODMR signal changes (contrast reduction and broadening), peaking sharply around an axial magnetic field of 51.2 mT, where NV and P1 energy level splittings coincide.
Simultaneous MW Coupling: A key finding is that the microwave (MW) radiation used to induce ODMR in the NV center simultaneously drives transitions in the P1 center via CR, significantly increasing the effective spin relaxation rate.
Signal Interpretation: The study provides a detailed analysis of CR resonance peaks, resolving transitions involving individual hyperfine components of the P1 center, which was not fully achieved in previous pulsed experiments.
Hyperfine Structure Importance: Accounting for the hyperfine structure and nuclear spin polarization of both NV and P1 centers was essential for accurately modeling the observed CR resonance positions and amplitudes.
Transition Classification: The CW ODMR method revealed high probabilities for transitions previously classified as “disallowed” in pulsed experiments, suggesting that continuous MW photons provide the necessary angular momentum balance.
Technological Relevance: The improved understanding of NV spin dynamics and CR pathways under external magnetic fields is critical for optimizing NV-diamond devices for quantum technologies, including q-bits, hyperpolarization, and field sensing.

Technical Specifications

Parameter	Value	Unit	Context
Diamond Type	HPHT	N/A	High-pressure, high-temperature synthesis.
Crystal Cut	(100)	N/A	Surface orientation.
Initial Nitrogen Conc.	~200	ppm	Concentration of ¹⁴N substitutional nitrogen (P1 centers).
NV Center Creation Dose	10¹⁸ e^-/cm²	N/A	Electron irradiation dose.
NV Center Creation Energy	10	MeV	Electron irradiation energy.
Annealing Temperature	750	°C	Annealing time was 3 hours.
Laser Wavelength	532	nm	Green laser used for optical initialization and readout.
Optical Fiber Core Diameter	400	µm	Used for both laser delivery and fluorescence collection.
NV Ground State ZFS (D_g)	2.87	GHz	Zero-field splitting of the ³A₂ ground state.
Primary CR Magnetic Field	~51.2	mT	Axial magnetic field where NV-P1 cross-relaxation peaks occur.
GSLAC Alignment Field	102.4	mT	Ground-State Level Anti-Crossing used for B-field alignment.
Low-Frequency MW Range	1.3 to 1.6	GHz	Corresponds to NV m_s=0 → m_s=-1 transition.
High-Frequency MW Range	4.1 to 4.6	GHz	Corresponds to NV m_s=0 → m_s=+1 transition.
P1 Hyperfine (A_14N\|\|)	113.98	MHz	Parallel component of P1 hyperfine interaction.
NV Hyperfine (A_NV\|\|)	-2.14	MHz	Parallel component of NV hyperfine interaction.

Key Methodologies

The experiment employed continuous-wave ODMR combined with precise magnetic field control and detailed spectral analysis:

Sample Preparation: A high-pressure, high-temperature (HPHT) diamond crystal with a (100) surface cut and an initial ¹⁴N concentration of 200 ppm was used.
NV Center Generation: NV centers were created by irradiating the crystal with 10 MeV electrons (dose 10¹⁸ e^-/cm²), followed by annealing at 750 °C for 3 hours.
Optical Setup: A 532 nm green laser was delivered via a 400 µm core optical fiber. Red fluorescence was collected through the same fiber, separated by a dichroic mirror, and measured.
Magnetic Field Alignment: The external magnetic field (B) was aligned axially along the NV center axis (z-axis) by monitoring the laser-induced fluorescence features, specifically the ground-state level anti-crossing (GSLAC) at 102.4 mT.
Microwave (MW) Application: MW radiation was delivered via a copper wire placed in close proximity (< 1 mm) to the diamond sample. Two frequency ranges were used to probe the two main NV transitions: 1.3-1.6 GHz (m_s=0 → m_s=-1) and 4.1-4.6 GHz (m_s=0 → m_s=+1).
ODMR Measurement: CW ODMR signals were measured by observing the decrease in red fluorescence intensity when the MW frequency was resonant with the NV spin transitions.
Data Analysis and Modeling: The contrast and width of the ODMR signals were extracted as a function of the external magnetic field. A rotating-frame Hamiltonian model, including electron and nuclear spins of both NV and P1 centers, was used to calculate the energy matching conditions and simulate the effects of simultaneous MW coupling.

Commercial Applications

The findings regarding controlled spin dynamics and cross-relaxation pathways are foundational for several quantum and sensing technologies:

Quantum Information Science (QIS):
- Development and implementation of robust solid-state q-bits using NV centers.
- Engineering quantum memory elements by controlling the coupling between NV electron spins and surrounding nuclear spin baths.
Nuclear Magnetic Resonance (NMR) Enhancement:
- Achieving efficient hyperpolarization of ¹³C nuclear spins in the diamond lattice or external molecules. This is crucial for enhancing the signal-to-noise ratio in NMR/MRI, particularly for studying large biological molecules.
High-Sensitivity Field Sensing:
- Optimization of NV-based magnetometers, electrometers, and thermometers. Understanding CR allows engineers to select operating magnetic fields that minimize relaxation losses, thereby maximizing sensor coherence time and sensitivity.
- Designing microwave-free magnetometry and nuclear magnetic resonance probes, which rely on intrinsic spin dynamics rather than external RF fields.
Defect Engineering and Material Science:
- Using NV centers as internal sensors to study the properties and dynamics of other point-like defects (like P1 centers) within the diamond crystal lattice.
- Developing strategies to mitigate detrimental cross-relaxation effects that limit the performance of NV-based quantum devices, especially in high-nitrogen concentration diamonds.

View Original Abstract

In this paper cross-relaxation between nitrogen-vacancy (NV) centers and substitutional nitrogen in a diamond crystal was studied. It was demonstrated that optically detected magnetic resonance signals (ODMR) can be used to measure these signals successfully. The ODMR were detected at axial magnetic field values around 51.2~~mT in a diamond sample with a relatively high (200~~ppm) nitrogen concentration. We observed transitions that involve magnetic sublevels that are split by the hyperfine interaction. Microwaves in the frequency ranges from 1.3 GHz to 1.6 GHz ($m_S=0\longrightarrow m_S=-1$ NV transitions) and from 4.1 to 4.6 GHz ($m_S=0\longrightarrow m_S=+1$ NV transitions) were used. To understand the cross-relaxation process in more detail and, as a result, reproduce measured signals more accurately, a model was developed that describes the microwave-initiated transitions between hyperfine levels of the NV center that are undergoing anti-crossing and are strongly mixed in the applied magnetic field. Additionally, we simulated the extent to which the microwave radiation used to induce ODMR in the NV center also induced transitions in the substitutional nitrogen via cross-relaxation. The improved understanding of the NV processes in the presence of a magnetic field will be useful for designing NV-diamond-based devices for a wide range of applications from implementation of q-bits to hyperpolarization of large molecules to various quantum technological applications such as field sensors.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.103.134104