Solid-state electron spin lifetime limited by phononic vacuum modes

At a Glance

Metadata	Details
Publication Date	2017-06-29
Journal	arXiv (Cornell University)
Authors	Thomas Astner, Johannes Gugler, Johannes Majer, P. Mohn, Jörg Schmiedmayer
Citations	1
Analysis	Full AI Review Included

6CCVD Technical Analysis: Solid-State Electron Spin Lifetime in Diamond NV^- Centers

Executive Summary

This documentation analyzes a core research paper detailing ultra-long longitudinal electron spin relaxation times (T₁) in diamond Nitrogen-Vacancy (NV^-) centers, highlighting the critical role of material quality for quantum applications.

Record Spin Lifetime: Demonstrated extremely long T₁ relaxation times, reaching up to 8 hours at ultra-low temperatures (T < 400 mK), crucial for high-fidelity quantum memory.
Fundamental Limit Identified: The T₁ limit in the quantum regime (T << ħw_s/k_B) is governed solely by the spontaneous emission of phonons into the phononic vacuum, validating the use of diamond as an exceptionally quiet quantum host.
Material Quality is Paramount: The research established that the spin relaxation rate (Γ) depends strongly on lattice damage (created during irradiation/vacancy creation) and is largely independent of the NV^- concentration (10 ppm to 40 ppm).
Optimal Sample Preparation: Samples prepared using optimized low-energy electron irradiation and high-temperature annealing (800 °C to 1000 °C) achieved relaxation rates matching theoretical ab initio predictions, confirming the necessity of high structural integrity.
Methodology: Spin state monitored via cavity frequency shift (χ) using a high-Q (60000) 3D superconducting microwave resonator (w_c/2π = 3.04 GHz) in an adiabatic demagnetization refrigerator (ADR).
6CCVD Value Proposition: The requirement for high-purity, low-strain material is perfectly met by 6CCVD’s specialized Microwave Plasma Chemical Vapor Deposition (MPCVD) Single Crystal Diamond (SCD), offering a superior starting substrate for NV creation.

Technical Specifications

The following hard data points define the parameters and achievements extracted from the research on NV^- diamond spin relaxation.

Parameter	Value	Unit	Context
Maximum Longitudinal Relaxation Time (T₁)	~8	hours	Observed in optimized low-damage samples (E1, E2)
Lowest Relaxation Rate (Γ₀)	3.14 x 10^-5	s^-1	Baseline rate determined by spontaneous phonon emission
NV^- Zero-Field Splitting (D/h)	2.88	GHz	NV^- ground state spin triplet
Resonator Fundamental Frequency (w_c/2π)	3.04	GHz	3D Lumped Element Aluminum Cavity
Resonator Quality Factor (Q)	60000	Dimensionless	High-Q factor for dispersive spin readout
Operating Temperature Range	50 - 400	mK	Cryogenic regime maintained by ADR/Dilution Refrigerator
Irradiation Energy (Electron)	2.0 or 6.5	MeV	Used for controlled vacancy creation
Irradiation Dose (Electron, E1 Sample)	1.1 x 10¹⁹	cm^-2	Highest dose used for high-purity optimization
Annealing Temperature (E1, E2)	1000	°C	Maximum temperature used for lattice recovery
Initial Nitrogen Concentration ([N]_initial)	50 to 200	ppm	Type-Ib HPHT starting material concentration

Key Methodologies

The experiment utilized highly controlled material processing and state-of-the-art cryogenic microwave techniques to achieve and measure the spin-lattice relaxation.

Diamond Source Material: Used Type-Ib high-pressure, high-temperature (HPHT) diamond samples with natural ¹³C abundance and varying initial nitrogen concentrations (50 ppm to < 200 ppm).
Vacancy Creation: Samples were irradiated using either neutrons (0.1-2.5 MeV, high lattice damage) or high-energy electrons (2 MeV or 6.5 MeV, lower lattice damage) to create vacancies necessary for NV^- formation.
NV Activation & Damage Mitigation: Samples were subsequently annealed at high temperatures (750 °C to 1000 °C) to mobilize vacancies, form NV centers, and partially repair lattice damage. Optimal results (E1, E2) were achieved with annealing at 1000 °C.
Microwave Resonator Fabrication: A 3D lumped element superconducting cavity was machined from EN AW 6066 aluminum and polished to a roughness of ≈ 0.25 µm.
Thermal Coupling: Diamond samples were bonded into the resonator structure using vacuum grease to ensure excellent thermal contact, critical for temperature regulation at mK levels.
Cryogenic Operation: The system was mounted in an Adiabatic Demagnetization Refrigerator (ADR) for precise temperature regulation (50 mK to 400 mK). Lower temperature data (< 50 mK) utilized a standard dilution refrigerator.
Relaxation Measurement (T₁): The spin ensemble was initialized in a high-temperature thermal steady state (2.7 K), then non-adiabatically switched to the target temperature. The time evolution of the spin state was monitored by measuring the shift (χ) of the resonator frequency using a Vector Network Analyzer (VNA).
Theoretical Modeling: Density Functional Theory (DFT) calculations using VASP/PHONOPY/WANNIER90 packages were performed on a 64-site supercell to derive the ab initio relaxation rate (Γ₀) caused by the electronic response to ionic motion.

6CCVD Solutions & Capabilities

This research confirms that minimizing lattice damage is the primary path toward achieving and leveraging diamond’s intrinsic quantum properties. 6CCVD is uniquely positioned to supply the foundational materials and engineering support required to replicate and advance this work.

Applicable Materials

The study highlights that crystal purity and low structural damage are more important than initial nitrogen or final NV concentration for achieving long T₁. 6CCVD’s MPCVD Single Crystal Diamond (SCD) provides the ideal platform for next-generation quantum studies.

Research Requirement	6CCVD Solution	Advantage for Qubit Research
Ultra-low lattice damage (post-irradiation)	Optical Grade SCD (High Purity)	MPCVD growth offers significantly lower intrinsic strain and defect density than HPHT, minimizing required damage remediation during annealing.
Nitrogen Control	Doping Specification (N or ¹⁵N)	Allows researchers precise control over the initial nitrogen concentration, facilitating highly consistent NV^- center ensembles.
Tailored Spin Environments	Boron-Doped Diamond (BDD)	For experiments requiring conductive layers or specific surface electronic properties not detailed here, 6CCVD offers BDD thin films (SCD or PCD).

Customization Potential for Quantum Devices

The experiment required precise handling of milligram-sized crystals and integration into a sophisticated superconducting circuit. 6CCVD’s in-house engineering and manufacturing services directly support these customization needs.

Custom Dimensions & Geometry: The samples used were small (10-45 mg). 6CCVD provides precision laser cutting and shaping to produce plates, chips, or wafers in custom sizes necessary for precise integration into 3D microwave resonators or cryogenic setups, offering plates/wafers up to 125mm (PCD).
Thickness Control: We offer precise thickness control for SCD and PCD films from 0.1 µm up to 500 µm, ensuring optimal interaction depth with the resonator’s electromagnetic field. Substrates up to 10 mm are available.
Metalization Services: While the resonator itself was aluminum, integrating contacts or specialized surface structures often requires thin-film deposition. 6CCVD provides custom internal metalization (Au, Pt, Pd, Ti, W, Cu) essential for creating superconducting contacts or integrated circuit elements on the diamond surface.
Surface Preparation: Maintaining low surface roughness is key for consistent spin physics. 6CCVD guarantees ultra-smooth polishing down to Ra < 1 nm (SCD) and Ra < 5 nm (Inch-size PCD), minimizing surface defects that can degrade qubit performance.

Engineering Support & Global Logistics

The complexity of NV center research, involving precise irradiation/annealing recipes, requires deep material understanding.

Engineering Support: 6CCVD’s in-house PhD team can assist researchers in selecting the appropriate SCD grade, optimizing orientation (e.g., standard <100> or <111>), and advising on material specifications needed for post-processing steps (like electron or neutron irradiation) necessary to maximize the T₁ coherence time in similar solid-state quantum memory projects.
Global Shipping: We facilitate research worldwide, offering Global Shipping with DDU (Delivery Duty Unpaid) as the default option, and DDP (Delivery Duty Paid) available upon request, ensuring fast and reliable delivery of time-critical materials.

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

View Original Abstract

Longitudinal relaxation is the process by which an excited spin ensemble decays into its thermal equilibrium with the environment. In solid-state spin systems relaxation into the phonon bath usually dominates over the coupling to the electromagnetic vacuum. In the quantum limit the spin lifetime is determined by phononic vacuum fluctuations. However, this limit was not observed in previous studies due to thermal phonon contributions or phonon-bottleneck processes. Here we use a dispersive detection scheme based on cavity quantum electrodynamics (cQED) to observe this quantum limit of spin relaxation of the negatively charged nitrogen vacancy ($\mathrm{NV}^-$) centre in diamond. Diamond possesses high thermal conductivity even at low temperatures, which eliminates phonon-bottleneck processes. We observe exceptionally long longitudinal relaxation times $T_1$ of up to 8h. To understand the fundamental mechanism of spin-phonon coupling in this system we develop a theoretical model and calculate the relaxation time ab initio. The calculations confirm that the low phononic density of states at the $\mathrm{NV}^-$ transition frequency enables the spin polarization to survive over macroscopic timescales.

Tech Support

Original Source

DOI: https://doi.org/10.48550/arxiv.1706.09798