Torsional cooling of a nanodiamond via the interaction with the electron spin of the embedded nitrogen-vacancy center

At a Glance

Metadata	Details
Publication Date	2018-10-09
Journal	Physical review. A/Physical review, A
Authors	Li Ge, Nan Zhao
Institutions	Hangzhou Dianzi University, Beijing Computational Science Research Center
Citations	10
Analysis	Full AI Review Included

6CCVD Technical Analysis: Diamond NV-Center Spin-Rotation Cooling

This document analyzes the theoretical framework presented in the paper, Cooling of the rotation of a nanodiamond via the interaction with the electron spin of the contained NV-center, and connects its core material requirements to 6CCVD’s advanced MPCVD diamond capabilities.

Executive Summary

The research outlines a novel theoretical scheme for cooling the rotational degrees of freedom of a levitated nanodiamond containing a Nitrogen-Vacancy (NV) center, demonstrating a path to reaching the quantum ground state.

Core Mechanism: Achieves mechanical rotation cooling via spin-rotation coupling. The NV-center electron spin, modulated by external static ($B_0$) and oscillating ($B_1$) fields, dissipates rotational energy through optical pumping.
Target Application: Ultrasensitive torque balance, quantum information processing, and fundamental studies of quantum-classical boundaries.
Critical Material: High-purity nanodiamonds housing a single, isolated NV-center with stable spin coherence properties.
Cooling Achievement: Theoretical calculation demonstrates the feasibility of reaching temperatures as low as $T_f \approx 0.6 \times 10^{-4}\text{K}$, achieving the quantum regime defined by $\hbar\omega_0/k_B$.
Methodology: Requires precise external field control, including a $532\text{nm}$ laser for optical pumping and carefully selected static magnetic fields ($B_0$) positioned $45^\circ$ from the X-axis, ensuring the friction force is positive.
6CCVD Value Proposition: 6CCVD specializes in the high-purity Single Crystal Diamond (SCD) necessary for producing large, high-quality NV precursors, enabling controlled creation and implantation of color centers required for scaling this quantum technology.

Technical Specifications

The following parameters define the setup and performance targets for the nanodiamond rotation cooling scheme:

Parameter	Value	Unit	Context
Material Shape	Spheroid	N/A	Levitation geometry for optical trapping
Semi-Major Axis ($a$)	40	nm	Nanoparticle dimension
Semi-Minor Axis ($b$)	20	nm	Nanoparticle dimension
Dielectric Constant ($\varepsilon_r$)	5.7	N/A	Standard CVD Diamond
Trap Laser Power ($P$)	100	mW	Optical Tweezer power
Trap Waist ($\pi w^2$)	2	µm²	Focus area of the optical tweezer
Initial Trap Temperature ($T_0$)	~400	K	Baseline temperature confinement
NV Zero-Field Splitting ($D$)	2.87	GHz	Energy difference between $
Optical Pumping Wavelength	532	nm	Required wavelength for spin initialization/pumping
Target Static Field ($\gamma B_0$)	$2\pi \times 100$	MHz	Modulates NV energy levels upon rotation
Microwave Field ($\gamma B_1$)	$2\pi \times 1$	MHz	Induces transitions between $
Damping Timescale ($\tau$)	$2.8 \times 10^{-4}$	s	Time required to dissipate rotational energy
Achieved Cooling Temperature ($T_f$)	$~0.6 \times 10^{-4}$	K	Lowest theoretical temperature reached
Quantum Regime Temperature ($\hbar\omega_0/k_B$)	$~10^{-4}$	K	Order of magnitude required for ground state rotation

Key Methodologies

The theoretical scheme requires a complex integration of optical trapping, magnetic field modulation, and quantum state control, analogous to atomic laser cooling:

Optical Trapping: A diamond nanoparticle (spheroid, $a=40\text{nm}, b=20\text{nm}$) containing a single NV-center is levitated and confined using a linearly polarized optical tweezer (e.g., $P=100\text{mW}$ laser focused to $2\mu\text{m}^2$).
NV Spin Modulation (Static Field): A static magnetic field ($B_0$) is applied, strategically placed (e.g., $45^\circ$ angle to the X axis). The rotation of the nanodiamond causes the NV-center spin to experience a varying external field, coupling mechanical motion to the spin state (spin-rotation coupling).
Optical Pumping (Dissipation): A $532\text{nm}$ laser beam optically pumps electrons from higher energy levels ($| \pm 1\rangle$ spin sublevels) in the ground state (GS) configuration to the $m_s = 0$ state, dissipating the rotational energy through spontaneous emission.
Microwave Field Application: An oscillating microwave field ($B_1$) is required to induce transitions between the $|0\rangle$ and $| \pm 1\rangle$ states, preventing all electrons from accumulating in the field-insensitive $|0\rangle$ state, thereby sustaining the cooling cycle.
Parameter Optimization: The microwave frequency ($\omega$) and static magnetic field ($B_0$) must be chosen such that the effective energy level split ($\delta_+$) remains positive throughout the confined rotation range, ensuring the force exerted on the nanodiamond is always frictional.

6CCVD Solutions & Capabilities

This research validates the use of NV-center diamond as a foundational material for high-precision quantum optomechanics and ultrasensitive sensing. 6CCVD is positioned to supply the advanced diamond platforms required to realize and scale these experiments.

Applicable Materials

The foundation of this research is a highly coherent, stable NV-center within the diamond matrix. Replicating or extending this work necessitates extremely high-purity precursor material for precise NV creation (via controlled nitrogen incorporation or subsequent ion implantation).

Research Requirement	Recommended 6CCVD Material	Key Advantage
High Spin Coherence	Optical Grade SCD (Single Crystal Diamond)	Extremely low nitrogen and substitutional defect concentration, crucial for maximum NV coherence time ($T_2^*$) necessary for quantum manipulation.
Scalable Substrates	SCD Plates (up to 125mm)	Provides large area platforms for developing integrated arrays of levitation traps or microwave delivery structures on-chip, moving beyond single-nanoparticle experiments.
Electrode Integration	Boron-Doped Diamond (BDD)	If electrical fields or on-chip microwave delivery is required, BDD can be fabricated adjacent to the SCD cooling zone for integrated electronic functionality.
Custom Nanostructuring	SCD or PCD Layers (0.1µm to 500µm)	Allows researchers to define thin, high-quality diamond layers suitable for subsequent lift-off, etching, and milling processes to create the required nanodiamond spheroids or dielectric waveguides.

Customization Potential

The experimental setup demands precise control over material geometry and integration with external electronics. 6CCVD provides end-to-end customization services for quantum applications:

Precision Thickness Control: We provide SCD and PCD plates with thickness tolerances tailored for lift-off and nanostructure fabrication, ranging from $0.1\mu\text{m}$ films up to $500\mu\text{m}$ thick substrates.
Custom Wafer Dimensions: While the paper uses nanodiamonds, the manufacturing base requires large, high-quality diamond wafers. 6CCVD offers custom plates and wafers up to $125\text{mm}$ in diameter.
Integrated Metalization: If future iterations require on-chip microwave delivery (replacing the external $B_1$ field) or anchoring the nanodiamond to a larger system, 6CCVD offers internal thin-film metalization services, including Au, Pt, Pd, Ti, W, and Cu deposition.
Ultra-Smooth Polishing: Our high-quality SCD surfaces (Ra < 1nm) and inch-size PCD surfaces (Ra < 5nm) minimize scattering losses, critical for efficient optical trapping and $532\text{nm}$ pumping applications described in the research.

Engineering Support

The convergence of quantum mechanics and mechanical motion requires specialized material knowledge. 6CCVD’s in-house PhD team provides expert consultation on:

NV Precursor Optimization: Assistance with selecting diamond growth recipes (pressure, temperature, gas mixture) to achieve optimal nitrogen incorporation control for desired NV density and spin characteristics.
Optomechanical Material Selection: Guidance on utilizing specific diamond types (e.g., highly pure SCD vs. high-strength PCD) for similar Levitated Optomechanics and Ultrasensitive Torque Sensing projects.
Custom Fabrication Pathways: Support for defining post-processing steps (laser cutting, etching) necessary to transform bulk 6CCVD diamond plates into the specialized nanostructures required for levitation experiments.

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

View Original Abstract

We propose a way to cool the rotation of a nanodiamond, which contains a NV-center and is levitated by an optical tweezer. Following the rotation of the particle, the NV-center electron spin experiences varying external fields and so leads to spin-rotation coupling. By optically pumping the electrons from a higher energy level to a lower level, the rotation energy is dissipated. We give the analytical result for the damping torque exerted on the nanodiamond, and evaluate the final cooling temperature by the fluctuation-dissipation theorem. It’s shown that the quantum regime of the rotation can be reached with our scheme.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.98.043415

References

2006 - Optical Trapping and Manipulation of Neutral Particles Using Lasers [Crossref]