Cooling a mechanical resonator to the quantum regime by heating it

At a Glance

Metadata	Details
Publication Date	2016-11-18
Journal	Physical review. A/Physical review, A
Authors	Yue Ma, Zhang‐qi Yin, Pu Huang, W. L. Yang, Jiangfeng Du
Institutions	Chinese Academy of Sciences, Tsinghua University
Citations	24
Analysis	Full AI Review Included

Technical Documentation & Analysis: Quantum Regime Cooling in Diamond Resonators

This documentation analyzes the key material requirements and experimental methodologies described in the paper “Cooling a Mechanical Resonator to Quantum Regime by heating it” and connects them directly to 6CCVD’s advanced CVD diamond capabilities.

Executive Summary

This research demonstrates a novel and counter-intuitive method for cooling a diamond mechanical resonator to the quantum regime by leveraging a thermal bath (heating). The core requirements for replicating and extending this work rely entirely on ultra-high quality MPCVD Single Crystal Diamond (SCD) material, which 6CCVD specializes in.

Core Achievement: Demonstrated quantum regime cooling (average phonon number < 1) of a higher-frequency mechanical mode ($\omega_b$) by driving a lower-frequency mode ($\omega_a$) with a hot thermal bath.
Material Criticality: The experiment utilizes a nano-diamond cantilever resonator containing an electron spin Nitrogen-Vacancy (NV) center, requiring high-purity, defect-controlled Single Crystal Diamond.
Key Requirement: Achievement of ultra-high mechanical Quality Factors (Q factors up to 10⁷) to ensure intrinsic decay rates ($\gamma$) are low (approx. 2π × 1 Hz).
Coupling Mechanism: A second-order magnetic gradient ($G_2$) is used to induce coupling between the two mechanical modes and the NV center spin.
Feasibility Confirmation: The simulation confirms that ground state cooling is possible under current experimental conditions, specifically requiring the NV center decay rate ($\Gamma$) to be actively tuned (e.g., via laser initialization).
6CCVD Value: 6CCVD provides the necessary high-purity Single Crystal Diamond substrates and custom fabrication/polishing required for these high-coherence, nanoscale quantum devices.

Technical Specifications

The following critical parameters were extracted from the theoretical model and experimental feasibility discussion (Appendix A):

Parameter	Value	Unit	Context
Material Substrate	Single Crystal Diamond	N/A	Used for cantilever resonator
Estimated Resonator Size	3 x 0.05 x 0.05	µm	Ultra-thin nano-cantilever geometry
Mechanical Q Factor (Target)	10⁷	N/A	Required for low intrinsic decay
Cooled Mode Frequency ($\omega_b$/2π)	30	MHz	Higher frequency mode (mode b)
Heated Mode Frequency ($\omega_a$/2π)	10	MHz	Lower frequency mode (mode a)
Spin Split Frequency ($\omega_z$/2π)	~20	MHz	Tuned to match $\omega_b - \omega_a$
Mechanical Decay Rate ($\gamma_{a,b}$/2π)	1	Hz	Intrinsic loss rate
NV Center Decay Rate ($\Gamma$/2π)	Up to 120	Hz	Tuned via laser initialization for optimal cooling
Second-Order Magnetic Gradient ($G_2$)	5 x 10¹⁴	T ⋅ m^-2	Required maximum coupling strength
Cooling Result	Average Phonon Number < 1	N/A	Quantum regime achieved

Key Methodologies

The theoretical scheme and experimental feasibility rely on precise control over material structure, external fields, and energy dissipation:

Material Construction: Fabrication of a thin diamond cantilever resonator (estimated 3 µm x 50 nm cross-section) with a single Nitrogen-Vacancy (NV) center located at the end.
Spin-Mechanical Coupling: Application of a static external magnetic field ($B_{ext}$) along the z-axis and two magnetic tips creating a second-order magnetic gradient ($G_2$) along the x-axis to couple the mechanical modes (a and b) with the NV center spin states (|-1> and |0>).
Frequency Matching: Tuning the magnetic field such that the NV center energy split ($\omega_z$) matches the difference between the two mechanical mode frequencies ($\Delta = \omega_b - \omega_a$).
NV Spin Initialization: Continuous laser initialization of the NV center electron spin to the ground state, causing the NV center to act as an effective vacuum bath for mode b.
Thermal Drive: Application of an incoherent driving (thermal bath) on the lower frequency mode ($\omega_a$), increasing its average phonon number ($\bar{n}_a$).
Observed Effect: Increased thermal input into mode $\omega_a$ paradoxically leads to significant cooling (lower phonon number $\bar{n}_b$) of the higher frequency mode $\omega_b$, demonstrating the heat-engine mechanism.

6CCVD Solutions & Capabilities

The demanding material requirements—ultra-low loss, high Q factor, precise geometry, and controlled defect hosting—are perfectly aligned with 6CCVD’s expertise in specialized MPCVD diamond.

Applicable Materials

To replicate and extend this quantum phononics research, the highest grade material is mandatory:

Optical Grade Single Crystal Diamond (SCD): Required for achieving the mechanical quality factors (Q > 10⁷) and low intrinsic loss rates (2π × 1 Hz) necessary for quantum coherence. Our SCD plates offer extreme purity, essential for hosting high-coherence, long-lifetime NV centers utilized in this scheme.
Custom SCD Substrates: The research requires the fabrication of a micro/nano-scale cantilever. 6CCVD supplies SCD material optimized for subsequent processing (e.g., etching or focused ion beam milling) into the required high-aspect-ratio structures.

Customization Potential

The experimental feasibility hinges on creating microstructures from bulk diamond. 6CCVD’s manufacturing capabilities enable engineers to meet these stringent dimensional requirements:

Custom Dimensions: While the cantilever is nanoscale (3 µm), 6CCVD supplies SCD plates up to 500 µm thickness and inch-scale lateral dimensions from which these devices can be fabricated.
Precision Fabrication: We offer laser cutting and dicing services to provide pre-forms or custom-shaped substrates tailored for subsequent etching into high-Q cantilevers.
Polishing Standards: Our SCD surfaces can be polished to an ultra-smooth Ra < 1 nm, critical for minimizing scattering and surface defects that could reduce mechanical Q factor or NV center performance.

Engineering Support

Quantum information and sensing applications place unique demands on material selection and geometry.

Expert Consultation: 6CCVD’s in-house team of PhD material scientists and quantum engineers are available to assist clients with material selection for similar NV center-based hybrid quantum systems and Optomechanical/Phononic cooling projects.
Material Optimization: We assist in specifying SCD growth parameters (such as nitrogen incorporation levels and orientation) optimized for high-yield, high-coherence NV center creation via subsequent implantation or growth processes.
Global Logistics: We provide reliable global shipping options (DDU or DDP) ensuring timely delivery of sensitive quantum-grade materials worldwide.

Call to Action

To achieve high mechanical Q factors and the necessary NV spin coherence required for quantum regime cooling, choose 6CCVD’s specialized MPCVD Single Crystal Diamond. For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

We consider a mechanical resonator made of diamond, which contains a nitrogen-vacancy center (NV center) locating at the end of the oscillator. A second order magnetic gradient is applied and inducing coupling between mechanical modes and the NV center. By applying proper external magnetic field, the energy difference between NV center electron spin levels can be tuned to match the energy difference between two mechanical modes $a$ and $b$. A laser is used for continuously initializing the NV center electron spin. The mode $a$ with lower frequency is driven by a thermal bath. We find that the temperature of the mode $b$ is significantly cooled when the heating bath temperature is increased. We discuss the conditions that quantum regime cooling requires, and confirm the results by numerical simulation. Finally we give the intuitive physical explanation on this unusual effect.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.94.053836