Acoustic diamond resonators with ultrasmall mode volumes

At a Glance

Metadata	Details
Publication Date	2020-07-28
Journal	Physical Review Research
Authors	Mikołaj K. Schmidt, Christopher G. Poulton, M. J. Steel
Institutions	University of Technology Sydney, Macquarie University
Citations	11
Analysis	Full AI Review Included

Technical Analysis: Ultra-Small Mode Volume Acoustic Diamond Resonators

Source Paper: Schmidt, Poulton, and Steel, “Acoustic diamond resonators with ultra-small mode volumes” (arXiv:2003.01834v2)

Executive Summary

This research proposes a high-performance diamond acoustic cavity design for Quantum Acoustodynamics (QAD), demonstrating exceptional strain localization and coupling potential for solid-state quantum emitters.

Ultra-Small Mode Volume: Achieves effective acoustic mode volumes ($V_{eff,a}$) of approximately $10^{-4}\lambda^{3}$ by utilizing a non-resonant “acoustic lightning-rod effect” in a tapered bridge structure.
High Quality Factor: Calculations project an acoustic quality factor (Q) up to $10^{6}$, with a conservative operational estimate of $Q = 10^{5}$ at cryogenic temperatures (4 K).
GHz Operation: The Phononic Crystal Waveguide (PnCW) design creates a complete acoustic bandgap spanning 2.3 GHz to 3.2 GHz, enabling operation in the critical GHz frequency range.
High Cooperativity: The design supports high-cooperativity coupling between the acoustic mode and embedded Nitrogen-Vacancy (NV$^-$) centers, reaching $C_{E1} \approx 8$ for parametric coupling.
SiV Potential: Projected performance for Silicon-Vacancy (SiV) centers shows even higher potential cooperativity ($C_{SiV} \approx 110$ at 4 K), making this architecture highly versatile for quantum memory applications.
Material Requirement: The structure requires a high-purity, thin single-crystalline diamond (SCD) slab (0.5 µm thickness) fabricated using state-of-the-art lithography (features down to 50 nm).

Technical Specifications

The following hard data points were extracted from the analysis of the diamond PnCW cavity design and its coupling characteristics:

Parameter	Value	Unit	Context
Effective Mode Volume ($V_{eff,a}$)	10^-4	$\lambda^{3}$	Achieved via non-resonant strain localization
Acoustic Quality Factor (Q)	10⁵	Dimensionless	Conservative estimate for mechanical Q
Calculated Q Factor	10⁶	Dimensionless	Calculated for finite PnC (4 unit cells)
Operating Frequency ($\Omega_{\alpha}/2\pi$)	2.838	GHz	Tuned mode frequency (center of bandgap)
Bandgap Range	2.3 - 3.2	GHz	Complete acoustic bandgap
Diamond Slab Thickness (t)	0.5	µm	Required thickness for the PnCW structure
Minimum Feature Size (d)	50	nm	Required lithography precision for the bridge
Parametric Coupling ($g_{E1}/2\pi$)	5	MHz	Maximum calculated NV$^-$ coupling
Resonant Coupling ($g_{E2}/2\pi$)	1.5	MHz	Maximum calculated NV$^-$ coupling
Parametric Cooperativity ($C_{E1}$)	$\approx$ 8	Dimensionless	NV$^-$ at 4 K
Resonant Cooperativity ($C_{E2}$)	$\approx$ 0.7	Dimensionless	NV$^-$ at 4 K
Projected SiV Cooperativity ($C_{SiV}$)	$\approx$ 110	Dimensionless	SiV at 4 K (due to higher strain susceptibility)
Diamond Young’s Modulus (E)	1050	GPa	Isotropic approximation
Diamond Density ($\rho$)	3500	kg/m³	Isotropic approximation

Key Methodologies

The proposed acoustic resonator relies on a combination of Phononic Crystal Waveguide (PnCW) design and a novel strain localization mechanism, simulated using finite element methods.

Material Basis: Single-crystalline diamond (SCD) is used as the base material, approximated as an isotropic medium for initial calculations.
Structure Definition: A quasi-1D PnCW is designed in a thin SCD slab (0.5 µm thickness). The crystal orientation is specified as X || [110], Y || [110], Z || [001].
Bandgap Engineering: The PnCW unit cell geometry (defined by parameters A, B, R) is optimized to create a broad, complete acoustic bandgap between 2.3 GHz and 3.2 GHz, suppressing radiative phonon dissipation.
Strain Localization Defect: A tapered bridge structure is introduced as the central cavity defect. This geometry implements a non-resonant “acoustic lightning-rod effect,” concentrating strain energy into a deeply sub-wavelength volume ($V_{eff,a} \approx 10^{-4}\lambda^{3}$).
Simulation and Analysis: COMSOL Multiphysics® software was used to calculate phononic dispersion, displacement fields, energy density distribution, and effective mode volumes ($V_{eff,a}$).
Quantum Emitter Integration: NV$^-$ centers are modeled as being positioned 5 nm below the diamond surface. Coupling strengths ($g_{E1}, g_{E2}$) are calculated by transforming the simulated strain tensor ($\hat{\epsilon}_{\alpha}$) from the laboratory frame (X, Y, Z) to the local NV coordinate system (x, y, z).

6CCVD Solutions & Capabilities

The successful replication and extension of this high-impact QAD research hinges on access to ultra-high purity, precisely dimensioned, and expertly processed diamond materials. 6CCVD is uniquely positioned to supply the foundational materials and advanced processing required for these next-generation quantum devices.

Applicable Materials

The high Q factors ($10^{5}$ to $10^{6}$) and the requirement for coherent coupling with NV$^-$ and SiV centers necessitate diamond with extremely low intrinsic defect density and high crystalline quality.

Research Requirement	6CCVD Solution	Technical Justification
High Purity Substrate	Optical Grade Single Crystal Diamond (SCD)	Essential for minimizing non-radiative phonon dissipation and achieving high Q. Low nitrogen content is critical for long NV$^-$ coherence times.
Thin Film Structure	Custom SCD Plates/Wafers	We supply SCD layers with precise thickness control from 0.1 µm up to 500 µm, perfectly matching the required 0.5 µm slab thickness.
Alternative Emitters	Electronic Grade SCD or Boron-Doped Diamond (BDD)	For SiV integration, high purity is key. BDD can be supplied for alternative electro-acoustic transduction mechanisms, if required for future device iterations.

Customization Potential

The PnCW design requires precise geometry, sub-micron thickness control, and potentially advanced surface preparation for subsequent ion implantation.

Research Requirement	6CCVD Capability	Engineering Advantage
Custom Dimensions	Plates up to 125mm (PCD) / Custom SCD	We provide custom-sized plates and wafers, ensuring compatibility with standard lithography equipment and large-scale array fabrication.
Surface Quality	Ultra-Low Roughness Polishing	We guarantee surface roughness $R_{a} < 1$ nm for SCD, which is critical for minimizing surface scattering losses and maximizing the acoustic Q factor.
Complex Shaping	Precision Laser Cutting & Shaping	We offer in-house services for pre-shaping or dicing complex geometries, assisting in the fabrication of the PnCW structure and anchoring points (PMLs).
Defect Integration	Custom Metalization Services	Although not explicitly used for transduction in this paper, 6CCVD offers metalization (Au, Pt, Ti, W, Cu) for future integration of piezoelectric transducers or electrical contacts necessary for advanced QAD control.

Engineering Support

The successful implementation of this QAD cavity requires expertise in crystal orientation and material preparation for quantum emitter integration.

QAD Material Consultation: 6CCVD’s in-house PhD team specializes in material selection and orientation control for quantum applications. We can assist researchers in selecting the optimal SCD orientation (e.g., [110] or [100]) necessary for maximizing the strain coupling constants ($\lambda_{E}, \lambda_{E’}$) with NV or SiV centers.
Substrate Preparation for Implantation: We provide substrates with specified surface termination and low subsurface damage, crucial for subsequent low-energy ion implantation techniques used to position NV/SiV centers 5 nm below the surface, as discussed in the paper.
Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) to deliver sensitive, high-value diamond materials directly to your fabrication facility worldwide.

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

View Original Abstract

Quantum acoustodynamics (QAD) is a rapidly developing field of research,\noffering possibilities to realize and study macroscopic quantum-mechanical\nsystems in a new range of frequencies, and implement transducers and new types\nof memories for hybrid quantum devices. Here we propose a novel design for a\nversatile diamond QAD cavity operating at GHz frequencies, exhibiting effective\nmode volumes of about $10^{-4}\lambda^3$. Our phononic crystal waveguide cavity\nimplements a non-resonant analogue of the optical lightning-rod effect to\nlocalize the energy of an acoustic mode into a deeply-subwavelength volume. We\ndemonstrate that this confinement can readily enhance the orbit-strain\ninteraction with embedded nitrogen-vacancy (NV) centres towards the\nhigh-cooperativity regime, and enable efficient resonant cooling of the\nacoustic vibrations towards the ground state using a single NV. This\narchitecture can be readily translated towards setup with multiple cavities in\none- or two-dimensional phononic crystals, and the underlying non-resonant\nlocalization mechanism will pave the way to further enhance optoacoustic\ncoupling in phoxonic crystal cavities.\n