Strain Coupling of a Mechanical Resonator to a Single Quantum Emitter in Diamond

At a Glance

Metadata	Details
Publication Date	2016-09-12
Journal	Physical Review Applied
Authors	Kenneth W. Lee, Donghun Lee, Preeti Ovartchaiyapong, Joaquín Minguzzi, Jero Maze
Institutions	University of California, Santa Barbara, Korea University
Citations	94
Analysis	Full AI Review Included

Technical Analysis and Material Sourcing Documentation for NV-Phonon Coupling in Diamond

Executive Summary

This research demonstrates a significant advancement in hybrid quantum systems by achieving dynamic, strain-mediated coupling between the orbital states of a single Nitrogen-Vacancy (NV) defect center and the resonant mechanical motion of a single-crystal diamond (SCD) cantilever.

Core Achievement: Observation of dynamic NV strain-orbit coupling exceeding 10 GHz using only a few nanometers of cantilever displacement, demonstrating deterministic control over NV optical transitions.
Enhanced Coupling: The measured strain-mediated single-phonon coupling strengths (up to 3 kHz) are three to five orders of magnitude higher than those previously demonstrated using NV electron spin.
Qubit Control: Successful demonstration of dynamically matching the frequency and polarization dependence of the zero-phonon lines (ZPLs) of two spatially separated NV centers, crucial for generating indistinguishable photons and realizing multipartite entanglement.
Material Necessity: The monolithic architecture requires extremely high-purity, low-strain SCD substrates to maintain the long coherence times and high mechanical quality factors (Q > 20,000 demonstrated; Q = 10⁶ projected).
Future Scaling: The results provide a pathway to the high-cooperativity regime ($\eta \approx 5$) essential for quantum applications such as phonon cooling, phononic quantum gates, and long-range qubit interactions.
6CCVD Value Proposition: 6CCVD is uniquely positioned to supply the high-quality SCD wafers and custom nanofabrication required for replicating and advancing these nanoscale diamond quantum devices.

Technical Specifications

The following quantitative data defines the experimental performance and required material properties for strain-coupled NV devices.

Parameter	Value	Unit	Context
NV Strain-Orbit Coupling (Observed)	> 10	GHz	Achieved with cantilever displacement of a few nm
Single Phonon Coupling Strength ($g$)	1 to 3	kHz	Maximal observed $g_{A_1}$ and $g_{E_1}$
Mechanical Quality Factor (Q)	20,000	Dimensionless	Measured at ~7 K, fundamental flexural mode
Cantilever Resonance Frequency ($\omega_c / 2\pi$)	870	kHz	Fundamental flexural mode
Operating Temperature (T)	~7	K	Cryogenic environment for resonant excitation spectroscopy (RES)
Zero-Phonon Line (ZPL) Transition	637	nm	Wavelength used for resonant excitation
Implantation Energy (N ions)	40	keV	Used to create near-surface NV centers
Implantation Dosage	$3 \times 10^{9}$	ion/cm²	Targeting single NV defects
Expected NV Center Depth ($d_N$)	$51.5 \pm 13.0$	nm	Calculated via SRIM simulations
Annealing Temperature/Pressure	800 °C / 10^-6	Torr	Required post-implantation treatment
Projected High-Coop. Nanobeam Dimensions	$2\ \text{µm} \times 100\ \text{nm} \times 50\ \text{nm}$	N/A	Future device design for $\eta \approx 5.2$ at 4 K
Projected High-Coop. Q Factor	10⁶	Dimensionless	Assumed Q for nanobeam at 4 K

Key Methodologies

The experiment relies on precise nanofabrication and highly stable optical measurements performed under cryogenic conditions.

Material Selection and Fabrication:
- Substrate: High-purity single-crystal diamond (SCD) was used as the base material for the monolithic device structure.
- Cantilever Fabrication: Cantilevers were fabricated using advanced nanofabrication techniques described in reference [17] (often involving etching high-quality SCD).
- NV Formation: Nitrogen atoms were implanted into the diamond (40 keV energy, $3 \times 10^{9}\ \text{ion}/\text{cm}^2$ dose) to create near-surface defects.
- Annealing: Samples were annealed under high vacuum (10^-6 Torr) at 800 °C for 3 hours to form the negatively-charged NV centers (NV⁻).
Experimental Setup and Actuation:
- Cryogenic Environment: Experiments were conducted at cryogenic temperatures (~7 K) using a closed-cycle cryostat to suppress phonon broadening of optical transitions.
- Optical Initialization: A 532 nm laser was used for off-resonant excitation, initializing the NV center into the $m_s = 0$ ground state and stabilizing the NV⁻ charge state.
- Mechanical Driving: A piezoelectric transducer (PZT) located below the sample holder mechanically actuated the cantilever.
- Motion Detection: A 450 nm laser was used for interferometric detection of the cantilever’s flexural motion.
Strain Characterization and Control:
- Measurement Technique: Resonant Excitation Spectroscopy (RES) using a tunable 637 nm diode laser monitored shifts in the zero-phonon line (ZPL) corresponding to the $^3A_2 \to\ ^3E$ transition.
- Dynamic Measurement: Continuous wave (CW) RES was used to observe modulation of the optical transitions under resonant mechanical driving.
- Stroboscopic RES: Synchronized photon detection (60 ns windows) relative to the cantilever’s oscillation (1.15 µs period) was used to deconvolve orbital dynamics and accurately measure strain coupling constants for specific cantilever positions.
- Strain Control Application: Dynamic tuning was demonstrated to match both the frequency (using amplitudes up to 43 nm) and the polarization dependence of two separate NV centers.

6CCVD Solutions & Capabilities

Replicating this foundational research, especially moving toward the projected high-cooperativity nanobeam devices, requires ultra-high-quality diamond engineering. 6CCVD’s expertise in MPCVD SCD and nanofabrication integration directly meets these stringent requirements.

Applicable Materials

To replicate the demonstrated cantilever devices and pursue nanoscale high-cooperativity designs (e.g., $2\ \text{µm} \times 100\ \text{nm} \times 50\ \text{nm}$ beams), the highest quality material is essential.

Research Requirement	6CCVD Material Solution	Engineering Rationale
Single-Crystal Diamond (SCD) Cantilever Substrate	Optical Grade SCD Wafers	SCD with ultra-low residual strain and low defect density is essential for achieving high mechanical Q factors ($Q > 10^6$) and maximizing NV coherence times (coherence approaching 1 second demonstrated in related literature).
Near-Surface NV Creation	Epitaxial SCD with controlled Nitrogen incorporation	While the paper used implantation, 6CCVD can provide high-purity SCD with low, controlled background nitrogen concentration or pre-grown layers optimized for shallow implantation yield and reduced lattice damage, facilitating NV center stability.
Cantilever Thickness Control	SCD/PCD Wafers: 0.1 µm to 500 µm	Future devices require precise material layers. 6CCVD offers custom thickness control crucial for releasing precisely dimensioned nanomechanical structures (e.g., 50 nm thickness).

Customization Potential

The success of this experiment hinges on the precise geometry of the mechanical resonator and the localized implantation process. 6CCVD supports the complete engineering lifecycle for these devices:

Custom Dimensions: 6CCVD supplies SCD plates and wafers up to 125 mm (PCD equivalent) with custom geometries. We offer precision laser cutting and micro-machining services to define the overall footprint and features for subsequent cleanroom etching/release processes used in cantilever fabrication.
Surface Preparation: Achieving a high-Q resonator requires ultra-smooth surfaces. 6CCVD guarantees SCD polishing to Ra < 1 nm, minimizing surface scattering losses and optimizing cantilever performance.
Implantation Support: Although NV creation was achieved via standard ion implantation, 6CCVD can work with customer teams to define materials or provide implantation mask readiness, supporting specific NV depths ($51.5 \pm 13.0\ \text{nm}$ depth is feasible on 6CCVD material).
Metalization for Transduction: While this study used PZT actuation, future designs for on-chip control or detection may require electrical leads (e.g., for integrated interdigitated transducers). 6CCVD offers in-house, custom thin-film metalization capabilities, including common stack materials like Ti, Pt, Au, Pd, W, and Cu, compatible with diamond surface chemistry.

Engineering Support

The successful development of strain-coupled quantum emitters requires complex balancing of crystal orientation, mechanical geometry, and defect engineering.

6CCVD’s in-house PhD material science and engineering team provides expert consultation for projects leveraging dynamic strain control in diamond. We specialize in:

Optimizing SCD substrate orientation (e.g., [110] axis cantilever alignment shown in Figure 7) to maximize strain coupling for specific NV axes.
Material selection to ensure low residual strain necessary for minimizing intrinsic splitting ($\Delta f_0$) and optimizing optical properties.
Designing SCD wafers compatible with aggressive nanofabrication and high-temperature annealing protocols required for quantum device manufacturing.

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

View Original Abstract

The recent maturation of hybrid quantum devices has led to significant enhancements in the functionality of a wide variety of quantum systems. In particular, harnessing mechanical resonators for manipulation and control has expanded the use of two-level systems in quantum information science and quantum sensing. In this letter, we report on a monolithic hybrid quantum device in which strain fields associated with resonant vibrations of a diamond cantilever dynamically control the optical transitions of a single nitrogen-vacancy (NV) defect center in diamond. We quantitatively characterize the strain coupling to the orbital states of the NV center, and with mechanical driving, we observe NV-strain couplings exceeding 10 GHz. Furthermore, we use this strain-mediated coupling to match the frequency and polarization dependence of the zero-phonon lines of two spatially separated and initially distinguishable NV centers. The experiments demonstrated here mark an important step toward engineering a quantum device capable of realizing and probing the dynamics of non-classical states of mechanical resonators, spin-systems, and photons.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevapplied.6.034005