Multiphonon interactions between nitrogen-vacancy centers and nanomechanical resonators

At a Glance

Metadata	Details
Publication Date	2019-10-18
Journal	Physical review. A/Physical review, A
Authors	Xing‐Liang Dong, Fuli Li
Institutions	Xi’an Jiaotong University
Citations	22
Analysis	Full AI Review Included

Technical Documentation & Analysis: Multi-Phonon Interactions in NV-Nanomechanical Systems

Reference: arXiv:1908.03727v1 [quant-ph] (Dong & Li, 2019)

Executive Summary

This research successfully demonstrates enhanced multi-phonon interactions between a single Nitrogen-Vacancy (NV) center in diamond and a nanomechanical resonator, crucial for advancing quantum acoustics and information processing.

Core Achievement: Realization of strong, nonlinear multi-phonon coupling (up to 4-phonon) using Mollow and Lamb-Dicke sideband engineering techniques.
Coupling Strength: Achieved second sideband coupling rates up to 2$\pi$ x 10 kHz, three orders of magnitude higher than typical direct coupling methods.
Material Requirement: The scheme relies fundamentally on the long coherence times and robust spin properties of solid-state defect centers in diamond.
Quantum State Preparation: The enhanced coupling enables the coherent preparation and manipulation of nonclassical states, including Schrödinger cat states and phononic Fock states.
Feasibility: The model requires high-quality factor (Q > 10⁶) resonators and low-noise, high-purity diamond substrates for optimal NV center performance.
6CCVD Value Proposition: We provide the necessary high-purity Single Crystal Diamond (SCD) substrates with ultra-low surface roughness (Ra < 1nm) and custom dimensions required for subsequent nanofabrication and strong coupling regimes.

Technical Specifications

The following hard data points were extracted from the analysis of the hybrid spin-mechanical system:

Parameter	Value	Unit	Context
NV Center Zero-Field Splitting (D)	2 x 2.87	GHz	S=1 spin triplet state
Resonator Fundamental Frequency ($\omega_r$)	2$\pi$ x 5	MHz	Typical Si cantilever dimensions
Magnetic Coupling Strength ($\lambda$)	2$\pi$ x 150	kHz	Si cantilever, h = 25 nm tip distance
Second Sideband Coupling ($\lambda^{(2)}$)	2$\pi$ x 10	kHz	Mollow regime, enhanced nonlinear interaction
Third Sideband Coupling ($\lambda^{(3)}$)	2$\pi$ x 1	kHz	Mollow regime
Magnetic Field Gradient ($G_m$)	10⁷	T/m	Required for strong magnetic coupling
Mechanical Quality Factor (Q)	> 10⁶	-	Required for low damping
Operating Temperature (T)	~ 10	mK	Dilution refrigerator environment
Spin Dephasing Time ($T_2$)	~ 10	ms	Mollow scheme (low temperature)
SCD Cantilever Dimensions (l, w, t)	(20, 8, 0.8)	µm	Alternative, more realistic diamond resonator

Key Methodologies

The experiment relies on precise control of the NV center spin state and its coupling to the mechanical resonator through microwave (mw) field engineering.

System Setup: A single NV center is positioned at a distance ($h$) below a nanomechanical cantilever (Si or SCD) tipped with a sharp magnet. The system is immersed in a static magnetic field ($B_{static}$).
Spin-Mechanical Coupling: The mechanical oscillation induces a magnetic field gradient ($G_m$), coupling the resonator position operator ($\hat{a} + \hat{a}^{\dagger}$) to the NV spin operator ($\hat{S}_z$).
Mollow Sideband Scheme: Three microwave fields are applied to strongly drive the NV center, resulting in dressed spin states. This scheme yields the highest coupling strengths (up to 2$\pi$ x 10 kHz for 2-phonon).
Lamb-Dicke Sideband Scheme: A single microwave driving field is applied, and the interaction is analyzed in the Lamb-Dicke regime, viewing the system as a solid-state analog to trapped ion schemes.
Effective Hamiltonian Derivation: Perturbation theory (Rayleigh-Schrödinger) is used to derive an effective n-phonon Hamiltonian, confirming that the enhanced nonlinear interaction dominates the system dynamics.
Quantum State Dynamics: Master equations and quantum jump approaches are used to model the system under engineered dissipation, demonstrating the creation of motional cat states and Fock states.

6CCVD Solutions & Capabilities

The successful replication and extension of this research require diamond materials optimized for quantum applications, specifically high-purity substrates suitable for NV center creation and subsequent nanofabrication.

Applicable Materials

To achieve the long coherence times ($T_2$ up to 10 ms) and low noise required for quantum control, researchers must start with the highest quality diamond.

Material	6CCVD Specification	Application Context
Single Crystal Diamond (SCD)	High Purity, Low Strain (Optical Grade)	Essential starting material for creating high-coherence NV centers via implantation or in-situ growth. Minimizes decoherence from nuclear spin baths.
SCD Thin Films	Thickness: 0.1 µm - 500 µm	Provides the necessary thin layer for subsequent focused ion beam (FIB) or etching processes to fabricate the nanomechanical cantilevers (e.g., 0.8 µm thick diamond cantilever discussed).
Polycrystalline Diamond (PCD)	High Thermal Grade (Optional)	While SCD is preferred for NV coherence, high-purity PCD wafers (up to 125mm) can serve as robust, large-area platforms for integrating multiple NV-resonator hybrid systems.

Customization Potential

6CCVD’s advanced fabrication capabilities directly address the unique geometric and integration challenges presented by NV-nanomechanical systems:

Custom Dimensions: We supply SCD plates and wafers in custom sizes, providing the foundation for the $\mu$m-scale cantilevers and resonators discussed (e.g., 20 µm x 8 µm x 0.8 µm).
Ultra-Low Roughness Polishing: NV centers near the surface are highly sensitive to surface defects. 6CCVD guarantees Ra < 1nm polishing on SCD, minimizing surface-related decoherence and ensuring optimal coupling geometry.
Metalization Services: Although the paper uses an external magnetic tip, future integrated designs may require on-chip microwave delivery or magnetic field generation. We offer internal metalization capabilities including Au, Pt, Ti, and W for custom microwave striplines or integrated magnetic elements.
Substrate Thickness: We provide substrates up to 10mm thick, ensuring mechanical stability for the low-temperature (10 mK) experimental setup, while offering thin SCD layers (down to 0.1 µm) for cantilever fabrication.

Engineering Support

6CCVD’s in-house team of PhD material scientists specializes in MPCVD diamond growth tailored for quantum applications. We offer comprehensive engineering support for projects involving:

Optimizing diamond purity and nitrogen concentration for targeted NV center density and coherence.
Assisting with material selection and geometry design for achieving the strong coupling regime ($\lambda \gg \gamma_m, \gamma_s$) required for multi-phonon interactions.
Consulting on surface preparation and metalization schemes for integrated quantum acoustic devices.

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

View Original Abstract

We investigate the multi-phonon interactions in a hybrid system composed of a nitrogen-vacancy center and a mechanical resonator.We show that, through appropriate sideband engineering analogy to the Mollow or Lamb-Dicke dynamics, the enhanced nonlinear interactions can dominate the coupled system. As an example, we show the preparation of nonclassical states of the mechanical motion and explore the quantum correlation of $n$-phonon with the engineered dissipation,based on the large multi-phonon coupling strength attainable in this sideband structure. This work takes full advantage of the structure and coherence features of defect centers in diamond, and may be useful for quantum information processing.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.100.043825