Entanglement dynamics of two nitrogen vacancy centers coupled by a nanomechanical resonator

At a Glance

Metadata	Details
Publication Date	2017-01-20
Journal	Journal of Physics B Atomic Molecular and Optical Physics
Authors	Z. Toklikishvili, L. Chotorlishvili, S. K. Mishra, S. Stagraczyński, Michael Schüler
Institutions	Banaras Hindu University, Tbilisi State University
Citations	5
Analysis	Full AI Review Included

Technical Documentation & Analysis: Entanglement Dynamics in NV-Center Diamond Systems

Executive Summary

This document analyzes the research concerning the entanglement dynamics of remote Nitrogen Vacancy (NV) Centers in diamond coupled via a dual-mode nanomechanical resonator. This work is highly relevant to quantum computing and sensing applications, requiring ultra-high purity diamond materials.

Core Achievement: Analytical solution demonstrating the time evolution of entanglement (measured by Negativity) between two remote NV Centers mediated by a dual-mode nanomechanical cantilever.
Quantum Mechanism: Indirect spin-spin coupling achieved through the time-varying magnetic field generated by the vibrating magnetic tips attached to the resonator.
Key Phenomena: Observation and analytical modeling of entanglement sudden death and periodic revivals, influenced significantly by quantum decoherence (modeled via the Lindblad master equation).
Material Criticality: The success of this quantum architecture relies fundamentally on high-quality diamond hosting NV centers with long coherence times (SCD).
Tunability: System parameters (Rabi frequencies, detuning, coupling constants) are shown to be controllable by tuning the cantilever geometry and the applied external magnetic field.
6CCVD Value Proposition: 6CCVD provides the necessary high-purity Single Crystal Diamond (SCD) substrates, custom dimensions, and precision polishing required for subsequent nanofabrication of such complex quantum devices.

Technical Specifications

The following hard data points were extracted from the analysis of the prototype nanomechanical resonator and the NV center system parameters:

Parameter	Value	Unit	Context
Diamond Component	NV Centers	Defect	Quantum spin system (S=1 triplet)
NV Transition Frequency (ω₀/2π)	≈ 2.88	GHz	Spin sub-state separation
NV-Tip Distance (h₁, h₂)	≈ 25	nm	Distance for magnetic coupling
Cantilever Material (Prototype)	Si(100)	Material	Used for nanomechanical resonator
Young’s Modulus (Y)	130	GPa	Si(100) material property
Density (ρ)	2.33 x 10³	kg/m³	Si(100) material property
Cantilever Quality Factor (Q_1,2)	≈ 10⁵	Dimensionless	High mechanical quality
Cantilever Length (L₁)	15	µm	First rod length
Cantilever Thickness (d₁)	30	nm	First rod thickness
Free Resonant Frequency (ν_1-0)	≈ 0.54	MHz	Low-frequency mode
Free Resonant Frequency (ν_2-0)	≈ 1.7	MHz	High-frequency mode
System Frequency (ω₁)	≈ 1.2	MHz	Coupled system frequency
System Frequency (ω₂)	≈ 1.4	MHz	Coupled system frequency

Key Methodologies

The experimental setup and theoretical modeling relied on precise control over material properties and advanced quantum mechanical tools:

Physical Setup: A dual-mode nanomechanical resonator (cantilever) was designed, consisting of two coupled rods (L₁ ≈ 15 µm, L₂ ≈ 9 µm).
Coupling Mechanism: Two magnetic tips were attached to the small cantilever, placed symmetrically at a distance of approximately 25 nm from the two remote NV Centers embedded in the diamond substrate.
Interaction Modeling: The vibration of the cantilever generates a time-varying magnetic field, leading to an indirect, non-direct interaction Hamiltonian between the two NV spins.
Decoherence Analysis: Quantum decoherence effects were incorporated using the Lindblad master equation, accounting for spontaneous decay rates (γ_e and γ_d) from the excited states (|2> and |3>) to the ground state (|1>).
Entanglement Quantification: The degree of entanglement between the two NV spins was measured analytically using the Negativity N(ρ).
Parameter Control: The study highlights that critical quantum parameters (Rabi frequency Ω, detuning δ, and coupling constants α, β) can be tuned by adjusting the geometrical characteristics of the cantilever and the strength of the external magnetic field (B₀).

6CCVD Solutions & Capabilities

This research demonstrates a critical need for high-quality diamond substrates to realize robust, scalable quantum devices. 6CCVD is uniquely positioned to supply the foundational materials necessary to replicate and advance this work.

Applicable Materials

To achieve the long coherence times and low defect density required for stable NV center operation in quantum applications, Optical Grade Single Crystal Diamond (SCD) is essential.

Material Recommendation: Optical Grade SCD
- Purity: Ultra-high purity MPCVD growth ensures minimal background defects that could reduce NV center coherence time (T₂).
- NV Integration: Ideal for controlled NV creation via implantation or in-situ growth techniques, providing a stable quantum platform.

Customization Potential for Quantum Nanomechanics

The paper emphasizes that system tunability is achieved through precise geometry. 6CCVD’s advanced fabrication capabilities ensure the diamond substrate meets the stringent requirements for subsequent nanofabrication steps (e.g., cantilever etching, magnetic tip placement).

Requirement from Research	6CCVD Capability	Technical Advantage
Substrate Dimensions	Custom plates/wafers up to 125mm	Supports large-scale device arrays and prototyping.
Thickness Control	SCD thickness from 0.1µm to 500µm	Enables precise integration with nanomechanical structures and thin-film deposition.
Surface Quality	Polishing to Ra < 1nm (SCD)	Essential for high-resolution lithography, precise magnetic tip placement (25 nm distance), and minimizing surface-related decoherence.
Interconnects/Tips	Custom Metalization (Au, Pt, Pd, Ti, W, Cu)	Allows for the deposition of magnetic tips or electrical contacts necessary for external control and readout.
Substrate Preparation	Substrates up to 10mm thick	Provides robust mechanical support for complex hybrid systems involving Si cantilevers and diamond NV platforms.

Engineering Support

The analytical complexity of this model, particularly the influence of decoherence parameters (γ_e, γ_d) on entanglement dynamics, requires deep material expertise.

6CCVD’s in-house PhD team specializes in MPCVD growth optimization for quantum applications. We can assist researchers and engineers in selecting the optimal SCD grade, nitrogen concentration, and surface termination necessary to maximize NV center yield and coherence time for similar NV-Center Quantum Information projects.
We offer consultation on integrating diamond substrates with complex hybrid systems, ensuring compatibility with micro- and nanofabrication processes like those used to create the dual-mode cantilever.

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

View Original Abstract

In this paper we study the time evolution of the entanglement between two\nremote NV Centers (nitrogen vacancy in diamond) connected by a dual-mode\nnanomechanical resonator with magnetic tips on both sides. Calculating the\nnegativity as a measure for the entanglement, we find that the entanglement\nbetween two spins oscillates with time and can be manipulated by varying the\nparameters of the system. We observed the phe- nomenon of a sudden death and\nthe periodic revivals of entanglement in time. For the study of quantum deco-\nherence, we implement a Lindblad master equation. In spite of its complexity,\nthe model is analytically solvable under fairly reasonable assumptions, and\nshows that the decoherence influences the entanglement, the sudden death, and\nthe revivals in time.\n

Tech Support

Original Source

DOI: https://doi.org/10.1088/1361-6455/aa5a69