Nitrogen-Vacancy Center Coupled to an Ultrasmall-Mode-Volume Cavity - A High-Efficiency Source of Indistinguishable Photons at 200 K

At a Glance

Metadata	Details
Publication Date	2021-03-10
Journal	Physical Review Applied
Authors	Joe A. Smith, Chloe Clear, Krishna C. Balram, Dara P. S. McCutcheon, John Rarity
Institutions	University of Bristol
Citations	13
Analysis	Full AI Review Included

Technical Documentation & Analysis: High-Efficiency NV Centre Photon Sources

Research Paper Analyzed: The NV centre coupled to an ultra-small mode volume cavity: A high-efficiency source of indistinguishable photons at 200 K (arXiv:2005.13478v2)

Executive Summary

This research demonstrates a critical advancement toward scalable, non-cryogenic quantum network components by achieving high indistinguishability ($I$) from Nitrogen Vacancy (NV) centers in diamond operating at 200 K.

Non-Cryogenic Operation: Achieved high performance in the Peltier cooling regime (200 K), overcoming the complexity and constraints associated with liquid helium cooling (4 K).
High Indistinguishability: Demonstrated an optimal indistinguishability of $I = 0.54$ (unfiltered) and $I = 0.73$ (with external filtering) at 200 K, representing a nine-order-of-magnitude improvement over room temperature performance.
Ultra-Small Mode Volume: Utilized a Photonic Crystal Cavity (PhCC) design with ultra-small mode volumes ($V_m$ down to $0.0052 (\lambda/n)³$) to maximize the atom-cavity coupling rate ($g$).
Overcoming Dephasing: The strong coupling rate ($g$) successfully overcomes the high thermal dephasing rate ($\gamma^* = 1$ THz at 200 K), allowing photons to leave the atom-like environment faster than dephasing processes occur.
Scalable Design: The optimized planar silicon nitride PhCC design is compact (< 10 µm total length) and compatible with standard silicon planar lithography, facilitating dense, chip-scale integration.
Robustness: The final cavity design is optimized for robustness against variations in the cavity Q factor and the stochastic location/orientation of the NV center within the nanodiamond.

Technical Specifications

The following hard data points were extracted from the simulation and design analysis:

Parameter	Value	Unit	Context
Operating Temperature (Target)	200	K	Peltier cooling regime
Optimal Indistinguishability ($I$)	0.54	Dimensionless	Unfiltered emission at 200 K
Filtered Indistinguishability ($I$)	0.73	Dimensionless	Achieved with external filter ($\kappa_f = 0.3$ THz)
Extraction Efficiency ($\beta$)	29	%	Corresponding to $I = 0.73$
ZPL Linewidth ($\gamma^*$) at 200 K	1	THz	Thermal broadened linewidth
ZPL Linewidth ($\gamma^*$) at 300 K	15	THz	Room temperature broadened linewidth
Cavity Mode Volume ($V_m$) (Bow Tie)	0.0052	$(\lambda/n)³$	Initial ultra-small mode volume design
Cavity Mode Volume ($V_m$) (Planar, Loaded)	0.075	$(\lambda/n)³$	Optimized, robust design for 200 K
Optimal Cavity Q Factor	1000	Dimensionless	Used for $V_m = 0.075 (\lambda/n)³$ design
Nanodiamond Model Size	20	nm cube	Refractive index $n=2.4$
Waveguide Material Refractive Index	2.0	Dimensionless	Silicon Nitride (SiN)
Total Cavity Length	< 10	µm	Compact footprint for chip-scale integration

Key Methodologies

The experimental design relies on advanced cavity QED modeling and nanophotonic engineering:

Cavity Structure: A Photonic Crystal Cavity (PhCC) was designed in a 200 nm thick silicon nitride (n=2.0) waveguide, utilizing a modified cylinder unit cell containing a “bow tie” structure for in-plane mode concentration.
Mode Volume Reduction: Initial designs achieved ultra-small $V_m$ by thinning the center of the bow tie via a V-groove etch for out-of-plane (z-direction) confinement. The final, more robust design utilized a planar structure with quadratically tapered air holes (Gaussian mode) to achieve the desired Q factor (10 mirror pairs, 5 taper pairs).
NV Center Modeling: The NV center was modeled as a two-level system (extended to a three-level system in Section V) with pure dephasing, coupled to a single-mode cavity.
Integration Simulation: The NV center was integrated into the SiN cavity by modeling the nanodiamond host as a 20 nm cube with a refractive index of $n=2.4$ loaded at the cavity center.
Quantum Dynamics: The system dynamics were analyzed using the Lindblad Master Equation, explicitly incorporating the effects of the broad NV center phonon sideband and ZPL broadening ($\gamma^*$).
Optimization Strategy: Parameters were optimized to maximize the Purcell-enhanced spontaneous emission rate ($R \sim g²/\kappa_c$) relative to the dephasing rate ($\gamma^*$), ensuring the cavity acts as a spectral filter to suppress the incoherent sideband emission.

6CCVD Solutions & Capabilities

6CCVD provides the foundational diamond materials and precision engineering services required to replicate, optimize, and scale the NV center quantum emitter platform described in this research.

Research Requirement	6CCVD Solution & Capability	Technical Advantage for Quantum Applications
Ultra-High Purity Diamond (for NV creation)	Optical Grade Single Crystal Diamond (SCD)	Essential for maximizing NV center coherence time and minimizing spectral diffusion caused by background defects (e.g., nitrogen, substitutional defects).
Substrate Material (for nanodiamond precursor)	Custom SCD Plates (0.1 µm to 500 µm)	We supply high-quality, low-strain SCD substrates required for subsequent nanodiamond fabrication or direct integration via etching/implantation.
Surface Quality (NV centers near surface are sensitive to charge noise)	Precision Polishing (Ra < 1 nm for SCD)	Ultra-smooth surfaces minimize surface charge traps and reduce effective linewidth broadening ($\gamma^*$), critical for maintaining high indistinguishability when the emitter is close to the PhCC interface.
Scalable Integration (Compact, chip-scale design)	Large-Format PCD/SCD Wafers (up to 125 mm)	Our capability to supply inch-size PCD and large-area SCD supports high-throughput fabrication and dense integration of multiple < 10 µm cavity devices on a single chip.
Emitter Control & Tuning (Need for vector electric fields/strain tuning)	Custom Metalization Services	We offer in-house deposition of Au, Pt, Pd, Ti, W, and Cu contacts, enabling researchers to apply vector electric fields to dynamically stabilize optical resonances or reorient strain-induced linear dipoles (as discussed in Section V).
Advanced Material Integration	Boron-Doped Diamond (BDD)	For applications requiring integrated electrical conductivity or electrochemical sensing alongside quantum emitters, BDD films are available in custom thicknesses.

Engineering Support

6CCVD’s in-house team of PhD material scientists and engineers specializes in MPCVD diamond growth and processing. We offer comprehensive consultation to assist researchers in selecting the optimal diamond material (purity, orientation, thickness) for Solid-State Quantum Emitter projects, ensuring maximum coherence and coupling efficiency.

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View Original Abstract

Solid state atom-like systems have great promise for linear optic quantum\ncomputing and quantum communication but are burdened by phonon sidebands and\nbroadening due to surface charges. Nevertheless, coupling to a small mode\nvolume cavity would allow high rates of extraction from even highly dephased\nemitters. We consider the nitrogen vacancy centre in diamond, a system\nunderstood to have a poor quantum optics interface with highly distinguishable\nphotons, and design a silicon nitride cavity that allows 99 % efficient\nextraction of photons at 200 K with an indistinguishability of > 50%,\nimprovable by external filtering. We analyse our design using FDTD simulations,\nand treat optical emission using a cavity QED master equation valid at and\nbeyond strong coupling and which includes both ZPL broadening and sideband\nemission. The simulated design is compact (< 10 um), and owing to its planar\ngeometry, can be fabricated using standard silicon processes. Our work\ntherefore points towards scalable fabrication of non-cryogenic atom-like\nefficient sources of indistinguishable photons.\n

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Original Source

DOI: https://doi.org/10.1103/physrevapplied.15.034029