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Optimizing a dynamical decoupling protocol for solid-state electronic spin ensembles in diamond

MetadataDetails
Publication Date2015-08-24
JournalPhysical Review B
AuthorsDemitry Farfurnik, Andrey Jarmola, Linh Pham, Z. H. Wang, V. V. Dobrovitski
InstitutionsUniversity of Southern California, Center for Astrophysics Harvard & Smithsonian
Citations103
AnalysisFull AI Review Included

Technical Documentation & Analysis: Optimized Dynamical Decoupling in NV Diamond

Section titled “Technical Documentation & Analysis: Optimized Dynamical Decoupling in NV Diamond”

This research demonstrates a significant advancement in extending the spin coherence time (T2) of Nitrogen-Vacancy (NV) center ensembles in diamond, a critical step for scaling quantum sensing and information technologies.

  • Coherence Extension: Achieved an extension of the transverse spin coherence time (T2) from a baseline of ~0.7 ms (Hahn-Echo) up to ~30 ms at 77 K, representing a factor of ~40 improvement.
  • Optimal Protocol: Identified the Concatenated XY8 pulse sequence as the most robust Dynamical Decoupling (DD) protocol for preserving an arbitrary NV ensemble spin state by compensating for higher-order pulse errors.
  • Material Requirement: Experiments relied on high-quality, isotopically pure (99.99% 12C) MPCVD diamond to minimize spin bath decoherence.
  • Methodology: Suppression of longitudinal relaxation (T1) effects achieved by cooling the sample to 77 K (liquid nitrogen).
  • Application Impact: The optimized protocol immediately improves the sensitivity of AC magnetometry and paves the way for creating collective, non-classical NV spin states necessary for advanced quantum computing architectures.
  • 6CCVD Value Proposition: 6CCVD specializes in delivering the high-purity, isotopically controlled Single Crystal Diamond (SCD) substrates required to replicate and scale this cutting-edge quantum research.

The following hard data points were extracted from the analysis of the optimized dynamical decoupling experiment:

ParameterValueUnitContext
Initial Coherence Time (T2*)~0.7msMeasured via Hahn-Echo
Optimized Coherence Time (T2)~30msAchieved using Concatenated XY8 DD
Coherence Improvement Factor~40FactorImprovement in arbitrary spin state preservation
Operating Temperature77KLiquid Nitrogen cooling to suppress T1 effects
Diamond Isotopic Purity99.99%Carbon-12 (12C) purity
Nitrogen Concentration (N)~2 x 1017cm-3Sample specification (N precursor density)
NV Center Concentration~4 x 1014cm-3Resulting NV density
Static Magnetic Field (B0)~300GApplied along NV axis to polarize 14N nuclear spins
Microwave (MW) Rabi Frequency~15MHzUsed to overcome hyperfine splitting detuning
NV Hyperfine Splitting~2.2MHzSource of pulse imperfection mitigated by strong MW field
Pulse Imperfection (Rotation Angle)ε ≈ 0.15N/AEstimated remaining error after optimization
Pulse Imperfection (Rotation Axis)nz ≈ 0.25N/AEstimated remaining error after optimization

The successful extension of NV ensemble coherence time relied on precise material engineering and rigorous optimization of the microwave control sequence:

  1. Material Selection: Used isotopically pure (99.99% 12C) diamond grown via Chemical Vapor Deposition (CVD) to minimize the dominant 13C spin bath noise.
  2. Thermal Management: The sample was placed in a continuous flow cryostat and cooled to 77 K to significantly reduce phonon-induced decoherence and suppress T1 relaxation effects.
  3. Magnetic Field Control: A static magnetic field (B0 ~ 300 G) was applied along the NV symmetry axis to Zeeman split the ms = ±1 sublevels and polarize the 14N nuclear spins into a single hyperfine state.
  4. Microwave (MW) Pulse Optimization: A strong MW field (Rabi frequency ~15 MHz) was applied via a 70-”m diameter wire, ensuring the driving frequency was much greater than the NV hyperfine splitting (~2.2 MHz) to mitigate pulse errors.
  5. Dynamical Decoupling Protocol: Compared CPMG, XY8, and Knill DD (KDD). The Concatenated XY8 sequence was identified as superior, recursively constructed to correct for higher orders of pulse timing, amplitude, and phase errors, thereby maximizing robustness for arbitrary spin state preservation.

6CCVD is uniquely positioned to supply the advanced diamond materials and fabrication services necessary to replicate, scale, and extend the quantum sensing and computing applications demonstrated in this research.

To achieve T2 times in the millisecond regime, the research requires extremely low concentrations of paramagnetic impurities and high isotopic purity.

Research Requirement6CCVD Material RecommendationTechnical Rationale
Isotopically Pure SubstrateOptical Grade Single Crystal Diamond (SCD)Guaranteed 12C purity (up to 99.999%) is essential for minimizing the 13C spin bath, which limits T2 coherence. Our SCD is optimized for quantum applications.
Controlled NV Ensemble DensityCustom Doped SCDWe offer precise control over nitrogen incorporation during MPCVD growth, allowing engineers to tune the N concentration (e.g., 1015 cm-3 to 1018 cm-3) to optimize the resulting NV density (4 x 1014 cm-3 used here) for ensemble sensing or to push toward NV-NV interaction time scales (~150 ms).
High-Quality Surface FinishPolished SCD WafersRequired for subsequent lithography steps (e.g., fabricating the MW striplines). Our SCD surfaces achieve Ra < 1 nm, ensuring minimal scattering losses and high-fidelity device integration.

The experiment utilized an external 70-”m wire for MW delivery. 6CCVD can integrate these structures directly onto the diamond substrate, enhancing device performance and scalability.

  • Integrated Microwave Structures: 6CCVD offers in-house custom metalization services, including deposition of Au, Pt, Pd, Ti, W, and Cu. We can fabricate high-fidelity microwave striplines directly onto the SCD surface, replacing external wires and ensuring superior field homogeneity and pulse control for DD protocols.
  • Custom Dimensions: While the measurement volume was small, scaling quantum devices requires large substrates. 6CCVD provides SCD plates up to 500 ”m thick and PCD plates up to 125 mm in diameter, enabling the fabrication of large-scale quantum sensor arrays.
  • Precision Fabrication: We offer laser cutting and shaping services to deliver custom geometries required for mounting in cryostats or integrating with specific optical/MW setups (e.g., creating specific facets or trenches for fiber coupling or wire bonding).

The optimization of DD protocols, particularly the Concatenated XY8 sequence, relies heavily on minimizing pulse imperfections. 6CCVD’s in-house PhD team provides expert consultation to ensure material properties support advanced quantum control:

  • Material Selection for Quantum Control: Our experts assist researchers in selecting the optimal SCD grade and nitrogen doping level to balance high NV density (for sensitivity) against long coherence times (T2).
  • Thermal and Magnetic Integration: We provide guidance on substrate preparation and dimensioning to ensure seamless integration into complex cryogenic and high-field magnetic environments, crucial for replicating the 77 K operation demonstrated here.

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

View Original Abstract

We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to 77 K suppresses longitudinal spin relaxation T1 effects and DD microwave pulses are used to increase the transverse coherence time T2 from ∌0.7ms up to ∌30ms. We extend previous work of single-axis (Carr-Purcell-Meiboom-Gill) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the optimal control scheme for preserving an arbitrary spin state is a recursive protocol, the concatenated version of the XY8 pulse sequence. The improved spin coherence might have an immediate impact on improvements of the sensitivities of ac magnetometry. Moreover, the protocol can be used on denser diamond samples to increase coherence times up to NV-NV interaction time scales, a major step towards the creation of quantum collective NV spin states.