Experimental realization of time-dependent phase-modulated continuous dynamical decoupling

At a Glance

Metadata	Details
Publication Date	2017-07-25
Journal	Physical review. A/Physical review, A
Authors	Demitry Farfurnik, N. Aharon, I. Cohen, Yonatan Hovav, Alex Retzker
Institutions	Hebrew University of Jerusalem
Citations	43
Analysis	Full AI Review Included

6CCVD Technical Analysis: Phase-Modulated Dynamical Decoupling in NV Ensemble Diamond

Executive Summary

This documentation analyzes the experimental realization of time-dependent phase-modulated continuous dynamical decoupling (DD) in a dense ensemble of Nitrogen-Vacancy (NV) centers, demonstrating a significant advancement in quantum coherence control for ensemble-based sensing and computation.

Core Challenge Addressed: Mitigating limitations in continuous DD schemes caused by amplitude fluctuations in the microwave driving source, which previously capped achievable coherence times (T₂).
Material Basis: The experiment utilized an isotopically pure (99.99% ¹²C) Chemical Vapor Deposition (CVD) diamond sample with specific, high concentrations of nitrogen (P1 defects, ~ 2 x 10¹⁷ cm^-3) to form a dense NV ensemble.
Methodology: Implementation of a technically advantageous time-dependent phase modulation approach during continuous microwave driving (Rabi frequency Ω₁ ≈ 9 MHz).
Key Achievement (T₂): Achieved an order-of-magnitude improvement in off-axis coherence time (T₂), increasing the measured value from 0.81 µs (conventional driving) to 8.3 µs using optimal phase modulation strength (a = 0.1).
Arbitrary State Preservation: Demonstrated successful preservation of arbitrary spin states up to T₂ ≈ 8 µs while maintaining reasonable signal contrast (1.26%), making the technique viable for robust quantum sensing applications.
Future Advantage: Phase modulation is predicted to outperform amplitude modulation when higher phase accuracy AWGs become available, suggesting a critical path for next-generation quantum hardware.

Technical Specifications

The following hard data points were extracted from the experimental measurements and system parameters:

Parameter	Value	Unit	Context
Diamond Isotope Purity	99.99%	¹²C	Minimizing ¹³C nuclear spin bath noise.
Nitrogen (P1) Concentration	~ 2 x 10¹⁷	cm^-3	Required high density for ensemble measurement.
NV Center Concentration	~ 4 x 10¹⁴	cm^-3	Density of the active quantum sensor ensemble.
Laser Excitation Wavelength	532	nm	Optical readout and initialization source.
Continuous Driving Frequency (Ω₁)	≈ 9	MHz	Applied resonant Rabi frequency.
Conventional T₂ Coherence Time	0.81	µs	Baseline coherence time (single continuous driving).
Optimized T₂ Coherence Time	8.3	µs	Achieved with phase modulation (a=0.1).
Maximum Simulated T₂	≈ 15	µs	Predicted maximum coherence time (at a≈0.3).
Optimal Modulation Strength (a)	0.1	unitless	Optimized for T₂ improvement and contrast preservation.
Conventional On-Axis T_1ρ	≈ 1800	µs	Relaxation time under conventional spin-locking.
AWG Sampling Rate	1	GHz	Limit of the microwave signal generation hardware.
Relative Amplitude Fluctuation (ΔA/A)	≈ 0.75	%	Measured experimental system error.
Phase Fluctuation (Δφ)	≈ 7	mrad	Measured experimental system error.

Key Methodologies

The experiment successfully implemented time-dependent phase-modulated continuous driving using high-quality MPCVD diamond and precise microwave engineering:

Material Selection and Preparation: Measurements were performed on an isotopically pure ¹²C diamond sample grown via Chemical Vapor Deposition (CVD). This material incorporated a high P1 nitrogen concentration (~ 2 x 10¹⁷ cm^-3) necessary for generating a dense ensemble of NV centers.
Spin Initialization: The NV ensemble state was initialized along the z-axis using a long (~ 10 µs) 532 nm laser pulse, followed by subsequent microwave π/2 pulses to rotate the state to the desired axis (x or y).
Magnetic Field Application: A static external magnetic field (~ 40 Gauss) was used to Zeeman-split the ground state energy levels, allowing resonant targeting of the |0> ↔ |1> transition.
Microwave Control Generation: The continuous driving field (Ω₁) was provided by a standard signal generator. The time-dependent phase modulation (d(t)) was introduced via I/Q modulation using two channels of an Arbitrary Waveform Generator (AWG) operating at a 1 GHz sampling rate.
Decoupling Sequence: The phase-modulated continuous driving was applied, reproducing the effective Hamiltonian H₁₂, which decoupled the spin state from high-frequency spin-bath noise, thereby extending T₂.
Readout and Fidelity Calculation: The fidelity of the final spin state was determined by projecting the state using resonant π/2 pulses onto the z and -z axes. The resulting fluorescence contrast C = (r₁ - r₂) / (r₁ + r₂) quantified the coherence.

6CCVD Solutions & Capabilities

6CCVD provides the specialized MPCVD diamond material and engineering services essential for replicating and scaling the results demonstrated in this breakthrough research. Our products directly address the purity, doping, and surface quality requirements demanded by high-fidelity quantum control experiments.

Applicable Materials

To achieve optimal coherence times and robust NV ensemble performance, 6CCVD recommends:

Optical Grade Single Crystal Diamond (SCD): Required to match or exceed the 99.99% ¹²C isotopic purity used in the study. High-purity SCD minimizes decoherence caused by ¹³C nuclear spins, critical for achieving long T₂ in quantum applications.
Custom Controlled Doping (High NV Density): The research requires Nitrogen concentrations (P1 defects) around 2 x 10¹⁷ cm^-3. 6CCVD specializes in precisely controlling nitrogen incorporation during CVD growth to achieve target concentrations for dense ensemble sensing, ensuring uniform NV yield across the wafer.
Custom Substrates: We provide diamond substrates (up to 10mm thick) that offer superior thermal management and reduced strain for stable, high-power quantum setups.

Customization Potential

The optimization of continuous dynamical decoupling relies heavily on integrating high-frequency microwave components and precise device dimensions. 6CCVD offers full-stack engineering support:

Service	Requirement Satisfied	6CCVD Capability
Custom Dimensions/Shapes	Producing micro-devices or specialized plates required for integrated microwave circuitry.	We supply precision diamond wafers and plates up to 125mm (PCD) and offer custom laser cutting for unique geometries.
Metalization Services	Integrating microwave strip lines, contacts, or antennae directly onto the diamond surface to minimize coupling noise and amplitude/phase fluctuations (a limiting factor in this research).	Internal capability for multi-layer Ti/Pt/Au, W, Cu, Pd metalization stacks, allowing engineers to design optimized on-chip microwave delivery systems.
Ultra-Low Roughness Polishing	Maximizing the signal contrast and minimizing optical scattering loss from the 532 nm excitation laser.	SCD surfaces are polished to Ra < 1 nm, and Inch-size PCD to Ra < 5 nm, ensuring research-grade optical quality.

Engineering Support

The paper identifies that achieving higher phase accuracy in the driving source will further enhance the phase-modulated decoupling technique. 6CCVD’s in-house PhD team provides consultative support on material selection, NV incorporation strategies (implantation vs. in-situ doping), and surface preparation necessary to integrate diamond into complex quantum systems designed to reduce these experimental noise limits.

We assist engineers and scientists in selecting the ideal SCD or PCD material specifications—including thickness (0.1µm - 500µm), doping levels, and surface finishing—for quantum information processing, quantum computing, and high-sensitivity AC magnetometry projects.

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

View Original Abstract

The coherence times achieved with continuous dynamical decoupling techniques\nare often limited by fluctuations in the driving amplitude. In this work, we\nuse time-dependent phase-modulated continuous driving to increase the\nrobustness against such fluctuations in a dense ensemble of nitrogen-vacancy\ncenters in diamond. Considering realistic experimental errors in the system, we\nidentify the optimal modulation strength, and demonstrate an improvement of an\norder of magnitude in the spin-preservation of arbitrary states over\nconventional single continuous driving. The phase-modulated driving exhibits\ncomparable results to previously examined amplitude-modulated techniques, and\nis expected to outperform them in experimental systems having higher phase\naccuracy. The proposed technique could open new avenues for quantum information\nprocessing and many body physics, in systems dominated by high frequency\nspin-bath noise, for which pulsed dynamical decoupling is less effective.\n

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Original Source

DOI: https://doi.org/10.1103/physreva.96.013850