Coherence protection and decay mechanism in qubit ensembles under concatenated continuous driving

At a Glance

Metadata	Details
Publication Date	2020-12-01
Journal	New Journal of Physics
Authors	Guoqing Wang, Yi Xiang Liu, Paola Cappellaro, Guoqing Wang, Yi Xiang Liu
Institutions	Massachusetts Institute of Technology
Citations	26
Analysis	Full AI Review Included

Technical Documentation & Analysis: Coherence Protection in NV Ensembles via CCD

Executive Summary

This research demonstrates a highly effective method for protecting qubit coherence in large, dense Nitrogen-Vacancy (NV) ensembles using Concatenated Continuous Driving (CCD), achieving coherence times previously limited to single-qubit systems.

Record Coherence Enhancement: The CCD scheme achieved a 500-fold improvement in coherence time (T_1ρρ) for known, arbitrary quantum states, reaching approximately 0.5 ms.
Scalability Demonstrated: The experiments successfully manipulated and protected the coherence of a massive ensemble containing 10¹⁰ NV spins simultaneously, validating the technique for large-scale quantum sensing and simulation.
Mode Control for Robustness: By synchronizing the qubit state evolution to the Mollow triplet center band, the protocol achieved robustness against frequency and driving field inhomogeneities inherent in large ensembles.
Material Requirement: The success hinges on high-quality, low-strain diamond substrates suitable for creating dense NV ensembles and integrating complex microwave control structures.
6CCVD Value Proposition: 6CCVD provides the necessary Single Crystal Diamond (SCD) substrates, offering superior purity, large dimensions (up to 125mm PCD), and ultra-low surface roughness (Ra < 1nm) critical for minimizing noise and maximizing coherence.
Engineering Insight: The study provides a generalized Bloch equation (GBE) framework to analyze noise sources (S_x, S_z, S_Ω, S_εm), enabling precise optimization of driving parameters for future robust pulse design.

Technical Specifications

Parameter	Value	Unit	Context
Qubit System	Dense NV Ensemble	N/A	~10¹⁰ spins addressed simultaneously
NV Transition Energy Gap	2.207	GHz
Static Magnetic Field (B₀)	~230	G	Applied along the NV axis
Normal Rabi Coherence Time (T_2ρ)	~1	µs	Coherence limit without CCD
Improved Sideband Coherence (T_2ρρ)	~15	µs	15-fold improvement (arbitrary, unknown state)
Improved Center Band Coherence (T_1ρρ)	~0.5	ms	500-fold improvement (arbitrary, known state)
Modulation Frequency (ω_m/2π)	7.5	MHz	Used for strong modulation experiments
Rabi Frequency (Ω/2π)	7.5	MHz	Used for strong modulation experiments
Laser Spot Size	30	µm	Used for green laser illumination (0.4mW)
Driving Inhomogeneity (σ_Ω)	~1.6	%Ω	Estimated distribution parameter
Static Field Inhomogeneity (σ_ω/2π)	0.32	MHz	Estimated distribution parameter

Key Methodologies

The experiment utilized a highly controlled setup involving NV centers in diamond, leveraging advanced microwave control techniques and theoretical modeling:

NV Ensemble Preparation: A dense ensemble of NV centers in a diamond substrate was initialized using 0.4mW green laser illumination focused to a 30µm spot, polarizing the electronic spin to |m_s = 0> and the ¹⁴N nuclear spin to |m_I = 1>.
Microwave Delivery & Control: Coherent control was implemented using an arbitrary waveform generator mixing a ~100MHz frequency with a carrier microwave frequency, delivered via a 0.7mm loop structure on a PCB.
Concatenated Continuous Driving (CCD): The CCD scheme was applied using amplitude-modulated or phase-modulated waveforms, consisting of multiple resonant modulated fields to combat external noise and control field fluctuations.
Mode Evolution Control: By tuning the driving phases (φ₀, φ_m), the effective driving field in the second rotating frame was aligned with the initial state, synchronizing the evolution to the robust Mollow triplet center band (T_1ρρ mode).
Theoretical Modeling: Floquet theory was used to predict the dynamics, giving rise to the Mollow triplet structure. The generalized Bloch equation (GBE) framework was extended to the CCD scenario to analyze the Power Spectral Density (PSD) of various noise sources (S_x, S_z, S_Ω, S_εm) and optimize coherence times.
Inhomogeneity Characterization: The power and detuning dependence of the Rabi coherence were measured and simulated to extract the inhomogeneity distributions of the driving field (σ_Ω) and the static field (σ_ω).

6CCVD Solutions & Capabilities

The successful replication and extension of this high-impact quantum research require diamond materials with exceptional purity, precise geometry, and advanced surface preparation—all core competencies of 6CCVD.

Applicable Materials

Research Requirement	6CCVD Solution	Technical Advantage
High Purity Substrate	Optical Grade Single Crystal Diamond (SCD)	Essential for minimizing background defects and maximizing NV creation yield and homogeneity. SCD offers the lowest strain and highest thermal conductivity.
Large Ensemble Area	Polycrystalline Diamond (PCD) Plates	For scaling up quantum sensing arrays beyond current limits, 6CCVD offers PCD plates up to 125mm in diameter, providing large-area coverage for 10¹⁰+ spin ensembles.
Noise Characterization	Boron-Doped Diamond (BDD)	For related electrochemical or sensing applications, BDD films (0.1µm - 500µm) offer tunable conductivity and robust chemical inertness.

Customization Potential

The complexity of the CCD experiment, which relies on precise microwave delivery and optical access, highlights the need for custom material engineering:

Custom Dimensions and Thickness: The experiment requires a substrate large enough to support a 10¹⁰ spin ensemble. 6CCVD provides custom SCD/PCD plates and wafers up to 125mm and substrate thicknesses up to 10mm, ensuring compatibility with large-scale quantum setups.
Integrated Microwave Structures: The paper uses a 0.7mm loop structure. 6CCVD offers in-house metalization services (Au, Pt, Pd, Ti, W, Cu) allowing researchers to pattern microwave transmission lines (e.g., coplanar waveguides) directly onto the diamond surface for superior coupling and reduced noise.
Ultra-Low Surface Roughness: Surface noise is a major decoherence mechanism. 6CCVD guarantees superior polishing: Ra < 1nm for SCD and Ra < 5nm for inch-size PCD, minimizing surface-related spin relaxation.
Precision Laser Cutting: For integrating the diamond into complex PCB or cryogenic setups, 6CCVD offers precision laser cutting to achieve unique geometries and tight tolerances required for optimal microwave coupling and optical alignment.

Engineering Support

The analysis of noise sources (S_Ω, S_εm, S_x, S_z) via the generalized Bloch equation is critical for optimizing CCD performance. 6CCVD’s in-house PhD team specializes in the material science underlying these quantum defects and can assist researchers with:

Material Selection: Guiding the choice between SCD and PCD based on required NV density, optical access, and thermal management for similar Robust Pulse Design and Quantum Sensing projects.
Defect Engineering: Consulting on optimal growth parameters and post-processing techniques (e.g., implantation, annealing) to achieve desired NV concentration and depth profiles.
Global Logistics: Ensuring reliable, fast global shipping (DDU default, DDP available) for time-sensitive research projects worldwide.

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

View Original Abstract

Abstract Dense ensembles of spin qubits are valuable for quantum applications, even though their coherence protection remains challenging. Continuous dynamical decoupling can protect ensemble qubits from noise while allowing gate operations, but it is hindered by the additional noise introduced by the driving. Concatenated continuous driving (CCD) techniques can, in principle, mitigate this problem. Here we provide deeper insights into the dynamics under CCD, based on Floquet theory, that lead to optimized state protection by adjusting driving parameters in the CCD scheme to induce mode evolution control. We experimentally demonstrate the improved control by simultaneously addressing a dense nitrogen-vacancy (NV) ensemble with 10 10 spins. We achieve an experimental 15-fold improvement in coherence time for an arbitrary, unknown state, and a 500-fold improvement for an arbitrary, known state, corresponding to driving the sidebands and the center band of the resulting Mollow triplet, respectively. We can achieve such coherence time gains by optimizing the driving parameters to take into account the noise affecting our system. By extending the generalized Bloch equation approach to the CCD scenario, we identify the noise sources that dominate the decay mechanisms in NV ensembles, confirm our model by experimental results, and identify the driving strengths yielding optimal coherence. Our results can be directly used to optimize qubit coherence protection under continuous driving and bath driving, and enable applications in robust pulse design and quantum sensing.

Tech Support

Original Source

DOI: https://doi.org/10.1088/1367-2630/abd2e5

References

1950 - Spin echoes [Crossref]
1954 - Effects of diffusion on free precession in nuclear magnetic resonance experiments [Crossref]
1958 - Modified spin-echo method for measuring nuclear relaxation times [Crossref]
2010 - Robust decoupling techniques to extend quantum coherence in diamond [Crossref]
2012 - Robust dynamical decoupling [Crossref]
2007 - Keeping a quantum bit alive by optimized π-pulse sequences [Crossref]
2008 - Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation [Crossref]
2009 - Optimized dynamical decoupling in a model quantum memory [Crossref]
2010 - Universal dynamical decoupling: two-qubit states and beyond [Crossref]
2003 - Robust dynamical decoupling of quantum systems with bounded controls [Crossref]