Characterizing spin-bath parameters using conventional and time-asymmetric Hahn-echo sequences

At a Glance

Metadata	Details
Publication Date	2020-03-09
Journal	Physical review. B./Physical review. B
Authors	Demitry Farfurnik, Nir Bar‐Gill
Institutions	Hebrew University of Jerusalem
Citations	6
Analysis	Full AI Review Included

Technical Documentation & Analysis: Spin-Bath Characterization in Diamond Qubits

6CCVD Reference Document: QUBIT-HE-2020-001 Source Paper: Farfurnik & Bar-Gill, “Characterizing spin-bath parameters using conventional and time-asymmetric Hahn-echo sequences” (arXiv:1904.01233v3)

Executive Summary

This research proposes a highly efficient, single-pulse method for characterizing spin-bath noise in solid-state quantum systems, specifically utilizing Nitrogen-Vacancy (NV) centers in diamond. The core value proposition for engineers and scientists is the significant reduction in experimental complexity and time required for noise spectroscopy.

Novel Methodology: Introduction of a time-asymmetric Hahn-echo sequence (single $\pi$-pulse applied at $T_{p} = \alpha T$) to extract spin-bath correlation time ($\tau_{c}$) and coupling strength ($b$).
Enhanced Accuracy: The method requires fitting coherence curves to the explicit general physical expression (Eq. 9), avoiding the inaccurate “slow noise regime” assumption often used in conventional analysis.
Mitigation of Technical Drifts: By combining data from multiple asymmetry parameters ($\alpha$), the technique effectively filters out the effects of long time-scale technical drifts and constant noise floors (e.g., 5% noise floor simulated).
Precision Improvement: Simulations demonstrate a factor of >3 improvement in the precision of extracted parameters ($b$ and $\tau_{c}$) compared to conventional Hahn-echo fitting under realistic noise conditions.
Efficiency Gains: The single-pulse approach offers an order-of-magnitude reduction in total experiment time compared to complex, multi-pulse Dynamical Decoupling (DD) sequences (e.g., CPMG, DYSCO).
Material Requirement: Successful implementation relies critically on high-quality, low-nitrogen Single Crystal Diamond (SCD) to achieve the long coherence times ($T_{2}$) necessary for effective spin-bath characterization.

Technical Specifications

The following hard data points were extracted from the simulation and experimental requirements outlined in the paper:

Parameter	Value	Unit	Context
Simulated Correlation Time ($\tau_{c}$)	100	µs	Target for typical ppm Nitrogen regime
Simulated Coupling Strength ($b$)	5	kHz	Target for typical ppm Nitrogen regime
Extracted $\tau_{c}$ (Asymmetric Method)	$95 \pm 15$	µs	Achieved precision under 5% noise floor
Extracted $b$ (Asymmetric Method)	$5.00 \pm 0.17$	kHz	Achieved precision under 5% noise floor
Measurement Noise Floor	5	%	Realistic experimental scenario
Parameter Uncertainty Improvement	>3	Factor	Improvement over conventional Hahn-echo fitting
Pulse Temporal Resolution	2	ns	Required for $\pi$-pulse implementation
Coherence Time Ratio Requirement	$T_{2}(\alpha=0.5)/T_{2}^{*} < 100$	Ratio	Requirement for effective asymmetric Hahn-echo
Asymmetry Parameters ($\alpha$) Used	0, 0.1, 0.2, 0.3, 0.4, 0.5	N/A	Set of independent experiments

Key Methodologies

The proposed noise characterization method relies on precise microwave (MW) control and advanced data analysis:

Qubit Initialization: The addressable spin qubit (NV center) is initialized to a specific state.
Control Sequence Application: A single resonant MW $\pi$-pulse (Hahn-echo) is applied during the free evolution time $T$.
Asymmetry Variation: The pulse timing is varied by setting the asymmetry parameter $\alpha$ such that the pulse occurs at $T_{p} = \alpha T$, where $0 < \alpha < 1$.
Coherence Measurement: The total evolution time $T$ is swept while $\alpha$ is held constant, yielding the coherence curve $W(T, \alpha)$.
Explicit Fitting: The measured coherence curve is fitted using a least-square algorithm to the explicit coherence function (Eq. 9), which is derived assuming Gaussian statistics and a Lorentzian noise spectrum.
Parameter Extraction: The correlation time ($\tau_{c}$) and coupling strength ($b$) are extracted.
Drift Mitigation: Data from multiple independent $\alpha$ experiments are intersected to filter the shared parameter pairs, significantly reducing uncertainties caused by technical drifts and noise floors.

6CCVD Solutions & Capabilities

This research highlights the critical need for high-purity diamond materials and precision fabrication to enable next-generation quantum sensing and information processing. 6CCVD is uniquely positioned to supply the required materials and custom engineering services.

Applicable Materials

The long coherence times ($\tau_{c} = 100$ µs) simulated in this paper are only achievable in diamond with extremely low concentrations of background nitrogen impurities (P1 centers), which form the dominant spin bath.

6CCVD Material Solution	Specification & Relevance
Electronic Grade Single Crystal Diamond (SCD)	Requirement: Ultra-low nitrogen concentration (Type IIa, typically < 1 ppm N). This purity is essential to minimize the density of P1 centers, thereby maximizing the spin-bath correlation time ($\tau_{c}$) and the qubit coherence time ($T_{2}$).
Optical Grade SCD	Requirement: High optical quality for efficient NV center initialization and readout via laser excitation and photon detection.
Custom SCD Thickness	Capability: SCD plates available from 0.1 µm up to 500 µm thickness, allowing optimization for specific MW coupling geometries or integration into complex device stacks.

Customization Potential

The implementation of Hahn-echo sequences requires precise microwave delivery, often achieved using on-chip strip lines or antennas fabricated directly onto the diamond surface.

Research Requirement	6CCVD Customization Service
Microwave Pulse Delivery	Custom Metalization: We offer internal metalization capabilities including Ti, Pt, Au, Pd, W, and Cu deposition. This is crucial for fabricating high-frequency MW strip lines directly onto the SCD surface for precise $\pi$-pulse generation.
Device Integration & Geometry	Custom Dimensions & Polishing: We provide SCD plates with ultra-low surface roughness (Ra < 1 nm) to ensure minimal surface defects that could introduce additional noise. Custom dimensions and laser cutting services ensure seamless integration into existing quantum setups.
Large-Scale Integration	PCD Wafers: For scaling up quantum devices or sensing arrays, 6CCVD offers Polycrystalline Diamond (PCD) wafers up to 125 mm in diameter, with thicknesses up to 500 µm and polishing down to Ra < 5 nm.

Engineering Support

The successful replication and extension of this work—moving from theoretical simulation to robust experimental implementation—requires deep expertise in solid-state spin dynamics and MPCVD material science.

In-House PhD Team: 6CCVD’s engineering and scientific staff, holding advanced degrees in materials science and physics, are available to consult on material selection, nitrogen doping control, and surface preparation protocols necessary for similar NV Center Quantum Sensing and Spectroscopy projects.
Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) of sensitive diamond materials, supporting research teams worldwide.

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

View Original Abstract

Spin-bath noise characterization, which is typically performed by multi-pulse\ncontrol sequences, is essential for understanding most spin dynamics in the\nsolid-state. Here, we theoretically propose a method for extracting the\ncharacteristic parameters of a noise source with a known spectrum, using a\nsingle modified Hahn-echo sequence. By varying the application time of the\npulse, measuring the coherence curves of an addressable spin, and fitting the\ndecay coefficients to a theoretical function derived by us, we extract\nparameters characterizing the physical nature of the noise. Assuming a\nLorentzian noise spectrum, we illustrate this method for extracting the\ncorrelation time of a bath of nitrogen paramagnetic impurities in diamond, and\nits coupling strength to the addressable spin of a nitrogen-vacancy center.\nConsidering a realistic experimental scenario with $5\%$ measurement error, the\nparameters can be extracted with an accuracy of $\sim 10 \%$. The scheme is\neffective for samples having a natural homogeneous coherence time ($T_2$) up to\ntwo orders of magnitude greater than the inhomogeneous coherence time\n($T_2^*$), and mitigates technical noise when further averaging is irrelevant.\nBeyond its potential for reducing experiment times by an order-of-magnitude,\nsuch single-pulse noise characterization could minimize the effects of long\ntime-scale drifts and accumulating pulse imperfections and numerical errors.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.101.104306