Characterizing spin-bath parameters using conventional and time-asymmetric Hahn-echo sequences
At a Glance
Section titled “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 |
Executive Summary
Section titled “Executive Summary”- Novel Characterization Method: The paper proposes using a single, time-asymmetric Hahn-echo pulse sequence, varying the pulse timing (α), to characterize solid-state spin-bath noise.
- Efficiency and Robustness: This method offers a potential order-of-magnitude reduction in experiment time compared to conventional multi-pulse Dynamical Decoupling (DD) sequences, minimizing vulnerability to long-term drifts and accumulating pulse imperfections.
- Analytical Accuracy: It requires fitting the measured coherence curve to a newly derived explicit analytical function (Eq. 9), demonstrating that common assumptions of a “slow noise regime” lead to inaccurate parameter extraction (e.g., 40% error in coupling strength).
- Precision Improvement: In realistic scenarios dominated by a technical noise floor (simulated at 5%), the asymmetric Hahn-echo scheme improves the precision of extracted parameters (correlation time τc and coupling strength b) by more than a factor of 3 over conventional Hahn-echo fitting.
- Target System: The simulations focus on characterizing the nitrogen paramagnetic impurity bath surrounding nitrogen-vacancy (NV) centers in diamond, a critical system for quantum technologies.
- Engineering Value: Provides a faster, more precise, and computationally simpler alternative to spectral decomposition for quality control and optimization of quantum materials and qubit environments.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Simulated Spin-Bath Correlation Time (τc) | 100 | µs | True value for typical NV center environment. |
| Simulated Spin-Qubit Coupling Strength (b) | 5 | kHz | True value for typical NV center environment. |
| Extracted τc (Asymmetric Fit, 5% Noise Floor) | 95 ± 15 | µs | Achieved precision using the novel method (Factor >3 improvement). |
| Extracted b (Asymmetric Fit, 5% Noise Floor) | 5.00 ± 0.17 | kHz | Achieved precision using the novel method (Factor >3 improvement). |
| Conventional Fit Error (Slow Noise Assumption) | 40 | % | Error in coupling strength (b) if explicit function is not used (b = 2.88 kHz extracted vs. 5 kHz true). |
| Technical Noise Floor (Simulated) | 5 | % | Constant noise floor unmitigable by averaging (e.g., laser/modulator instability). |
| Required Pulse Temporal Resolution | 2 | ns | Minimum resolution required for common pulsing cards to implement the asymmetric scheme. |
| Experiment Time Reduction Potential | Order-of-magnitude | N/A | Reduction compared to multi-pulse spectral decomposition sequences. |
| Precision Improvement Factor | greater than 3 | N/A | Improvement in parameter uncertainty over conventional Hahn-echo fitting under noise floor saturation. |
Key Methodologies
Section titled “Key Methodologies”The proposed method utilizes a time-asymmetric Hahn-echo sequence combined with analytical fitting to extract spin-bath parameters (τc and b).
- Control Sequence Design: A single microwave (π)-pulse is applied during the total free evolution time T at an intermediate time T = αT. The asymmetry parameter α is varied between 0 (Free Induction Decay, FID) and 1 (FID), with α = 0.5 representing the conventional Hahn-echo.
- Coherence Curve Measurement: For a fixed value of α, the total time T is swept, and the coherence function W(T, α) (fidelity between initial and final state) is measured.
- Noise Model Assumption: The method assumes Gaussian statistics for the noise n(t) and a known functional form for the noise spectrum S(ω), specifically a Lorentzian spectrum, which is relevant for spin-baths in solids.
- Analytical Coherence Function: The measured coherence curve W(T, α) is fitted directly to the derived explicit analytical function (Eq. 9), which accounts for both the spin refocusing (due to the π-pulse) and the remaining FID dynamics.
- Parameter Extraction: A simple least-square fitting procedure is used across multiple independent experiments (varying α) to evaluate the realistic noise parameters b and τc.
- Noise Floor Mitigation: By combining data from multiple asymmetric experiments (different α values), the shared parameter pairs are filtered, significantly reducing the uncertainties caused by technical drifts and constant noise floors unmitigable by simple averaging.
Commercial Applications
Section titled “Commercial Applications”This research is foundational for improving the performance and characterization of solid-state quantum devices.
- Quantum Computing and Information Processing (QIP): Essential for characterizing and mitigating decoherence sources in solid-state qubits (e.g., NV centers in diamond, phosphorus donors in silicon) to achieve longer coherence times necessary for scalable quantum processors.
- Quantum Metrology and Sensing: Enables rapid and precise characterization of the noise environment, which is critical for optimizing AC magnetometers and other quantum sensors based on NV centers.
- Materials Engineering and Quality Control: Provides a fast, standardized method for material scientists to assess the quality of quantum materials (like isotopically purified diamond or silicon) by quantifying the density (b) and dynamics (τc) of residual paramagnetic impurities.
- Advanced Semiconductor Devices: Applicable to any solid-state system where spin dynamics are limited by a surrounding spin-bath, aiding in the development of next-generation spintronic and quantum memory devices.
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