Wavelet resolved coherence beating in the Overhauser field of a thermal nuclear spin ensemble
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-02-14 |
| Journal | Physical review. B./Physical review. B |
| Authors | Ekrem Taha GĂźldeste, Ceyhun Bulutay |
| Institutions | Bilkent University |
| Citations | 5 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research introduces the Synchrosqueezed Wavelet Transform (SST) as a powerful post-processing tool to analyze coherent dynamics within a Nuclear Spin Bath (NSB) coupled to a Central Spin (CS) qubit.
- Spatial Fingerprinting: SST scalograms reveal unique coherence beating patterns (in the 0Q, 1Q, and 2Q transition channels) that act as fingerprints for the spatial distribution, distance, and alignment of proximal spin clusters relative to the CS.
- Enhanced Spectral Resolution: The SST significantly improves the frequency resolution of the Continuous Wavelet Transform (CWT), allowing simultaneous, high-fidelity observation of both temporal and spectral characteristics of nuclear spin noise.
- Directional Probing: By systematically reorienting the hyperfine (hf) axis (which serves as the spin quantization axis), engineers can directionally probe the NSB environment, enabling the identification of nearest-neighboring spin clusters and their displacement vector alignment.
- Decoherence Mechanism Insight: The beating patterns are shown to originate from small inhomogeneous detunings induced by dipole-dipole interactions among nearly resonant transitions within the NSB.
- Noise Resilience: Wavelet domain thresholding techniques (using the Stationary Wavelet Transform, SWT) are demonstrated to effectively denoise scalograms, successfully recovering the underlying coherence beating patterns even when masked by strong classical noise sources like Random Telegraph Noise (RTN).
- 3D Reconstruction Aid: This wavelet-resolved analysis provides crucial, complementary information that can simplify and enhance the task of 3D reconstruction and atomic-scale imaging of nuclear spin sites.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| CS Zeeman Frequency (Typical) | 1011 | s-1 | Scale for electronic spin under 1 T external field. |
| Hyperfine (hf) Coupling Scale (Typical) | 106 | s-1 | Scale for nuclear spins (NSB). |
| Electron Confinement Radius (L0) | 3.4 | nm | Model parameter for hf coupling distribution. |
| Diamond Lattice Constant (a0) | 3.567 | Angstrom | Used for diamond crystal structure simulations. |
| Silicon Lattice Constant (a0) | 5.43 | Angstrom | Used for silicon crystal structure simulations. |
| Spinful Abundance Ratio (Ď) | 0.01 | None | Example: 13C in diamond (dilute NSB). |
| Spinful Abundance Ratio (Ď) | 0.05 | None | Example: 29Si in silicon. |
| Mean hf Coupling (A) (Simulation) | 13.5 to 13.9 | MHz | Used in Cluster Correlation Expansion (CCE) simulations. |
| RTN Weak Coupling Regime (Ρ) | â 0.01 | None | Noise resilience test parameter (dimensionless). |
| RTN Strong Coupling Regime (Ρ) | â 100 | None | Noise resilience test parameter (dimensionless). |
| RTN Switching Frequency (Î) (Weak) | 10 | kHz | Used in weak noise regime simulation (Fig. 8). |
| RTN Switching Frequency (Î) (Strong) | 100 | kHz | Used in strong noise regime simulation (Fig. 8). |
| CCE Order Used for Dilute NSB | CCE-3 or CCE-4 | None | Required for convergence in long-time dynamics. |
Key Methodologies
Section titled âKey MethodologiesâThe study is computational, employing a specialized pipeline for simulating and analyzing nuclear spin bath dynamics:
- Hamiltonian Formulation: The system is modeled using a pure dephasing Hamiltonian conditioned on the Central Spin (CS) state, incorporating Zeeman, hyperfine (hf), and nuclear dipole-dipole (d-d) interactions.
- Dynamics Calculation (CCE): The two-point correlation function C(t), representing the NSB coherent dynamics, is computed using the Cluster Correlation Expansion (CCE) method. CCE-3 or CCE-4 orders are used to ensure convergence for the long-time behavior of dilute spin baths.
- Initial Time-Frequency Analysis (CWT): The normalized correlation function C(t) is analyzed using the Continuous Wavelet Transform (CWT) with the Bump Wavelet basis function, chosen for its superior frequency domain localization.
- Spectral Sharpening (SST): The Synchrosqueezed Wavelet Transform (SST) is applied to the CWT results. This technique reallocates instantaneous frequencies, dramatically improving the resolution along the frequency axis without sacrificing time resolution.
- Spatial Probing: The hf axis (which defines the spin quantization axis) is rotated relative to the crystal structure. The resulting changes in the frequency and period of the coherence beating patterns (0Q, 1Q, 2Q transitions) are used to deduce the alignment and distance of proximal nuclear spin clusters.
- Noise Modeling: Classical noise is introduced via a stochastic time-dependent term (Random Telegraph Noise, RTN) added to the Hamiltonian, simulating weak (Ρ â 0.01) and strong (Ρ â 100) coupling regimes.
- Denoising: For noise mitigation, the Discrete Stationary Wavelet Transform (SWT) is employed, specifically using the Haar wavelet, combined with careful thresholding of the detailed coefficients at appropriate decomposition levels.
Commercial Applications
Section titled âCommercial ApplicationsâThe findings directly support advancements in quantum technology, particularly in areas requiring high-fidelity control and spatial mapping of solid-state spin environments.
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Quantum Computing and Registers:
- Improving the coherence time and fidelity of solid-state qubits (e.g., NV centers in diamond, quantum dots) by providing detailed spectral and temporal information necessary for designing optimized Dynamical Decoupling (DD) pulse sequences.
- Facilitating the embedding of CS states into proximal nuclear spins for creating long-lived quantum registers.
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Nanoscale Quantum Sensing and NMR:
- Enhancing atomic-scale imaging capabilities by providing a robust method to identify the distance and orientation of specific nuclear spin clusters surrounding a quantum sensor.
- Serving as a complementary post-processing tool for complex nuclear-nuclear double-resonance spectroscopy used in 3D reconstruction of spin environments.
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Materials Science and Defect Engineering:
- Gaining insight into the atomistic level composition and structural defects within semiconductor matrices (e.g., InGaAs quantum dots, Si:P donors, diamond NV centers) by mapping the structural origins of spin noise.
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Signal Processing in Physics:
- Applying advanced multi-resolutional analysis (SST) to experimental time series data in fields beyond spin physics, such as gravitational wave detection or general quantum coherence spectroscopy, where simultaneous high time and frequency resolution is critical.
View Original Abstract
This work introduces the so-called synchrosqueezed wavelet transform, to shed light on the dipolar fluctuations of a thermal ensemble of nuclear spins in a diamond crystal structure, hyperfine-coupled to a central spin. The raw time series of the nuclear spin bath coherent dynamics is acquired through the two-point correlation function computed using the cluster correlation expansion method. The dynamics can be conveniently analyzed according to zero-, single-, and double-quantum transitions derived from the dipolar pairwise spin flips. We show that in the early-time behavior when the coherence is preserved in the spin ensemble, the Overhauser field fluctuations are modulated by dipole-dipole-induced small inhomogeneous detunings of nearly resonant transitions within the bath. The resulting beating extending over relatively longer time intervals is featured on the scalograms where both temporal and spectral behaviors of nuclear spin noise are unveiled simultaneously. Moreover, a second kind of beating that affects faster dynamics is readily discernible, originating from the inhomogeneous spread of the hyperfine coupling of each nucleus with the central spin. Additionally, any quadrupolar nuclei within the bath imprint as beating residing in the zero-quantum channel. The nuclear spin environment can be directionally probed by orienting the hyperfine axis. Thereby, crucial spatial information about the closely separated spin clusters surrounding the central spin are accessible. Thus, a wavelet-based postprocessing can facilitate the identification of proximal nuclear spins as revealed by their unique beating patterns on the scalograms. Finally, when these features are overwhelmed by either weakly or strongly coupled classical noise sources, we demonstrate the efficacy of thresholding techniques in the wavelet domain in denoising contaminated scalograms.