Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-08-11 |
| Journal | Scientific Reports |
| Authors | Jeson Chen, Oliver Y. Chén, Huan‐Cheng Chang |
| Institutions | Institute of Atomic and Molecular Sciences, Academia Sinica, Feng Chia University |
| Citations | 5 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research investigates the fundamental spin relaxation dynamics, specifically the baseline decay (Tb), in dense ensembles of negatively charged nitrogen-vacancy (NV-) centers in diamond under continuous microwave (MW) driving.
- Core Achievement: First in-depth experimental measurement and analysis of the simple exponential (baseline) decay component of damped Rabi oscillations (RO) in high-density NV- ensembles.
- Power Dependence: The baseline decay time (Tb) decreases significantly (up to 50%) as the MW magnetic field strength (Rabi frequency, ΩR) increases, particularly above 1 MHz.
- Frequency Dependence: The dependence of Tb on MW detuning (δ) exhibits a clear Lorentzian-like spectral profile, with the minimum Tb occurring at the ODMR resonance frequency.
- Modeling Success: Excellent agreement between experimental Tb spectra and numerical simulations based on the Bloch formalism was achieved only after incorporating the effect of inhomogeneous broadening (modeled with a 7 MHz Lorentzian width).
- Decoherence Insight: The study confirms that MW-driven spin relaxation in dense ensembles consists of two distinct components: a fast, microsecond-scale oscillatory decay (Tr) and a slower, millisecond-scale baseline decay (Tb).
- Material Metrics: Measured intrinsic relaxation times were T1 = 1491 ± 257 µs and T2 = 1.70 ± 0.13 µs, highlighting the severe reduction in T2 coherence time typical of dense, Type-Ib diamond.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV Center Density | ~10 | ppm | Concentration in Type-Ib diamond microcrystal. |
| Substitutional N Density | ~150 | ppm | Concentration of intrinsic defects in the host matrix. |
| Sample Size | ~100 | µm | Diameter of the Fluorescent Microdiamond (FMD) crystal. |
| Laser Wavelength | 532 | nm | Continuous-wave (CW) laser for optical pumping and probing. |
| Laser Power Density | ~1 | kW/cm2 | Used throughout the study to minimize charge recombination effects. |
| Static Magnetic Field (B||) | ~6.6 | mT | Applied to lift the spin degeneracy (Zeeman splitting). |
| Zero Field Splitting (D) | 2.87 | GHz | Ground state transition frequency ( |
| Spin-Lattice Relaxation (T1) | 1491 ± 257 | µs | Measured intrinsic longitudinal relaxation time. |
| Spin-Spin Relaxation (T2) | 1.70 ± 0.13 | µs | Measured bath-decoupled transverse coherence time (Hahn echo). |
| Initialization Pulse Duration | 300 | µs | Optimized duration to reach saturation of spin polarization. |
| Readout Pulse Duration | 0.5 | µs | Minimum duration used for optical detection. |
| Inhomogeneous Broadening (Δωfs/2π) | ~7 | MHz | Width required in simulation for accurate frequency dependence modeling. |
| Baseline Decay Time (Tb) Change | Up to 50 | % | Decrease observed when Rabi frequency (ΩR/2π) exceeds 1 MHz. |
Key Methodologies
Section titled “Key Methodologies”The experiment utilized a home-built wide-field fluorescence imaging setup combined with pulsed laser and MW control sequences to measure spin relaxation dynamics.
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Experimental Setup:
- A 532 nm CW laser was used for optical pumping and probing, controlled by an acoustic optical modulator (AOM).
- Fluorescence was collected via a 40x objective and detected by an Intensified Charge-Coupled Device (ICCD) camera.
- MW fields were generated by a synthesizer and amplifier, fed through a gold wire placed approximately 5 µm from the FMD sample.
- A static magnetic field (B|| ≈ 6.6 mT) was applied to lift the spin degeneracy.
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Pulse Sequence and Normalization:
- The measurement sequence consisted of a laser initialization pulse (300 µs), followed by a variable delay time (t) where MW was applied (for driven relaxation) or absent (for MW-free depolarization), and concluded with an optical readout pulse (0.5 µs).
- Signals were normalized by alternating between a signal frame (variable t) and a reference frame (fixed 2 µs delay) to correct for low-frequency noise and laser intensity drift.
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Relaxation Time Characterization:
- MW-Free Depolarization: Measured using the sequence without MW driving; fitted with a stretched-exponential function (β ≈ 0.5) to determine the MW-off decay time (Toff).
- Intrinsic Times: T1 was measured using MW π pulses and optical readout; T2 was measured using the Hahn echo sequence.
- MW-Driven Baseline Decay (Tb): Measured by applying CW MW during the variable delay t; data fitted using a double-stretched exponential model (Eq. 3) to account for contributions from both MW-resonant and non-resonant NV- centers.
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Theoretical Modeling:
- The spin dynamics of a single NV center were modeled using the Bloch equations (density matrix formalism).
- The analytical solution for the baseline decay rate (1/Tb) was derived, showing dependence on Rabi frequency (ΩR), detuning (δ), T1, and T2.
- To match the experimental results from the dense ensemble, the single-spin Tb solution was convoluted with a Lorentzian function representing the 7 MHz inhomogeneous broadening (Δωfs/2π).
Commercial Applications
Section titled “Commercial Applications”The fundamental understanding of spin relaxation under continuous driving fields in dense NV ensembles is crucial for advancing solid-state quantum technologies, particularly those relying on high-density defect materials.
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Quantum Metrology and Sensing:
- High-Density Sensors: Enables better design and optimization of ensemble NV- sensors for large-scale sensing applications (e.g., magnetic field, temperature, strain) where high signal-to-noise ratio is critical.
- Continuous Wave Sensing: Provides a framework for understanding and optimizing CW-ODMR protocols, which are often used for high-bandwidth or continuous monitoring.
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Quantum Information Processing:
- Ensemble Quantum Computing: Essential for developing schemes for ensemble quantum computation, where the short coherence time (T2) and complex relaxation dynamics must be managed.
- Qubit Control Fidelity: The analysis of baseline decay (Tb) helps isolate and mitigate decoherence mechanisms that limit the fidelity of continuous quantum operations.
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Solid-State Physics and Materials Science:
- Defect Characterization: Provides a sensitive method to characterize the effects of spin baths and inhomogeneous broadening in high-defect-density solid-state materials beyond diamond.
- Dressed State Physics: The observed discrepancies at high MW power suggest the need for models incorporating dressed spin states, paving the way for advanced control techniques like decoherence suppression.