Optimal control of a nitrogen-vacancy spin ensemble in diamond for sensing in the pulsed domain
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-07-05 |
| Journal | Physical review. B./Physical review. B |
| Authors | Andreas F. L. Poulsen, Joshua D. Clement, James L. Webb, Rasmus Høy Jensen, Luca Troise |
| Institutions | Technical University of Denmark |
| Citations | 20 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Core Achievement: Demonstrated robust, coherent optimal control over a large, macroscopic ensemble of up to 4 x 109 Nitrogen-Vacancy (NV) centers in off-the-shelf diamond, overcoming challenges posed by spatial inhomogeneity.
- Sensitivity Gain: Shaped microwave control pulses, designed using Floquet theory and optimal control, achieved an 11% enhancement in the Optically Detected Magnetic Resonance (ODMR) slope (Câ) compared to the best conventional three-frequency flat pulse scheme.
- Performance Benchmark: This enhancement translates to a 78% improvement in sensitivity compared to standard single-frequency flat (Ď-)pulses commonly used in coherent control literature.
- Methodology Advancement: The optimal control algorithm explicitly included the effects of the 14N hyperfine interaction and ensemble inhomogeneity (detuning and Rabi frequency variation) to ensure simultaneous high-fidelity state transfer across all relevant spin transitions.
- Readout Optimization: Dynamical modeling showed that reliable, hysteresis-free contrast measurements can be achieved using short laser reinitialization pulses (3 ms), effectively controlling the high-intensity core (â 25% or 1 billion NV centers) of the ensemble, thereby maximizing measurement bandwidth.
- Practical Application: The successful operation at low Rabi frequencies (1.4 MHz) proves the viability of this technique for compact, low-power portable quantum sensor devices.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Grade | Optical-grade (Element 6) | N/A | Off-the-shelf material used. |
| NV- Concentration | ~0.5 | ppb | Bulk concentration. |
| Diamond Dimensions | 5 x 5 x 1.2 | mm3 | Sample size. |
| T1 Coherence Time | 7.1 | ms | Ensemble average measurement. |
| T2 Coherence Time | 7.0 | Âľs | Ensemble average measurement. |
| T2* Coherence Time | 0.44 | Âľs | Ensemble average measurement. |
| Maximum Ensemble Rabi Frequency (Rmax) | 3.2 | MHz | Maximum achievable experimental frequency. |
| Optimized Shaped Pulse Duration (tp) | 1.85 | Âľs | Duration of the best-performing pulse. |
| Microwave Carrier Frequency (ĎD) | â 2.8 | GHz | NV ground state splitting (with bias field). |
| 14N Hyperfine Splitting (δI) | 2.16 | MHz | Separation between hyperfine resonances. |
| Laser Wavelength | 532 | nm | DPSS pump laser. |
| Maximum Laser Power | 500 | mW | Delivered to the diamond. |
| Estimated Total Ensemble Size | â 4 x 109 | NV centers | Based on fluorescence emission volume. |
| Contributing Ensemble Size (Readout Core) | â 1 | billion | NV centers |
| Sensitivity Improvement (vs. 3-Freq Flat) | 11 | % | Increase in ODMR slope Câ. |
| Sensitivity Improvement (vs. Single-Freq Flat) | 78 | % | Increase in ODMR slope Câ. |
| Estimated Shot-Noise Sensitivity (Ρ) | â 10 | nT/sqrt(Hz) | Sensitivity estimate for the current setup. |
| Minimum Reinitialization Time (tI) | 3 | ms | Required for hysteresis-free contrast. |
Key Methodologies
Section titled âKey Methodologiesâ- Optimal Control Pulse Design: Shaped microwave pulses (defined by In-phase I(t) and Quadrature Q(t) components) were generated using smooth optimal control theory, maximizing the state transfer fidelity (Fst) from the bright state (|0>) to the dark state (|-1>).
- Floquet Theory Integration: The time-periodic Hamiltonian describing the system was solved using Floquet theory, allowing the explicit inclusion of the 14N hyperfine splitting (three levels) into the optimization algorithm.
- Ensemble Inhomogeneity Modeling: The optimization maximized the weighted average fidelity across a representative ensemble (12x12 defects) that modeled Gaussian distributions of frequency detuning (Î) and relative control amplitude (â) inhomogeneity.
- Pulse Generation and Delivery: Control pulses were created by an Arbitrary Waveform Generator (AWG) performing IQ modulation of a 2.8 GHz RF signal. The signal was amplified and delivered to the diamond via a near-field square split-ring resonator antenna.
- Pulsed ODMR Sequence: A repeating sequence was used: laser initialization (tI), microwave control pulse (tp), and laser readout (tR). The minimum tI was set to 3 ms to ensure reliable reinitialization of the high-intensity core of the ensemble.
- Noise Reduction Readout: Fluorescence was collected by an Avalanche Photodiode (APD). Contrast (C) was measured using software lock-in detection against a reference photodetector (Vref) to reject common-mode DC and high-frequency laser technical noise.
- Performance Quantification: The sensitivity of the control pulse was quantified by measuring the maximum slope (Câ) of the resulting ODMR spectrum, which is directly proportional to the sensorâs response strength.
Commercial Applications
Section titled âCommercial Applicationsâ- DC and Low-Frequency Quantum Sensing: The demonstrated robust control is ideal for applications requiring high sensitivity in the DC to low-frequency range, such as measuring slowly varying magnetic fields or temperature changes where long coherence times are beneficial.
- Biosensing and Medical Diagnostics: Diamondâs robustness and biocompatibility, combined with enhanced sensitivity, enable high-precision magnetic imaging of biological samples, including single-neuron action potential detection and real-time thermometry in living cells.
- Nanoscale Magnetic Resonance: The technique provides improved coherent control for large ensembles, enhancing the signal-to-noise ratio for bulk nanoscale Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR) experiments.
- Portable Sensor Devices: The ability to achieve high performance using low Rabi frequencies (low microwave power) makes this methodology suitable for integration into compact, battery-operated quantum magnetometer systems.
- Solid-State Quantum Computing/Control: The methodology for designing robust control pulses that compensate for inhomogeneous broadening is transferable to other solid-state quantum systems (e.g., defects in 2D materials) where coherent manipulation of large, imperfect ensembles is required.
View Original Abstract
Defects in solid state materials provide an ideal, robust platform for quantum sensing. To deliver maximum sensitivity, a large ensemble of non-interacting defects hosting coherent quantum states are required. Control of such an ensemble is challenging due to the spatial variation in both the defect energy levels and in any control field across a macroscopic sample. In this work we experimentally demonstrate that we can overcome these challenges using Floquet theory and optimal control optimization methods to efficiently and coherently control a large defect ensemble, suitable for sensing. We apply our methods experimentally to a spin ensemble of up to 4 $\times$ 10$^9$ nitrogen vacancy (NV) centers in diamond. By considering the physics of the system and explicitly including the hyperfine interaction in the optimization, we design shaped microwave control pulses that can outperform conventional ($\pi$-) pulses when applied to sensing of temperature or magnetic field, with a potential sensitivity improvement between 11 and 78%. Through dynamical modelling of the behaviour of the ensemble, we shed light on the physical behaviour of the ensemble system and propose new routes for further improvement.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
Section titled âReferencesâ- 2016 - Quantum Optics