| Metadata | Details |
|---|
| Publication Date | 2020-12-01 |
| Journal | New Journal of Physics |
| Authors | Guoqing Wang, Yi Xiang Liu, Paola Cappellaro, Guoqing Wang, Yi Xiang Liu |
| Institutions | Massachusetts Institute of Technology |
| Citations | 26 |
| Analysis | Full AI Review Included |
This research demonstrates optimal coherence protection for dense ensembles of Nitrogen-Vacancy (NV) center qubits using an optimized Concatenated Continuous Driving (CCD) scheme. The key innovation lies in synchronizing the qubit dynamics to the most robust mode of the resulting Mollow triplet structure.
- Core Achievement: Achieved robust, long-term coherence control over a large ensemble of ~1010 NV spins, overcoming limitations imposed by frequency and driving inhomogeneities.
- Known State Protection: Demonstrated a 500-fold improvement in coherence time (T1ρρ, corresponding to the Mollow center band) for an arbitrary, known initial state by aligning the driving field direction with the state vector.
- Unknown State Protection: Achieved a 15-fold improvement in coherence time (T2ρρ, corresponding to the Mollow sidebands) for generic, unknown states.
- Mechanism Insight: Used Floquet theory and extended the Generalized Bloch Equation (GBE) to analyze decay mechanisms, identifying static field inhomogeneity (Sz(0)) and driving field fluctuations (SΩ(Ω)) as dominant noise sources.
- Robustness: The strong modulation condition significantly improved the center band oscillation contrast, ensuring more spins in the inhomogeneous ensemble are effectively driven and synchronized.
- Engineering Tool: The theoretical framework allows for the reconstruction of the noise Power Spectral Density (PSD) and optimization of driving parameters for maximum coherence.
| Parameter | Value | Unit | Context |
|---|
| Qubit System | ~1010 | spins | Dense NV center ensemble in diamond. |
| Qubit Transition Frequency (ω0/2π) | 2.207 | GHz | Energy gap between |
| Static Magnetic Field (B0) | ~230 | G | Applied along the NV axis to lift degeneracy. |
| Baseline Rabi Coherence (T2ρ) | ~1 | µs | Coherence time under normal Rabi driving. |
| Sideband Coherence (T2ρρ) | ~15 | µs | Coherence time for arbitrary, unknown state (15-fold improvement). |
| Center Band Coherence (T1ρρ) | ~0.5 | ms | Coherence time for arbitrary, known state (500-fold improvement). |
| Modulation Frequency (ωm/2π) | 7.5 | MHz | Typical modulation frequency used in experiments. |
| Driving Inhomogeneity (σΩ) | ~1.6% | Ω | Estimated relative inhomogeneity of the Rabi frequency. |
| Static Field Inhomogeneity (σω/2π) | 0.32 | MHz | Estimated variance of the static field. |
| Green Laser Power | 0.4 | mW | Used for NV initialization and polarization. |
| Microwave Delivery | 0.7 | mm | Loop structure on a PCB board. |
| Nuclear Polarization (14N) | 73% | % | Polarization achieved in the |
- NV Ensemble Setup: A large ensemble of NV centers (~1010 spins) in diamond was used. Microwave control was delivered via a 0.7 mm loop structure on a PCB.
- Initialization and Polarization: A static magnetic field (B0 ≈ 230G) was applied. The NV electronic spin was initialized to |ms=0> and the 14N nuclear spin was polarized (73% in |mI=1>) using a 0.4 mW green laser focused to a 30 µm spot.
- Concatenated Continuous Driving (CCD) Implementation: Coherent control was implemented using an Arbitrary Waveform Generator (AWG) mixing a ~100 MHz frequency with a carrier microwave frequency to generate complex amplitude-modulated or phase-modulated waveforms.
- Mode Control and Synchronization: Driving parameters (Rabi frequency Ω, modulation strength εm, and phases φ0, φm) were precisely tuned to control the qubit evolution mode. Optimal coherence was achieved by synchronizing the state evolution to the Mollow center band (T1ρρ mode).
- Theoretical Modeling: Floquet theory was used to predict the precise dynamics and frequency components (Mollow triplet).
- Noise Analysis: The Generalized Bloch Equation (GBE) framework was extended to the CCD scenario to calculate longitudinal (T1ρρ) and transverse (T2ρρ) relaxation rates based on the Power Spectral Density (PSD) components of noise sources in the rotating frames.
- Parameter Optimization: Experimental coherence times were measured as a function of the second driving strength (εm) to validate the GBE model and identify the optimal driving parameters that minimize the effects of dominant noise sources (Sz(Ω-εm) and SΩ(εm)).
| Application Area | Specific Engineering Relevance |
|---|
| Quantum Sensing | Enables robust, narrow-bandwidth AC magnetic field sensing by utilizing the highly protected Mollow center band mode, improving sensitivity and stability in noisy environments. |
| Robust Pulse Design | Provides a validated theoretical and experimental framework for designing robust quantum control pulses and dynamical decoupling sequences that are inherently resilient to control field fluctuations and static inhomogeneities. |
| Quantum Simulation/Computing | Critical for scaling up ensemble-based quantum systems, allowing for robust collective manipulation and long coherence times in large volumes (1010 spins). |
| Noise Spectroscopy | The GBE extension allows engineers to reconstruct the Power Spectral Density (PSD) of various noise sources (e.g., spin bath, microwave phase noise) affecting the system by analyzing coherence decay rates. |
| Nuclear Spin Protection | The CCD scheme can be used to implement rapid flips of the NV electron spin, enabling indirect protection and enhanced coherence for associated nuclear spins (e.g., 14N). |
View Original Abstract
Abstract Dense ensembles of spin qubits are valuable for quantum applications, even though their coherence protection remains challenging. Continuous dynamical decoupling can protect ensemble qubits from noise while allowing gate operations, but it is hindered by the additional noise introduced by the driving. Concatenated continuous driving (CCD) techniques can, in principle, mitigate this problem. Here we provide deeper insights into the dynamics under CCD, based on Floquet theory, that lead to optimized state protection by adjusting driving parameters in the CCD scheme to induce mode evolution control. We experimentally demonstrate the improved control by simultaneously addressing a dense nitrogen-vacancy (NV) ensemble with 10 10 spins. We achieve an experimental 15-fold improvement in coherence time for an arbitrary, unknown state, and a 500-fold improvement for an arbitrary, known state, corresponding to driving the sidebands and the center band of the resulting Mollow triplet, respectively. We can achieve such coherence time gains by optimizing the driving parameters to take into account the noise affecting our system. By extending the generalized Bloch equation approach to the CCD scenario, we identify the noise sources that dominate the decay mechanisms in NV ensembles, confirm our model by experimental results, and identify the driving strengths yielding optimal coherence. Our results can be directly used to optimize qubit coherence protection under continuous driving and bath driving, and enable applications in robust pulse design and quantum sensing.
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