| Metadata | Details |
|---|
| Publication Date | 2020-04-13 |
| Journal | Physical review. B./Physical review. B |
| Authors | Damian Kwiatkowski, Piotr SzaĆkowski, Ćukasz CywiĆski |
| Institutions | Polish Academy of Sciences, Institute of Physics |
| Citations | 22 |
| Analysis | Full AI Review Included |
- Quantum Noise Signature: The study demonstrates that Dynamic Nuclear Polarization (DNP) applied to the 13C nuclear spin bath surrounding an NV center qubit induces a non-trivial, time-dependent phase shift (Ί(t)) in the spin echo coherence signal.
- Biased Coupling Requirement: This phase shift is significant only for qubits utilizing a âbiasedâ coupling (e.g., NV states m=0 and m=1), where the coupling strength depends on the qubit state (analogous to Hint ~ (1 + Ïz)V).
- Validation of Quantum Environment: The observation of this phase shift, even when the decoherence is well-described by the Gaussian approximation, serves as an unambiguous signature that the nuclear environment acts as a source of quantum noise (mediating qubit self-interaction), rather than a simple external classical noise field.
- Local DNP Probe: The amplitude of the phase shift is primarily determined by the nuclear polarization within a small radius (â 2 nm) of the NV center, making the qubit an effective local probe for measuring DNP efficiency.
- Non-Gaussian Witness: Comparing the coherence signals between biased (m=0, m=1) and unbiased (m=±1) NV qubits provides a method to detect non-Gaussian features in the environmental fluctuations.
- Applicability: The results are relevant for optimizing dynamical decoupling sequences and improving coherence times in solid-state qubits, including NV centers, quantum dots, and singlet-triplet qubits.
| Parameter | Value | Unit | Context |
|---|
| Qubit System | Nitrogen-Vacancy (NV) Center | N/A | Based on S=1 electronic spin manifold. |
| Environmental Nuclei | 13C | N/A | Spin-1/2 nuclear bath (natural concentration 1.1%). |
| Magnetic Field (B0) | 15.6 | mT | Standard field for single-nucleus dynamics studies. |
| Zero-Field Splitting (Î) | 2.87 | GHz | Intrinsic property of the NV center. |
| Electron Gyromagnetic Ratio (γe) | 28.02 | GHz/T | Used for calculating Zeeman splitting (Ω). |
| 13C Gyromagnetic Ratio (Îł) | 10.71 | MHz/T | Used for calculating nuclear Zeeman splitting (Ï). |
| Maximum Evolution Time (t) | 50 | ”s | Timescale where inter-nuclear interactions are negligible (CCE-1 approximation valid). |
| Critical Polarization (p) | â 0.5 | N/A | Required polarization degree for observable phase shift amplitude (up to a fraction of Ï). |
| Critical Polarization Radius (Rpol) | â 2 | nm | Distance from NV center determining the phase amplitude saturation. |
| Revival Period (Spin Echo) | â 10 | ”s | Characteristic period of spin echo oscillations at B0 = 15.6 mT. |
| Biased Coupling Manifold | { | 1, 0>, | 1, 1>} |
| Unbiased Coupling Manifold | { | 1, 1>, | 1, -1>} |
- Qubit Manifold Selection: The NV center S=1 ground state was used to define two effective qubit types: the biased coupling qubit (based on m=0 and m=1 states, where the coupling parameter η = 1) and the unbiased coupling qubit (based on m=±1 states, where η = 0).
- Hamiltonian Formulation: The system Hamiltonian included the NV center Zeeman and zero-field splitting terms, the hyperfine coupling (V) between the electronic spin and the nuclear bath, and the nuclear bath Hamiltonian (HE) incorporating Zeeman splitting and secular dipolar coupling (Bkl).
- Dynamic Nuclear Polarization (DNP) Initialization: The environment was modeled as being prepared in a polarized state (ÏE(0)), where the polarization pk of individual nuclei was varied (0.0 to 1.0) and limited to a specific radius (Rpol) around the NV center.
- Coherence Calculation via CCE-1: The spin echo coherence function W(t) was calculated using the Cluster-Correlation Expansion (CCE) method, specifically the CCE-1 approximation. This method treats each nuclear spin as an independent contributor, which is valid for the short timescales (t < 50 ”s) and low magnetic fields (B0 = 15.6 mT) studied.
- Approximation Analysis: The exact CCE-1 results were compared against the Weak-Coupling Approximation and the Gaussian Approximation to analytically derive and verify the conditions for the appearance of the bias-induced phase shift Ί(t).
- Spatial Realization Filtering: Numerical simulations utilized spatial realizations of the 13C bath that were purged of ânearbyâ nuclei (within 0.5 nm or 1.0 nm) to ensure the validity of the CCE-1 and Gaussian approximations for the mesoscopic bath regime.
- Quantum Sensing and Metrology: NV centers are critical components in high-sensitivity magnetometers and thermometers. Accurate modeling of the phase shift (Ί(t)) allows for improved design and calibration of dynamical decoupling sequences, enhancing the fidelity and stability of quantum sensors.
- Dynamic Nuclear Polarization (DNP) Optimization: The measured phase shift provides a direct, highly localized metric for the efficiency and spatial extent of DNP protocols, which are essential for hyperpolarizing nuclear spins for enhanced magnetic resonance imaging (MRI) or nuclear quantum memory.
- Solid-State Quantum Computing: The findings inform the design of robust quantum registers. By distinguishing between classical and quantum environmental noise, engineers can select appropriate qubit manifolds and control sequences to maximize coherence times in diamond-based quantum processors.
- Advanced Noise Spectroscopy: The methodology of comparing biased and unbiased qubit couplings offers a powerful tool for performing non-Gaussian noise spectroscopy, allowing for detailed characterization and mitigation of complex environmental fluctuations.
- Qubit Platform Generalization: The principle of bias-induced phase shifts applies to other solid-state qubits with similar coupling structures, including excitonic qubits in quantum dots and singlet-triplet spin qubits in double quantum dots, guiding decoherence mitigation in these emerging technologies.
View Original Abstract
We consider the spin echo dynamics of a nitrogen-vacancy center qubit based\nthe $S\!= \! 1$ ground state spin manifold, caused by a dynamically polarized\nnuclear environment. We show that the echo signal acquires then a nontrivially\ntime-dependent phase shift. This effect should be observable for polarization\n$\approx \! 0.5$ of nuclei within $\sim \! 1$ nm from the qubit, and for the NV\ncenter initialized in a superposition of $m\! = \! 0$ and either $m\! =\! 1$ or\n$m\! =\! -1$ states. This phase shift is much smaller when the NV center is\nprepared in a superposition of $m\! = \! 1$ and $m\! =\! -1$ states, i.e. when\nthe qubit couples to the spin environment in a way analogous to that of\nspin-$1/2$. For nuclear environment devoid of spins strongly coupled to the\nqubit, the phase shift is well described within Gaussian approximation, which\nprovides an explanation for the dependence of the shift magnitude on the choice\nof states on which the qubit is based, and makes it clear that its presence is\nrelated to the linear response of the environment perturbed by an evolving\nqubit. Consequently, its observation signifies the presence\nenvironment-mediated self-interaction of the qubit, and hence, it invalidates\nthe notion that the nuclear environment acts as a source of external noise\ndriving the qubit. We also show how a careful comparison of the echo signal\nfrom qubits based on $m\! = \! 0,1$ and $m\! =\! \pm 1$ manifolds, can\ndistinguish between effectively Gaussian and non-Gaussian environment.\n