Decoherence of nuclear spins in the frozen core of an electron spin
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2015-06-15 |
| Journal | Physical Review B |
| Authors | Roland Guichard, S. J. Balian, Gary Wolfowicz, Pierre-André Mortemousque, T. S. Monteiro |
| Institutions | London Centre for Nanotechnology, University College London |
| Citations | 18 |
| Analysis | Full AI Review Included |
Quantum Coherence Engineering: Leveraging Single Crystal Diamond for Long-Lived Qubit Registers
Section titled âQuantum Coherence Engineering: Leveraging Single Crystal Diamond for Long-Lived Qubit RegistersâThis technical analysis evaluates the mechanisms governing nuclear spin decoherence within the electron âfrozen core,â derived from research focused on the Silicon-Phosphorus (Si:P) donor system. The findings, which confirm second-scale coherence times (T2n ~ 1 s) for proximate nuclear spins, are directly applicable to optimizing solid-state quantum registers, particularly those based on Nitrogen Vacancy (NV) centers in diamondâa core competency of 6CCVD.
Executive Summary
Section titled âExecutive Summaryâ- Core Achievement: Demonstrated that proximate nuclear spins within the donor electronâs âfrozen coreâ function as long-lived quantum registers, achieving coherence times (T2n) of approximately 1 second via simulated Hahn echo sequences.
- Decoherence Mechanism: The primary limit on nuclear spin coherence arises from pair flip-flops of surrounding nuclear spins (e.g., 29Si or 13C).
- Critical Models: Coherence limits were quantified using two models: the Far Bath Model (requiring simulation of up to 5 x 108 distant spin pairs) and the novel Equivalent Pairs (EP) Model (focusing on a few dozen symmetrically sited pairs within the core).
- Material Analogy: The principles of spin bath engineering derived from the 29Si natural abundance (4.67%) system are directly analogous to the challenges and opportunities presented by 13C spins (1.1%) in natural diamond NV center systems.
- T2 Insensitivity: The coherence time (T2n) showed weak dependence on the electron-nuclear hyperfine coupling strength (J) across the tested range (0.1 MHz to 3.8 MHz).
- Engineering Requirement: Achieving high coherence in solid-state qubits necessitates precise control or minimization of the nuclear spin bath through isotopic purification, validating 6CCVDâs specialized material offerings.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Nuclear Spin Coherence Time (T2n) | ~1 | second | Calculated using Hahn echo sequences. |
| Electronic Spin Relaxation Time (T1) | > 1 | second | Required to maintain T2n, implies T < 5 K. |
| Frozen Core Radius (RFC) | ~80 | Ă | Estimated boundary for Si:P system. |
| Hyperfine Coupling Strength (J) Range | 0.1 to 3.8 | MHz | Range tested in Equivalent Pair (EP) model. |
| Far Bath Model Max Size | 5 x 108 | pairs | Total number of 29Si pairs included (R †350 à ). |
| Si Lattice Parameter (a0) | 5.43 | Ă | Reference parameter for Si crystal structure. |
| 29Si Impurity Abundance (p) | 4.67 | % | Natural concentration in Silicon, limits coherence. |
| Magnetic Field Orientation (B0) | [100] | N/A | Crystal orientation used in CCE calculations. |
Key Methodologies
Section titled âKey MethodologiesâThe researchers employed rigorous quantum bath modeling techniques to simulate decoherence in the low-temperature, strong-hyperfine coupling regime.
- Modeling Framework: Cluster Correlation Expansion (CCE) method, primarily using the pair correlation (CCE2) to model entanglement between the central qubit and the nuclear spin bath.
- Spin System: Focused on the central nuclear spin qubit of a Phosphorus donor in Silicon (Si:P).
- Decay Measurement: Simulated T2n coherence decay using the Hahn echo sequence.
- Hyperfine Calculation: Utilized the Kohn-Luttinger (KL) ground state wavefunction approximation for modeling the electron-nuclear hyperfine interaction (J).
- Decoherence Model 1: Far Bath:
- Simulated the cumulative effect of extremely large numbers (up to 5 x 108) of distant 29Si spin pairs lying outside the RFC (R = 50-350 Ă ).
- Decoherence Model 2: Equivalent Pairs (EP):
- Introduced a model focusing on a few dozen 29Si spin pairs located inside the frozen core. These pairs exhibit state-selective detuning due to symmetrical positioning relative to the central electron, allowing indirect flip-flop decoherence.
- Anisotropy Treatment: Used symmetry constraints based on magnetic field orientation (B0 = [100]) to estimate upper and lower bounds for T2n values, accounting for anisotropy effects that break spin symmetry.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe findings confirm that quantum register performance hinges on controlling the density and symmetry of the nuclear spin environment. 6CCVDâs expertise in high-purity Chemical Vapor Deposition (CVD) diamond offers the necessary platform for achieving and exceeding these benchmark coherence times in next-generation quantum devices (e.g., NV centers).
Applicable Materials
Section titled âApplicable MaterialsâTo replicate or extend this research onto the technologically superior diamond platform, 6CCVD recommends materials engineered specifically for low-noise spin environments:
| 6CCVD Material | Relevance to Research Requirements |
|---|---|
| Isotopically Purified Single Crystal Diamond (SCD) | Analogous to purifying Si away from 29Si, 6CCVD supplies SCD wafers with 13C concentrations < 0.01%, minimizing the nuclear spin bath and maximizing NV center T2 and T2n coherence. |
| Optical Grade SCD Wafers | Ideal platform for NV center creation and spin manipulation (analogous to the Si:P donor). Offers extreme crystalline purity essential for long electronic and nuclear coherence. |
| Boron-Doped Diamond (BDD) | For experiments requiring conductive substrates or specialized quantum electrodes, BDD layers can be grown and doped to specified conductivity levels (heavy or light doping). |
Customization Potential
Section titled âCustomization PotentialâThe complexity of frozen core engineering and quantum control often requires micro-scale customization and robust electrical interfacing.
- Precision Geometry and Dimensions: 6CCVD provides Custom Dimensions (plates/wafers up to 125mm for PCD) and high-precision Laser Cutting and etching services, essential for defining quantum circuits, micro-pillar arrays, or high-Q resonators around spin qubits.
- Optimized Surface Finish: To minimize surface noise and potential decoherence sources, 6CCVD offers Ultra-smooth Polishing capabilities, achieving Ra < 1 nm for SCD, surpassing typical material requirements for surface-sensitive quantum devices.
- Integrated Metalization Layers: Custom quantum architectures often require complex electrical contacts. 6CCVD provides In-house Multi-layer Metalization (Au, Pt, Pd, Ti, W, Cu) for robust, low-resistance cryogenic contacts and microwave delivery lines, crucial for pulsed ENDOR techniques cited in the paper.
Engineering Support
Section titled âEngineering SupportâThe theoretical framework, involving concepts like the âfrozen core,â Equivalent Pairs, and specific wavefunction symmetries (Kohn-Luttinger), demands expert material selection.
6CCVDâs in-house PhD engineering team specializes in diamond spin physics and can provide consultative support to assist researchers and technical engineers in defining:
- Optimal substrate thickness (SCD available from 0.1 ”m up to 500 ”m).
- Required isotopic purity levels to minimize 13C noise for high-coherence quantum register projects (e.g., NV center applications).
- Design specifications for custom metalization schemes tailored for cryo-electronic integration.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Hybrid qubit systems combining electronic spins with nearby (âproximateâ) nuclear spin registers offer a promising avenue towards quantum information processing, with even multi-spin error correction protocols recently demonstrated in diamond. However, for the important platform offered by spins of donor atoms in cryogenically-cooled silicon,decoherence mechanisms of $^{29}$Si proximate nuclear spins are not yet well understood.The reason is partly because proximate spins lie within a so-called âfrozen coreâ region where the donor electronic hyperfine interaction strongly suppresses nuclear dynamics. We investigate the decoherence of a central proximate nuclear qubit arising from quantum spin baths outside, as well as inside, the frozen core around the donor electron. We consider the effect of a very large nuclear spin bath comprising many ($\gtrsim 10^8$) weakly contributing pairs outside the frozen core. We also propose that there may be an important contribution from a few (of order $100$) symmetrically sited nuclear spin pairs (âequivalent pairsâ), which were not previously considered as their effect is negligible outside the frozen core. If equivalent pairs represent a measurable source of decoherence, nuclear coherence decays could provide sensitive probes of the symmetries of electronic wavefunctions. For the phosphorus donor system, we obtain $T_{2n}$ values of order 1 second for both the âfar bathâ and âequivalent pairâ models, confirming the suitability of proximate nuclei in silicon as very long-lived spin qubits.