Spin squeezing in an ensemble of nitrogen–vacancy centres in diamond
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2025-10-01 |
| Journal | Nature |
| Authors | Weijie Wu, Emily J Davis, Lillian Hughes, Bingtian Ye, Zilin Wang |
| Institutions | University of California, Santa Barbara, New York University |
| Citations | 2 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- First Solid-State Spin Squeezing: This work presents the first experimental demonstration of spin squeezing in a solid-state spin ensemble, utilizing nitrogen-vacancy (NV) centers in delta-doped diamond.
- Metrological Enhancement: The achieved spin squeezing parameter is $\xi^{2}$ = 0.89(2) (or -0.50 ± 0.10 dB), demonstrating entanglement-enhanced metrology beyond the standard quantum limit (SQL) in a practical, room-temperature solid-state sensor.
- Native Interaction Mechanism: Squeezing is generated by the native magnetic dipole-dipole interaction between NVs, which yields mean-field twisting dynamics analogous to the one-axis twisting (OAT) Hamiltonian.
- Disorder Mitigation: A central challenge—strong positional disorder leading to rapid collective spin decay—was overcome using two novel “lattice-engineering” protocols: frequency-selective shelving of strongly-coupled NV clusters (dimers) and adiabatic depolarization.
- Novel Readout Technique: The anisotropic quantum spin projection noise (variance) was measured using a new method called “interaction-enabled noise spectroscopy,” which tracks the decoherence dynamics (decay timescale T2) of the collective spin vector, eliminating the need for projection-noise-limited readout.
- Platform: Experiments were conducted on a strongly-interacting, two-dimensional ensemble of NV centers in a (111)-oriented diamond layer at room temperature.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Optimal Spin Squeezing ($\xi^{2}$) | 0.89(2) | Dimensionless | Achieved using adiabatic depolarization protocol. |
| Optimal Spin Squeezing (dB) | -0.50 ± 0.10 | dB | First observation of spin squeezing in solid-state. |
| Optimal Squeezing Time ($t_{g}$) | 1.6 | µs | Time required for Hamiltonian evolution. |
| NV-NV Dipolar Interaction Strength ($J_{0}$) | (2π) x 52 | MHz nm3 | Characterizes the strength of the native interaction. |
| NV Areal Density (Out-of-Plane Group) | 8 | ppm·nm | Density used for the active spin sub-ensemble. |
| Average NV Spacing | ~20 | nm | Corresponds to the 8 ppm·nm areal density. |
| Epilayer Isotopic Purity | 99.998% | 12C | Isotopically purified epilayer grown via PECVD. |
| Low 13C Density Layer Thickness | ~270 | nm | Defines the epilayer thickness. |
| Delta-Doped Layer Thickness | 7 ± 7/11 | nm | FWHM of the 15N peak extracted from SIMS. |
| Electron Irradiation Dosage | 1.29 x 1020 | e/cm2 | Dosage used to increase NV center density. |
| Magnetic Field ($B$) | 393 | Gauss | Aligned to the out-of-the-plane direction (quantization axis). |
| Nuclear Spin Polarization | 89(1)% | % | Measured via ODMR at 393 Gauss. |
| Microwave Rabi Frequency | ~ (2π) x 25 | MHz | Typical Rabi frequency achieved via stripline delivery. |
| NV-P1 Interaction Strength | ~ (2π) x 360 | kHz | Estimated from ODMR linewidth. |
Key Methodologies
Section titled “Key Methodologies”The experiment involved three main stages: sample preparation and lattice engineering, squeezing generation, and interaction-enabled readout.
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Sample Preparation (PECVD Growth and Post-Processing):
- Growth: Plasma-enhanced Chemical Vapor Deposition (PECVD) was used to grow a 99.998% 12C isotopically purified epilayer on a (001)-oriented CVD substrate sliced along the (111) plane.
- Doping: Nitrogen delta-doping (using 15N gas) was performed for 1 minute to create a thin, highly concentrated layer of defects.
- NV Formation: The sample was irradiated with 200 keV electrons (1.29 x 1020 e/cm2) followed by two-step annealing (400 °C for 2 hrs, then 850 °C for 4 hrs in 4 x 10-8 torr vacuum) to promote vacancy diffusion and NV creation.
- Cleaning: Final cleaning involved boiling in a tri-acid solution and annealing at 450 °C in air for 4 hrs.
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Lattice Engineering (Dimer Removal):
- Goal: Isolate a relatively ordered sub-ensemble by removing strongly-coupled NV dimers (which cause rapid spin decay).
- Method I: Frequency-Resolved Shelving: A weak, frequency-selective microwave $\pi$-pulse was applied to shelve dimers (high interaction strength $J$) into the unused $|m_{s} = +1\rangle$ state, effectively removing them from the active $|m_{s} = 0\rangle, |m_{s} = -1\rangle$ subspace.
- Method II: Adiabatic Depolarization: A strong, resonant transverse microwave field ($h_{x}S_{x}$) was ramped down adiabatically. Spins with interaction strength $J$ greater than the final field $h_{f}$ depolarized rapidly, while the remaining, less-coupled spins maintained their initial polarization.
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Squeezing Generation:
- Initialization: The remaining, ordered NV sub-ensemble was initialized into a spin-polarized state $|x\rangle$.
- Evolution: The system evolved under the native disordered dipolar HXXZ Hamiltonian for a time $t_{g}$ (optimal 1.6 µs), generating the spin-squeezed state via mean-field twisting dynamics.
- Decoupling: An XY-8 pulse sequence was continuously applied during evolution to dynamically decouple the NV ensemble from quasi-static fields and NV-P1 Ising interactions.
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Interaction-Enabled Readout:
- Rotation: A global spin rotation ($X_{\theta}$ pulse) was applied to map the collective spin operator $S_{\theta}$ (along the squeezing axis) onto the $S_{z}$ axis.
- Quench Dynamics: The anisotropic spin projection noise (variance Var($S_{\theta}$)) was measured indirectly by observing the decay of the collective spin length $\langle S_{x}(t_{r})\rangle$ during a subsequent quench protocol under HXXZ.
- Variance Extraction: The characteristic decay timescale $T_{2}$ was extracted from the decay profile, and a numerically determined mapping (benchmarked against DTWA and Krylov methods) was used to convert $T_{2}$ directly into the quantum variance Var($S_{\theta}$).
Commercial Applications
Section titled “Commercial Applications”The demonstration of entanglement in a robust, room-temperature solid-state platform like NV diamond opens pathways for quantum technologies, particularly in sensing and computing.
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Quantum Sensing and Metrology:
- Enhanced Magnetometry: Utilizing spin-squeezed states to achieve magnetic sensitivity beyond the standard quantum limit (SQL), crucial for probing biological systems, condensed matter physics, and materials science (e.g., nanoscale magnetic sensing, imaging ohmic transport).
- Quantum-Enhanced Sensors: Development of practical, room-temperature quantum sensors for biomedical applications and materials characterization.
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Quantum Information Processing:
- Quantum Networking: Spin-squeezed states are essential resources for distributed quantum sensing and quantum networking protocols.
- Quantum Computing/Simulation: NV ensembles serve as platforms for quantum simulation, and the control demonstrated here is fundamental for generating targeted entangled states necessary for scalable quantum computation.
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Diamond Materials Technology (Relevant to 6ccvd.com):
- High-Purity Diamond Substrates: The reliance on high-quality, isotopically purified (99.998% 12C) CVD diamond epilayers grown on (111)-oriented substrates highlights the need for advanced diamond synthesis capabilities.
- Controlled Doping and Defect Engineering: The use of nitrogen delta-doping and precise electron irradiation/annealing protocols for deterministic placement and density control of NV centers is a key material science challenge addressed by specialized CVD manufacturers.