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Spin squeezing in an ensemble of nitrogen–vacancy centres in diamond

MetadataDetails
Publication Date2025-10-01
JournalNature
AuthorsWeijie Wu, Emily J Davis, Lillian Hughes, Bingtian Ye, Zilin Wang
InstitutionsUniversity of California, Santa Barbara, New York University
Citations2
AnalysisFull AI Review Included
  • 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.
ParameterValueUnitContext
Optimal Spin Squeezing ($\xi^{2}$)0.89(2)DimensionlessAchieved using adiabatic depolarization protocol.
Optimal Spin Squeezing (dB)-0.50 ± 0.10dBFirst observation of spin squeezing in solid-state.
Optimal Squeezing Time ($t_{g}$)1.6µsTime required for Hamiltonian evolution.
NV-NV Dipolar Interaction Strength ($J_{0}$)(2π) x 52MHz nm3Characterizes the strength of the native interaction.
NV Areal Density (Out-of-Plane Group)8ppm·nmDensity used for the active spin sub-ensemble.
Average NV Spacing~20nmCorresponds to the 8 ppm·nm areal density.
Epilayer Isotopic Purity99.998%12CIsotopically purified epilayer grown via PECVD.
Low 13C Density Layer Thickness~270nmDefines the epilayer thickness.
Delta-Doped Layer Thickness7 ± 7/11nmFWHM of the 15N peak extracted from SIMS.
Electron Irradiation Dosage1.29 x 1020e/cm2Dosage used to increase NV center density.
Magnetic Field ($B$)393GaussAligned to the out-of-the-plane direction (quantization axis).
Nuclear Spin Polarization89(1)%%Measured via ODMR at 393 Gauss.
Microwave Rabi Frequency~ (2π) x 25MHzTypical Rabi frequency achieved via stripline delivery.
NV-P1 Interaction Strength~ (2π) x 360kHzEstimated from ODMR linewidth.

The experiment involved three main stages: sample preparation and lattice engineering, squeezing generation, and interaction-enabled readout.

  1. 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.
  2. 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.
  3. 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.
  4. 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($S_{\theta}$).

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.

  • 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.
  • 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.
  • 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.