Skip to content

Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble

MetadataDetails
Publication Date2017-03-03
JournalPhysical Review Letters
AuthorsJoonhee Choi, Soonwon Choi, Georg Kucsko, Peter C. Maurer, Brendan Shields
InstitutionsCenter for Integrated Quantum Science and Technology, Harvard University
Citations123
AnalysisFull AI Review Included

Technical Documentation & Analysis: Depolarization Dynamics in Dense NV Ensembles

Section titled “Technical Documentation & Analysis: Depolarization Dynamics in Dense NV Ensembles”

This document analyzes the research paper “Depolarization dynamics in a strongly interacting solid-state spin ensemble” (arXiv:1608.05471v2) to highlight the critical material requirements and demonstrate how 6CCVD’s advanced MPCVD diamond solutions meet and exceed the needs for replicating and extending this quantum many-body physics research.


This study successfully characterizes the anomalous spin depolarization in high-density Nitrogen-Vacancy (NV) ensembles in diamond, providing crucial insights for solid-state quantum computing and sensing applications.

  • High-Density Environment: The research utilized single crystal diamond with a high NV concentration (~45 ppm), resulting in a strong dipolar interaction strength of $J \sim (2\pi) 420$ kHz.
  • Anomalous Relaxation: Depolarization was observed to be anomalously fast, density-dependent, and non-exponential, fitting a stretched exponential decay profile ($P(t) = e^{-\sqrt{t/T_1}}$).
  • Microscopic Model Validation: The observations are quantitatively explained by a Spin-Fluctuator Model, where short-lived spins (fluctuators, $n_f \sim 16$ ppm) induce depolarization via dipolar interactions.
  • Charge Dynamics Confirmation: The fluctuator mechanism is strongly supported by charge dynamics measurements, confirming a rapid tunneling-mediated charge hopping timescale ($T_{hop} \sim 10$ ns).
  • Spin Lifetime Mitigation: Advanced dynamical decoupling techniques (spin-locking) were successfully employed to suppress flip-flop interactions, extending the spin lifetime well beyond the bare $T_1$ limit.
  • Material Requirement: Replication requires ultra-high purity single crystal diamond substrates suitable for precise post-growth irradiation and annealing to achieve controlled, high-density NV ensembles.

The following hard data points were extracted from the experimental results, defining the performance metrics achieved in the dense NV ensemble.

ParameterValueUnitContext
NV Center Concentration ($C_{NV}$)~45ppmHigh-density ensemble achieved via irradiation/annealing
Dipolar Interaction Strength ($J$)(2π) 420kHzTypical interaction strength, significantly faster than extrinsic decoherence
Ensemble $T_1$ (Initial $m_s=0\rangle$)56 ± 2”s
Ensemble $T_1$ (Initial $m_s=-1\rangle$)80 ± 2”s
Depolarization Decay Profile$e^{-\sqrt{t/T_1}}$N/AStretched exponential decay profile (exponent 1/2)
Inhomogeneous Linewidth ($W$)(2π) 9.3 ± 0.4MHzExtracted from Electron Spin Resonance (ESR) measurement
Fluctuator Density ($n_f$)~16ppmEstimated density of short-lived spins
Charge Recovery Time ($\tau_{rec}$)~100”sMeasured relaxation of non-equilibrium charge distribution
Charge Hopping Timescale ($T_{hop}$)~10nsPredicted timescale from classical diffusion model
Nanobeam Geometry (Spin Experiments)300 x 300 x 20nm x nm x ”mGeometry created via angle-etching

The experiment relied on precise material engineering and advanced quantum control techniques to characterize the spin ensemble dynamics.

  1. Material Synthesis and Defect Creation: Utilization of Type-Ib HPHT single crystal diamond, followed by electron beam irradiation and high-fluence in situ annealing. This process was critical to achieve the high NV concentration (~45 ppm) necessary for strong dipolar interaction while minimizing crystal lattice degradation.
  2. Nanostructure Fabrication: Creation of diamond nanobeams (300 nm x 300 nm x 20 ”m) via angle-etching to ensure high spatial control over the optical excitation region for spin measurements.
  3. Spin State Control: Optical initialization, manipulation, and readout of the NV spin-1 system at ambient conditions, leveraging the crystal field splitting ($\Delta_0 = (2\pi) 2.87$ GHz).
  4. Density Tuning: Application of an external magnetic field to tune the spectral overlap of the four crystallographic groups of NV centers (A, B, C, D), thereby controlling the effective density of resonant spins.
  5. Spin-Locking Measurement: Implementation of a spin-locking sequence (strong microwave driving at Rabi frequency $\Omega$) to suppress flip-flop interactions, demonstrating a mechanism for extending spin coherence time ($T_{\rho}$).
  6. Charge Dynamics Measurement: Optical induction of a non-equilibrium charge distribution using a 532 nm green laser (two-photon ionization) and monitoring the subsequent relaxation using a 594 nm yellow probe laser to measure the charge recovery timescale ($\sim 100$ ”s).

6CCVD provides the foundational MPCVD diamond materials and precision engineering services required to replicate and advance research into strongly interacting solid-state spin ensembles, quantum many-body dynamics, and high-density quantum sensing.

Research Requirement6CCVD Solution & CapabilityTechnical Advantage for Quantum Research
High-Purity Starting MaterialOptical Grade Single Crystal Diamond (SCD)We supply ultra-low nitrogen, high-purity SCD substrates, essential for controlled creation of NV centers via post-processing (irradiation/annealing) to achieve specific, high concentrations (e.g., ~45 ppm).
Custom NV ConcentrationCustom Doping and Material Selection6CCVD offers SCD substrates with tailored initial nitrogen content, allowing researchers to precisely control the final NV density, crucial for tuning the dipolar interaction strength ($J$) and studying density-dependent depolarization.
Nanostructure PrecursorsCustom Thickness and Wafer DimensionsWe provide SCD plates/wafers with thicknesses ranging from 0.1 ”m up to 500 ”m, ideal precursors for fabricating the 20 ”m thick nanobeams used in this study. Plates/wafers are available up to 125mm (PCD).
Precision Geometry & EtchingIn-House Laser Cutting and Micro-MachiningOur services support the creation of complex geometries, including the precise cutting of small samples or the preparation of substrates for subsequent high-fidelity etching (like the angle-etching used for the nanobeams).
Surface Quality for NanofabricationUltra-Low Roughness Polishing (Ra < 1 nm)High-quality surface preparation is mandatory for reliable nanofabrication. Our SCD polishing achieves Ra < 1 nm, minimizing surface defects that can introduce noise or degrade spin coherence near the surface.
Charge Dynamics ControlBoron-Doped Diamond (BDD) MaterialsThe paper suggests controlling depolarization by altering the Fermi level via doping [36]. 6CCVD offers BDD materials, enabling researchers to tune the charge state dynamics and potentially suppress the fluctuator mechanism.
Integrated Control StructuresCustom Metalization (Au, Pt, Pd, Ti, W, Cu)We offer internal metalization capabilities, allowing researchers to integrate microwave control lines directly onto the diamond surface for advanced dynamical decoupling sequences (like spin-locking) and coherent manipulation.

6CCVD’s in-house team of PhD material scientists and engineers specializes in diamond for quantum applications. We provide expert consultation on material selection, defect engineering recipes (irradiation/annealing parameters), and surface preparation necessary for complex quantum many-body dynamics experiments and high-sensitivity spin sensing projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and nonexponential spin relaxation. To explain these observations, we propose a microscopic model where an interplay of long-range interactions, disorder, and dissipation leads to predictions that are in quantitative agreement with both current and prior experimental results. Our results pave the way for controlled many-body experiments with long-lived and strongly interacting ensembles of solid-state spins.