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6CCVD Research

Nuclear-spin relaxation in solid-state-defect quantum bits via electron-phonon coupling in the optically excited state

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2025-10-09
JournalPhysical Review Applied
AuthorsGergƑ Thiering, Ádám Gali
InstitutionsHUN-REN Wigner Research Centre for Physics, Budapest University of Technology and Economics
Citations1
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”
  • Core Challenge Addressed: The study identifies and quantifies the mechanism causing significant 14N nuclear spin relaxation in the Nitrogen-Vacancy (NV) center during the optical readout cycle, a critical process for quantum memory operation.
  • Mechanism Identified: Relaxation is strongly enhanced in the 3E optical excited state due to the dynamic Jahn-Teller (JT) effect, which creates strong entanglement between the electron spin and orbital degrees of freedom.
  • Enhanced Relaxation Pathways: Two primary nuclear spin-flip channels were quantified:
    1. Coherent AmI = ±2 flips: Driven by the orbital-dependent nuclear quadrupole interaction (P(e)2), accumulating coherently over multiple cycles.
    2. Incoherent AmI = ±1 flips: Driven by the perpendicular hyperfine interaction (A(e)⊄), occurring randomly in each optical cycle.
  • Quantitative Impact: For a typical 20 ”s saturated optical readout sequence (approximately 1600 cycles), the cumulative 14N spin-flip probability is high: ~40% for AmI = ±2 transitions and ~22% for AmI = ±1 transitions.
  • Protocol Recommendation: The results suggest that long optical readout times (microsecond scale) severely degrade 14N nuclear spin memory fidelity, necessitating shorter readout protocols or specialized compensation techniques.
  • Methodology Development: A versatile ab initio density functional theory (DFT) and group theory framework was developed and implemented to accurately predict orbital-dependent spin Hamiltonian parameters (D, A, P tensors) for trigonal defects exhibiting orbital degeneracy.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Ground State ZFS (D(g))2.87GHz3A2 ground state, experimental
Excited State ZFS (D(e))1.6GHz3E excited state, theoretical (p.w.)
Excited State Spin-Orbit (λ(e))5.3GHz3E excited state, experimental/theoretical
14N Ground State Quadrupole (P(g))-4.96MHz3A2 ground state, experimental
14N Excited State Quadrupole (P(e))10.4kHz3E excited state, theoretical (p.w.)
14N Excited State Quadrupole (P(e)2)8.2kHzOrbital-dependent term, theoretical (p.w.)
14N Excited State Hyperfine (A(e)||)39MHzParallel component, theoretical (p.w.)
14N Excited State Hyperfine (A(e)⊄)25MHzPerpendicular component, theoretical (p.w.)
Radiative Lifetime (Trad)12ns3E excited state lifetime
Rabi Oscillation Period (A(e)⊄)0.43nsIncoherent AmI = ±1 transition
Rabi Oscillation Period (P(e)2)56”sCoherent AmI = ±2 transition
Ham Reduction Factor (p)0.262DimensionlessReduction factor for A2 symmetry terms (e.g., spin-orbit)
Ham Reduction Factor (q)0.631DimensionlessReduction factor for E symmetry terms (e.g., orbital flipping)
Total AmI = ±2 Flip Probability0.2 ± 0.1DimensionlessCumulative probability over 20 ”s readout

Key Methodologies

Section titled “Key Methodologies”
  1. DFT Setup and Optimization: Calculations were performed using the VASP code in a 512-atom diamond supercell. Atomic positions were optimized until forces were below 0.01 eV/A. A plane-wave cutoff of 370 eV was used.
  2. Jahn-Teller (JT) Parameterization: The adiabatic potential energy surface (APES) of the 3E excited state was computed using the Heyd-Scuzeria-Ernzerhof (HSE06) hybrid functional and the ASCF method to determine the parameters governing the strong electron-phonon coupling.
  3. Spin Hamiltonian Tensor Calculation: The magnetic parameters (D, A, P tensors) were calculated using the Perdew-Burke-Ernzerhof (PBE) functional within the projector augmented wave (PAW) framework.
  4. Orbital-Dependent Parameter Scheme: To compute the orbital flipping terms (Γ1, Γ2), the DFT self-consistent electronic cycle was run by manually enforcing full occupancy of a single orbital (|ex> or |ey>), without further atomic position optimization, yielding the necessary F(xx) or F(yy) tensors.
  5. Ham Reduction Application: The calculated spin parameters were scaled by Ham reduction factors (p = 0.262 for A2 terms, q = 0.631 for E terms) to account for the dynamic averaging of orbital degrees of freedom during the fast JT motion.
  6. Nuclear Spin-Flip Rate Modeling:
    • Incoherent AmI = ±1 transitions (driven by A(e)⊄) were calculated using Fermi’s golden rule, valid because the Rabi oscillation period (0.43 ns) is much shorter than the radiative lifetime (12 ns).
    • Coherent AmI = ±2 transitions (driven by P(e)2) were calculated by solving the Schrödinger equation, as the Rabi period (56 ”s) is much longer than the excited state lifetime, allowing coherent accumulation over multiple optical cycles.

Commercial Applications

Section titled “Commercial Applications”
Industry/FieldApplication/Product RelevanceTechnical Insight Provided
Quantum ComputingSolid-state quantum registers and quantum memories based on NV nuclear spins.Provides critical constraints on optical readout protocols; long readout times (”s scale) must be avoided to prevent nuclear spin decoherence.
Quantum SensingNanoscale magnetometry, gyroscopes, and NMR detection using NV centers.Optimizes the optical pumping and initialization stages by quantifying excited-state decoherence pathways, leading to higher sensor fidelity and sensitivity.
Quantum NetworkingNV-based quantum network nodes requiring robust, long-coherence memories.The derived D, A, and P tensors are essential inputs for Lindbladian simulations, allowing accurate modeling and optimization of quantum communication protocols.
Materials ScienceCharacterization and engineering of solid-state defect qubits with orbital degeneracy (e.g., SiV, GeV, SnV).The ab initio scheme for calculating orbital-dependent spin Hamiltonians is a general tool applicable to any trigonal defect exhibiting a 3E or 2E excited state.
Cryogenic TechnologyOptimization of NV center operation temperature.Suggests that elevated temperatures (above 4 K) may be beneficial in specific cases to suppress orbital decoherence processes, contrary to the general assumption that lower temperatures are always better for nuclear spin coherence.
View Original Abstract

Optically accessible solid state defect spins serve as a primary platform for quantum information processing, where precise control of the electron spin and ancillary nuclear spins is essential for operation. Using the nitrogen-vacancy (NV) color center in diamond as an example, we employ a combined group theory and density functional theory study to demonstrate that spin-lattice relaxation of the $^{14}$N nuclear spin is significantly enhanced due to strong entanglement with orbital degrees of freedom in the $|^3E\rangle$ optical excited state of the defect. This mechanism is common to other solid-state defect nuclear spins with similar optical excited states. Additionally, we propose a straightforward and versatile \textit{ab initio} scheme for predicting orbital-dependent spin Hamiltonians for trigonal defects exhibiting orbital degeneracy.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2014 - Quantum Information Processing with Diamond: Principles and Applications

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