Many-body CCE explanation of the missing isotope contrast

Determine whether a cluster-correlation-expansion treatment of nitrogen-vacancy ensemble decoherence, including near-degenerate as well as exactly degenerate P1–P1 flip-flop channels, produces a nitrogen-isotope coherence-time contrast large enough to account for the experimentally observed ratio of approximately 2.07, exceeding the semiclassical channel-counting prediction of approximately 1.12.

Background

The semiclassical spin-bath calculation predicts that the ratio T2(14N)/T2(15N) is 1.118 ± 0.011, whereas comparison with existing measurements gives 2.07 ± 0.25. The authors attribute the shortfall to physics beyond independent-pair rate equations, particularly correlated evolution of detuned P1 pairs that may be captured by a cluster-correlation-expansion calculation.

The proposed many-body treatment would account for the five distinct hyperfine energies of 14N compared with four for 15N and would therefore include near-degenerate channels omitted by the exact resonant-channel count. The unresolved issue is whether these additional many-body contributions are sufficient to close the measured-theoretical gap.

References

Since ${14}\mathrm{N}$ has five distinct hyperfine energies — $\mathrm{m_f} \in {-1, 0, +1}$ combined with the on-axis and off-axis $\mathrm{A_{eff}$ values — against four for ${15}\mathrm{N}$, a treatment sensitive to near-degenerate channels should produce a larger contrast than channel counting alone; whether it produces enough is the question a CCE calculation on this system is designed to answer.

— Semiclassical spin-bath calculation of the nitrogen-isotope effect on NV$^-$ ensemble coherence in diamond  (2609.37596 - Shinei, 29 Sep 2026) in Conclusion, final discussion of the semiclassical model and proposed CCE treatment

The stretching exponent $p = 1.14$ fitted in Ref. [3], closer to the motionally narrowed value $p = 1$ than to the quasi-static ensemble value $p \approx 3/2$ , is a reminder that the conversion is not settled; the significance of the discrepancy quoted in the main text is conditional on it.

— Semiclassical spin-bath calculation of the nitrogen-isotope effect on NV$^-$ ensemble coherence in diamond  (2609.37596 - Shinei, 29 Sep 2026) in Supplementary Material, Section S4, “Conversion from the Double-Quantum to the Single-Quantum Convention”