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arXiv:2601.00157 · Physical Review Applied

Towards a temperature-insensitive composite diamond clock

Sean Lourette, Andrey Jarmola, Jabir Chathanathil, Victor M. Acosta, A. Glen Birdwell, Peter Blümler, Dmitry Budker, Sebastián C. Carrasco, Tony G. Ivanov, Shimon Kolkowitz, Vladimir S. Malinovsky

quant-phphysics.app-phphysics.atom-phphysics.ins-detSubmitted Jan 1, 2026• Announced Jan 2, 2026• 0 citations
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Abstract

Frequency references based on solid state spins promise simplicity, compactness, robustness, multifunctionality, ease of integration, and high densities of emitters. Nitrogen-vacancy (NV) centers in diamond are a natural candidate, but the electronic zero-field splitting exhibits a large fractional temperature dependence, which has precluded its use as a stable clock transition. Here we show that this limitation can be overcome by forming a composite frequency reference that combines measurements of the electronic splitting D with the nuclear quadrupole splitting of the $^{14}$N nuclear spin intrinsic to the NV center. We further benchmark this composite approach against alternative strategies for mitigating temperature sensitivity. By implementing a specially designed pulse sequence with an eight-phase control scheme that suppresses pulse imperfections, we interleave measurements of D and Q in a high-density NV ensemble and demonstrate a temperature-compensated composite frequency reference. The stability of this composite diamond clock is characterized over a 10-day period at room temperature through a comparison to a Rb vapor-cell clock, yielding a fractional instability below $5 \times 10^{-9}$ for an averaging time of $τ= 200$ s and below $1 \times 10^{-8}$ at $τ= 2 \times 10^5$ s, corresponding to measured improvements by a factor of 4 and 200, respectively, over a clock based purely on the single frequency D for the same periods. By characterizing the residual sensitivity to magnetic fields, optical power, and radio-frequency drive amplitudes, we find that temperature is no longer the dominant source of instability. These results establish complementary electron- and nuclear-spin transitions in diamond as a viable route to thermally robust frequency metrology, providing a pathway toward compact, multifunctional solid-state clocks and quantum sensors.

Comments
14 pages, 6 figures

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Frequency references based on solid state spins promise simplicity, compactness, robustness, multifunctionality, ease of integration, and high densities of emitters. Nitrogen-vacancy (NV) centers in diamond are a natural candidate, but the electronic zero-field splitting exhibits a large fractional temperature dependence, which has precluded its use as a stable clock transition. Here we show that this limitation can be overcome by forming a composite frequency reference that combines measurements of the electronic splitting D with the nuclear quadrupole splitting of the 14^{14}14N nuclear spin intrinsic to the NV center. We further benchmark this composite approach against alternative strategies for mitigating temperature sensitivity. By implementing a specially designed pulse sequence with an eight-phase control scheme that suppresses pulse imperfections, we interleave measurements of D and Q in a high-density NV ensemble and demonstrate a temperature-compensated composite frequency reference. The stability of this composite diamond clock is characterized over a 10-day period at room temperature through a comparison to a Rb vapor-cell clock, yielding a fractional instability below 5×10−95 \times 10^{-9}5×10−9 for an averaging time of τ=200τ= 200τ=200 s and below 1×10−81 \times 10^{-8}1×10−8 at τ=2×105τ= 2 \times 10^5τ=2×105 s, corresponding to measured improvements by a factor of 4 and 200, respectively, over a clock based purely on the single frequency D for the same periods. By characterizing the residual sensitivity to magnetic fields, optical power, and radio-frequency drive amplitudes, we find that temperature is no longer the dominant source of instability. These results establish complementary electron- and nuclear-spin transitions in diamond as a viable route to thermally robust frequency metrology, providing a pathway toward compact, multifunctional solid-state clocks and quantum sensors.
Solid-state frequency references based on nitrogen-vacancy (NV) centers in diamond offer compactness, robustness, and high emitter density, but their electronic zero-field splitting DD exhibits substantial temperature sensitivity near room temperature. This study performs an independent structural analysis of the composite diamond-clock experiment reported by Lourette et al. (Physical Review Applied 25, 064046, 2026). The analysis identifies two experimentally distinct operations acting on different representational spaces. First, the two-tone zero-field-splitting protocol with eight-phase cycling (TTZFS-8) acts on phase-resolved observations to suppress pulse-error-generated spectral components and restore the desired half-sum transition mode. Second, a composite D/QD/Q estimator acts on the resulting two-channel detuning vector to preserve the common local-oscillator correction while nulling first-order thermal drift. In normalized form, the thermal operation satisfies the exact first-order conditions wTT1=1,wTTλ=0,\mathbf w_T^{\mathsf T}\mathbf 1=1, \qquad \mathbf w_T^{\mathsf T}\boldsymbol{\lambda}=0, exposing the estimator as a simultaneous preservation-and-annihilation functional. The unequal fractional thermal coefficients of DD and QQ further establish first-order identifiability of oscillator and temperature contributions. These operations compose into a typed nested architecture, (SD,SQ)→Rϕ,D⊕Rϕ,Q(d,q)→RTuψ.(\mathbf S_D,\mathbf S_Q) \xrightarrow{\mathcal R_{\phi,D}\oplus\mathcal R_{\phi,Q}} (d,q) \xrightarrow{\mathcal R_T} u_\psi . The published ten-day experiment provides the empirical witness: the composite reference becomes more stable than either individual channel beyond approximately 200200 s, with source-reported improvements of roughly 4×4\times at 200200 s and 200×200\times at 2×1052\times10^5 s relative to the DD-only reference. The source systematic budget reveals a further structural consequence. Once the dominant thermal contribution is suppressed, the ordering of the remaining error budget changes and radio-frequency power sensitivity becomes the leading estimated nonthermal residual among the tabulated composite contributions. This transition is formalized here as residual-burden migration: successful local closure can change the identity of the governing residual rather than abolishing burden altogether. Within Structura Reditus / Generative Collapse Dynamics, the resulting operators are interpreted as Tier-2 domain closures only. The analysis does not infer canonical τR\tau_R or welded continuity because the published experiment does not supply the frozen temporal return contract, seam-accounting profile, return credit, residual tolerance, or RunID required for a Tier-0 UMCP weld verdict. The native physical mapping is therefore supported while canonical weld status remains non-evaluable.
Solid-state frequency references based on nitrogen-vacancy (NV) centers in diamond offer compactness, robustness, and high emitter density, but their electronic zero-field splitting DD exhibits substantial temperature sensitivity near room temperature. This study performs an independent structural analysis of the composite diamond-clock experiment reported by Lourette et al. (Physical Review Applied 25, 064046, 2026). The analysis identifies two experimentally distinct operations acting on different representational spaces. First, the two-tone zero-field-splitting protocol with eight-phase cycling (TTZFS-8) acts on phase-resolved observations to suppress pulse-error-generated spectral components and restore the desired half-sum transition mode. Second, a composite D/QD/Q estimator acts on the resulting two-channel detuning vector to preserve the common local-oscillator correction while nulling first-order thermal drift. In normalized form, the thermal operation satisfies the exact first-order conditions wTT1=1,wTTλ=0,\mathbf w_T^{\mathsf T}\mathbf 1=1, \qquad \mathbf w_T^{\mathsf T}\boldsymbol{\lambda}=0, exposing the estimator as a simultaneous preservation-and-annihilation functional. The unequal fractional thermal coefficients of DD and QQ further establish first-order identifiability of oscillator and temperature contributions. These operations compose into a typed nested architecture, (SD,SQ)→Rϕ,D⊕Rϕ,Q(d,q)→RTuψ.(\mathbf S_D,\mathbf S_Q) \xrightarrow{\mathcal R_{\phi,D}\oplus\mathcal R_{\phi,Q}} (d,q) \xrightarrow{\mathcal R_T} u_\psi . The published ten-day experiment provides the empirical witness: the composite reference becomes more stable than either individual channel beyond approximately 200200 s, with source-reported improvements of roughly 4×4\times at 200200 s and 200×200\times at 2×1052\times10^5 s relative to the DD-only reference. The source systematic budget reveals a further structural consequence. Once the dominant thermal contribution is suppressed, the ordering of the remaining error budget changes and radio-frequency power sensitivity becomes the leading estimated nonthermal residual among the tabulated composite contributions. This transition is formalized here as residual-burden migration: successful local closure can change the identity of the governing residual rather than abolishing burden altogether. Within Structura Reditus / Generative Collapse Dynamics, the resulting operators are interpreted as Tier-2 domain closures only. The analysis does not infer canonical τR\tau_R or welded continuity because the published experiment does not supply the frozen temporal return contract, seam-accounting profile, return credit, residual tolerance, or RunID required for a Tier-0 UMCP weld verdict. The native physical mapping is therefore supported while canonical weld status remains non-evaluable.
Temperature Sensitivity of 14NV^{14}\mathrm{NV}14NV and 15NV^{15}\mathrm{NV}15NV Ground State Manifolds
We measure electron and nuclear spin transition frequencies in the ground state of nitrogen-vacancy (NV) centers in diamond for two nitrogen isotopes (14NV^{14}\mathrm{NV}14NV and 15NV^{15}\mathrm{NV}15NV) over temperatures ranging from 77 K to 400 K. Measurements are performed using Ramsey interferometry and direct optical readout of the nuclear and electron spins. We extract coupling parameters QQQ (for 14NV^{14}\mathrm{NV}14NV), DDD, A∣∣A_{||}A∣∣​, A⊥A_{\perp}A⊥​, γe/γnγ_e/γ_nγe​/γn​, and their temperature dependences for both isotopes. The temperature dependences of the nuclear-spin transitions within the ms=0m_s = 0ms​=0 spin manifold near room temperature are found to be +0.52(1) ppm/K for 14NV^{14}\mathrm{NV}14NV (∣mI=−1>↔∣mI=+1>|m_I=-1> \leftrightarrow |m_I=+1>∣mI​=−1>↔∣mI​=+1>) and -1.1(1) ppm/K for 15NV^{15}\mathrm{NV}15NV (∣mI=−1/2>↔∣mI=+1/2>|m_I=-1/2> \leftrightarrow |m_I=+1/2>∣mI​=−1/2>↔∣mI​=+1/2>). An isotopic shift in the zero-field splitting parameter DDD between 14NV^{14}\mathrm{NV}14NV and 15NV^{15}\mathrm{NV}15NV is measured to be ∼\sim∼ 120 kHz. Residual transverse magnetic fields are observed to shift the nuclear spin transition frequencies, especially for 15NV^{15}\mathrm{NV}15NV. We have precisely determined the set of parameters relevant for the development of nuclear-spin-based diamond quantum sensors with greatly reduced sensitivity to environmental factors.
The sensitivity of practical solid quantum sensing can be boosted up by increasing the number of probes. However, the effects of spin dephasing caused by inhomogeneous broadening and imperfect quantum control can reduce the fidelity of quantum control and the sensitivity of quantum sensing with the dense ensemble of probes, such as nitrogen-vacancy (NV) centers in diamond. Here, we present a robust and effective composite-pulse for high fidelity operation against inhomogeneous broadening and control errors via optimized modulation of the control field. Such a composite-pulse was verified on NV center to keep high fidelity quantum control up to a spectrum detuning as large as 110% of Rabi frequency. The sensitivity of the magnetometer with NV center ensemble was experimentally improved by a factor of 4, comparing to dynamical decoupling with a normal rectangular pulse. Our work marks an important step towards high trustworthy ultra-sensitive quantum sensing with imperfect quantum control in practical applications. The used principle is universal and not restricted to NV center ensemble magnetometer.
Color centers in diamond and silicon carbide, and molecular spins through a host matrix control are promising for nanoscale quantum sensing because they can be optically addressable, coherently controllable, and placed proximate to the targets. However, large transverse zero-field splitting (ZFS) is often inevitable due to their intrinsic symmetry and/or the high local strains of the host matrix. Although spin coherence can be extended due to magnetic noise-insensitive clock transitions at a vanishing magnetic field, the eigenstates of these sensors are not sensitive to weak magnetic signals in the linear order. We address this challenge by employing a combination of radio-frequency (rf) field driving along the NV orientation and microwave dynamic decoupling pulse sequences. Radio-frequency driving can effectively mitigate the transverse ZFS effect and enhance the NV center's sensitivity to ac magnetic field signals. This combination not only suppresses environmental noise but also enables quantum frequency mixing between the transverse ZFS and the signal. It also offers the potential to detect weak ac signals at intermediate and high frequencies with high resolution, a task difficult to achieve using conventional methods.
Nuclear spin ensembles in diamond are promising candidates for quantum sensing applications, including rotation sensing. Here we perform a characterization of the optically detected nuclear-spin transitions associated with the 14N nuclear spin within diamond nitrogen vacancy (NV) centers. We observe nuclear-spin-dependent fluorescence with the contrast of optically detected 14N nuclear Rabi oscillations comparable to that of the NV electron spin. Using Ramsey spectroscopy, we investigate the temperature and magnetic-field dependence of the nuclear spin transitions in the 77.5-420 K and 350-675 G range, respectively. The nuclear quadrupole coupling constant Q was found to vary with temperature T yielding d|Q|/dT=-35.0(2) Hz/K at T=297 K. The temperature and magnetic field dependencies reported here are important for quantum sensing applications such as rotation sensing and potentially for applications in quantum information processing.