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arXiv:2609.22661

Thermometry in Near-Degenerate Nitrogen-Vacancy Ensembles Enabled by Bright-Dark-State Mixing

Matt K. Fu, John O. Dabiri

quant-phSubmitted Sep 19, 2026• Announced Sep 22, 2026• 0 citations
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Abstract

Nitrogen-vacancy (NV) centers have emerged as a highly sensitive platform for spatially resolved temperature measurements. When the $\lvert0\rangle\to\lvert+1\rangle$ and $\lvert0\rangle\to\lvert-1\rangle$ transitions are nearly degenerate and the Rabi frequency is comparable to the transition splitting, the spin dynamics encountered during pulsed protocols for temperature measurement can significantly alter the intended accumulation of temperature-dependent phase. We investigate these triplet ($\lvert0\rangle$, $\lvert\pm1\rangle$) spin dynamics and their effect on pulsed thermometry protocols under these conditions. We find that the conventional thermal-echo timing produces negligible temperature-sensitive signal amplitudes at the common-mode detuning. However, we find that the nominal spin-echo timing produces resolvable oscillations at the common-mode detuning, leading to a strong temperature-sensitive carrier signal. This departure from the expected protocol behavior is qualitatively captured by an ensemble model of the triplet dynamics, which supports significant dark-state leakage as a plausible mechanism for the temperature-sensitive response. This mixing-enabled thermal echo uses a four-phase quadrature readout that resolves the signed oscillation frequency and is validated using independent sweeps of the microwave carrier frequency and fluid temperature. We further assess the ability of a four-refocusing-pulse (LDD4B) low-field dynamical-decoupling sequence to extend the NV coherence and find that while the echo retains a sensitivity to common-mode detuning, the effective phase-accumulation interval corresponds to approximately half the total evolution time. These findings could support the use of pulsed NV thermometry in biological or mobile applications where applying magnetic bias fields is impractical and microwave power may be limited.

Comments
25 pages, 7 figures, 3 tables; includes two appendices

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Nitrogen-vacancy (NV) centers have emerged as a highly sensitive platform for spatially resolved temperature measurements. When the ∣0⟩→∣+1⟩\lvert0\rangle\to\lvert+1\rangle∣0⟩→∣+1⟩ and ∣0⟩→∣−1⟩\lvert0\rangle\to\lvert-1\rangle∣0⟩→∣−1⟩ transitions are nearly degenerate and the Rabi frequency is comparable to the transition splitting, the spin dynamics encountered during pulsed protocols for temperature measurement can significantly alter the intended accumulation of temperature-dependent phase. We investigate these triplet (∣0⟩\lvert0\rangle∣0⟩, ∣±1⟩\lvert\pm1\rangle∣±1⟩) spin dynamics and their effect on pulsed thermometry protocols under these conditions. We find that the conventional thermal-echo timing produces negligible temperature-sensitive signal amplitudes at the common-mode detuning. However, we find that the nominal spin-echo timing produces resolvable oscillations at the common-mode detuning, leading to a strong temperature-sensitive carrier signal. This departure from the expected protocol behavior is qualitatively captured by an ensemble model of the triplet dynamics, which supports significant dark-state leakage as a plausible mechanism for the temperature-sensitive response. This mixing-enabled thermal echo uses a four-phase quadrature readout that resolves the signed oscillation frequency and is validated using independent sweeps of the microwave carrier frequency and fluid temperature. We further assess the ability of a four-refocusing-pulse (LDD4B) low-field dynamical-decoupling sequence to extend the NV coherence and find that while the echo retains a sensitivity to common-mode detuning, the effective phase-accumulation interval corresponds to approximately half the total evolution time. These findings could support the use of pulsed NV thermometry in biological or mobile applications where applying magnetic bias fields is impractical and microwave power may be limited.
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Dynamical decoupling multipulse sequences can be applied to solid-state spins for sensing weak oscillating fields from nearby single nuclear spins. By periodically reversing the probing system's evolution, other noises are counteracted and filtered out over the total evolution. However, the technique is subject to intricate interactions resulting in additional resonant responses, which can be misinterpreted with the actual signal intended to be measured. We experimentally characterize three of these effects present in single nitrogen-vacancy centers in diamond, where we also develop a numerical simulation model without rotating-wave approximation, showing robust correlation to the experimental data. Regarding centers with the N 15 nitrogen isotope, we observe that a small misalignment in the bias magnetic field causes the precession of the nitrogen nuclear spin to be sensed by the electronic spin of the center. Another studied case of ambiguous resonances comes from the coupling with lattice C 13 nuclei, where we use the echo modulation frequencies to obtain the interaction Hamiltonian and then utilize the latter to simulate multipulse sequences. Finally, we also measure and simulate the effects from the free evolution of the quantum system during finite pulse durations. Due to the large data volume and the strong dependence of these ambiguous resonances with specific experimental parameters, we provide a simulations data set with a user-friendly graphical interface, where users can compare simulations with their own experimental data for spectral disambiguation. Although focused on nitrogen-vacancy centers and dynamical decoupling sequences, these results and the developed model can potentially be applied to other solid-state spins and quantum sensing techniques.
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In this work, we optimize a dynamical decoupling (DD) protocol to improve the spin coherence properties of a dense ensemble of nitrogen-vacancy (NV) centers in diamond. Using liquid nitrogen-based cooling and DD microwave pulses, we increase the transverse coherence time T2 from ∼ 0.7 ms up to ∼ 30 ms. We extend previous work of single-axis (Carr-Purcell-Meiboom-Gill) DD towards the preservation of arbitrary spin states. After performing a detailed analysis of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the concatenated XY8 pulse sequences serves as the optimal control scheme for preserving an arbitrary spin state. Finally, we use the concatenated sequences to demonstrate an immediate improvement of the AC magnetic sensitivity up to a factor of two at 250 kHz. For future work, similar protocols may be used to increase coherence times up to NV-NV interaction time scales, a major step toward the creation of quantum collective NV spin states.