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arXiv:2609.21501

Optimal control for duty-cycle-limited interferometry with single-NV centers

Ugur Tamer, Sina Zeytinoglu, Ozgur E. Mustecaplioglu

quant-phSubmitted Sep 18, 2026• Announced Sep 21, 2026• 0 citations
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Abstract

Stimulus-responsive hydrogels convert temperature changes into magnetic-field shifts detectable by nitrogen-vacancy (NV) centers, enabling nanoscale thermometry in soft and biological environments. Existing hydrogel-nanodiamond demonstrations rely on NV ensembles, whose high photon throughput is accompanied by gradient-induced inhomogeneous broadening, while idealized single-NV projections assume high-fluence fluorescence/ODMR readout. Here we study a pulsed single-NV route for the same class of sensors and ask whether decoherence-aware coherent control can improve thermometric performance over optimized Ramsey interrogation at equal detected-photon budget. Using a sigmoidal volume-phase-transition model, dipolar magnetic transduction, and Lindblad master-equation simulations, we find a reproducible 25-27% per-shot sensitivity gain over optimized Ramsey, i.e., a 57-60% gain in Fisher information (1.57-1.60). The same gain carries over to the photon-normalized Fisher information. The rate gain is governed by the measurement duty cycle, the fraction of the experimental cycle spent accumulating signal rather than initializing, reading out or waiting, and becomes largest when the overhead or optical-dose constraint dominates the cycle time. The optimized trajectories reveal a response-shaping mechanism in which phase accumulation is concentrated near the end of the sequence, and a closed-form depth-two solution reproduces the numerical optimum and exhibits that mechanism analytically. The advantage is most pronounced when the dephasing time is short compared with the measurement overhead or dose-limited waiting time, which is the operating regime targeted by hydrogel-transduced single-spin biosensing.

Comments
24 pages, 12 figures, 4 tables

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Stimulus-responsive hydrogels convert temperature changes into magnetic-field shifts detectable by nitrogen-vacancy (NV) centers, enabling nanoscale thermometry in soft and biological environments. Existing hydrogel-nanodiamond demonstrations rely on NV ensembles, whose high photon throughput is accompanied by gradient-induced inhomogeneous broadening, while idealized single-NV projections assume high-fluence fluorescence/ODMR readout. Here we study a pulsed single-NV route for the same class of sensors and ask whether decoherence-aware coherent control can improve thermometric performance over optimized Ramsey interrogation at equal detected-photon budget. Using a sigmoidal volume-phase-transition model, dipolar magnetic transduction, and Lindblad master-equation simulations, we find a reproducible 25-27% per-shot sensitivity gain over optimized Ramsey, i.e., a 57-60% gain in Fisher information (1.57-1.60). The same gain carries over to the photon-normalized Fisher information. The rate gain is governed by the measurement duty cycle, the fraction of the experimental cycle spent accumulating signal rather than initializing, reading out or waiting, and becomes largest when the overhead or optical-dose constraint dominates the cycle time. The optimized trajectories reveal a response-shaping mechanism in which phase accumulation is concentrated near the end of the sequence, and a closed-form depth-two solution reproduces the numerical optimum and exhibits that mechanism analytically. The advantage is most pronounced when the dephasing time is short compared with the measurement overhead or dose-limited waiting time, which is the operating regime targeted by hydrogel-transduced single-spin biosensing.
Ensembles of nitrogen-vacancy (NV) centers in diamond are a well-established platform for quantum magnetometry under ambient conditions. One challenge arises from the hyperfine structure of the NV, which, for the common 14^{14}14N isotope, results in a threefold reduction of contrast and thus sensitivity. By addressing each of the NV hyperfine transitions individually, triple-tone microwave (MW) control can mitigate this sensitivity loss. Here, we experimentally and theoretically investigate the regimes in which triple-tone excitation offers an advantage over standard single-tone MW control for two DC magnetometry protocols: pulsed optically detected magnetic resonance (ODMR) and Ramsey interferometry. We validate a master equation model of the NV dynamics against ensemble NV measurements, and use the model to explore triple-tone vs single-tone sensitivity for different MW powers and NV dephasing rates. For pulsed ODMR, triple-tone driving improves sensitivity by up to a factor of three in the low-dephasing regime, with diminishing gains when dephasing rates approach the hyperfine splitting. In contrast, for Ramsey interferometry, triple-tone excitation only improves sensitivity if MW power is limited. Our results delineate the operating regimes where triple-tone control provides a practical strategy for enhancing NV ensemble magnetometry in portable and power-limited sensors.
Magnetic spectroscopy at the nanoscale provides unique insights into material properties and dynamics, with quantum sensors like nitrogen-vacancy (NV) centers being ideally suited for these scales. However, detecting low-frequency signals remains a challenge due to finite coherence times (T2∗T_2^*T2∗​), as signals oscillating slower than 1/T2∗1/T_2^*1/T2∗​ decay before sufficient phase accumulation occurs. We present RESOLUTE (Ramsey corrElation SpectroscOpy puLse seqUence wiTh phasE cycling), a protocol that overcomes these limitations by combining Ramsey measurements with correlation spectroscopy. By storing accumulated phase as a population imbalance during a correlation period (Tcorr<T1T_\mathrm{corr} < T_1Tcorr​<T1​) between two sensing periods, RESOLUTE generates an effective coherence time T2p>T2∗T_2^p > T_2^*T2p​>T2∗​. This shifts the frequency-matching condition to the correlation time, enabling detection in the previously inaccessible spectral region between 1/T11/T_11/T1​ and 1/T2p1/T_2^p1/T2p​. We experimentally demonstrate an extension of the effective coherence time from T2∗=0.38 μsT_2^* = 0.38\,μsT2∗​=0.38μs to T2p=5.1 μsT_2^p = 5.1\,μsT2p​=5.1μs, surpassing Hahn Echo measurements. The technique successfully detects 13^{13}13C nuclear spin Larmor precession at fields as low as 49 \,G ($\sim505050\,$kHz). We further provide theoretical insight using Fisher information to characterize RESOLUTE's frequency estimation capabilities compared to existing protocols. Finally, by integrating adiabatic pulses and phase cycling, we demonstrate robust spin control and effective DC signal extraction. These advancements provide enhanced sensitivity to weak dipolar interactions, essential for single-molecule imaging and quantum sensing applications.
Shallow nitrogen-vacancy (NV) centers are promising candidates for high-precision sensing applications; these defects, when positioned a few nanometers below the surface, provide an atomic-scale resolution along with substantial sensitivity. However, the dangling bonds and impurities on the diamond surface result in a complex environment which reduces the sensitivity and is unique to each shallow NV center. To avoid the environment's detrimental effect, we apply feedback-based quantum optimal control. We first show how a direct search can improve the initialization and readout process. In a second step, we optimize microwave pulses for pulsed optically detected magnetic resonance (ODMR) and Ramsey measurements. Throughout the sensitivity optimizations, we focus on robustness against errors in the control field amplitude. This feature not only protects the protocols' sensitivity from drifts but also enlarges the sensing volume. The resulting ODMR measurements produce sensitivities below $1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{T}$ ${\mathrm{Hz}}^{\ensuremath{-}\frac{1}{2}}$ for an 83% decrease in control power, increasing the robustness by approximately one third. The optimized Ramsey measurements produce sensitivities below 100 nT ${\mathrm{Hz}}^{\ensuremath{-}\frac{1}{2}}$ giving a twofold sensitivity improvement. Being on par with typical sensitivities obtained via single NV magnetometry, the complementing robustness of the presented optimization strategy may provide an advantage for other NV-based applications.
Shallow Nitrogen-Vacancy (NV) centers are promising candidates for high-precision sensing applications; these defects, when positioned a few nanometers below the surface, provide an atomic-scale resolution along with substantial sensitivity. However, the dangling bonds and impurities on the diamond surface result in a complex environment which reduces the sensitivity and is unique to each shallow NV center. To avoid the environment's detrimental effect, we apply feedback-based quantum optimal control. We first show how a direct search can improve the initialization/readout process. In a second step, we optimize microwave pulses for pulsed Optically Detected Magnetic Resonance (ODMR) and Ramsey measurements. Throughout the sensitivity optimizations, we focus on robustness against errors in the control field amplitude. This feature not only protects the protocols' sensitivity from drifts but also enlarges the sensing volume. The resulting ODMR measurements produce sensitivities below 1μμμT\,Hz−12^{-\frac{1}{2}}−21​ for an 83\% decrease in control power, increasing the robustness by approximately one third. The optimized Ramsey measurements produce sensitivities below 100\,nT\,Hz−12^{-\frac{1}{2}}−21​ giving a two-fold sensitivity improvement. Being on par with typical sensitivities obtained via single NV magnetometry, the complementing robustness of the presented optimization strategy may provide an advantage for other NV-based applications.
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.
Nitrogen-vacancy (NV) centers in diamond are a promising platform for ambient, high-spatial resolution magnetometry relevant to biological signals such as cardiac and muscle activity. One of the challenges is the development of pulse sequences tailored to biological signals in the near DC-range. The spatial environment of NV centers within the diamond lattice is highly complex, e.g. due to magnetic field inhomogeneities, limiting the sensors performance. To overcome these experimental constraints, quantum optimal control (QOC) aims at a precise manipulation of the systems dynamics via optimally shaped microwave pulses increasing the overall robustness of spin-based quantum sensors.