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Quantum Differential Decoherence Spectroscopy: Quantitative Limits on Systematic Suppression in Solid-State Quantum Sensors

Arturo Ramos Ruiz

Published Mar 21, 2026• 0 citations
Publisher

Abstract

The characterization of systematic decoherence backgrounds in solid-state quantum sensors constitutes a fundamental metrological challenge: model uncertainties on conventional decoherence sources (δΓ_model ∼ 2–5 Hz) exceed by orders of magnitude the precision required for emerging applications in quantum sensing, including proposals for ultralight dark matter detection where signal rates ΓDM ≲ 10⁻⁶ Hz demand fractional precisions of 10⁻⁶ to 10⁻¹¹. This work introduces Quantum Differential Decoherence Spectroscopy (QDIFF), a measurement methodology employing paired nitrogen-vacancy (NV) center diamond sensors that differ only in a controlled variable—primarily the crystallographic orientation of the NV axis—while sharing an identical cryogenic environment (T < 20 mK). By subtracting simultaneous decoherence rate measurements, QDIFF cancels common-mode systematics without requiring explicit background modeling. A rigorous quantitative analysis of residual noise channels—including thermal fluctuations, surface two-level systems (TLS), electromagnetic interference, measurement back-action, cross-correlations, and the systematic uncertainty of the additive Lindblad decomposition itself (α ≈ 0.15–0.30)—demonstrates improvement factors of 3–12× over absolute single-sensor measurements, depending on the dominant noise channel and fabrication scenario. The resulting residual floor (δΓ_residual ≈ 0.42–7.6 Hz) establishes QDIFF as a metrological tool for quantifying the irreducible systematic uncertainty floor in differential quantum sensors, while honestly acknowledging that direct competition with dedicated ultralight dark matter detectors (CASPEr, ABRACADABRA) remains out of reach. The explicit propagation of model-framework uncertainty constitutes a methodological standard for future proposals in differential quantum sensing.

DOI
10.5281/zenodo.19151907

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The characterization of systematic decoherence backgrounds in solid-state quantum sensors constitutes a fundamental metrological challenge: model uncertainties on conventional decoherence sources (δΓ_model ∼ 2–5 Hz) exceed by orders of magnitude the precision required for emerging applications in quantum sensing, including proposals for ultralight dark matter detection where signal rates ΓDM ≲ 10⁻⁶ Hz demand fractional precisions of 10⁻⁶ to 10⁻¹¹. This work introduces Quantum Differential Decoherence Spectroscopy (QDIFF), a measurement methodology employing paired nitrogen-vacancy (NV) center diamond sensors that differ only in a controlled variable—primarily the crystallographic orientation of the NV axis—while sharing an identical cryogenic environment (T < 20 mK). By subtracting simultaneous decoherence rate measurements, QDIFF cancels common-mode systematics without requiring explicit background modeling. A rigorous quantitative analysis of residual noise channels—including thermal fluctuations, surface two-level systems (TLS), electromagnetic interference, measurement back-action, cross-correlations, and the systematic uncertainty of the additive Lindblad decomposition itself (α ≈ 0.15–0.30)—demonstrates improvement factors of 3–12× over absolute single-sensor measurements, depending on the dominant noise channel and fabrication scenario. The resulting residual floor (δΓ_residual ≈ 0.42–7.6 Hz) establishes QDIFF as a metrological tool for quantifying the irreducible systematic uncertainty floor in differential quantum sensors, while honestly acknowledging that direct competition with dedicated ultralight dark matter detectors (CASPEr, ABRACADABRA) remains out of reach. The explicit propagation of model-framework uncertainty constitutes a methodological standard for future proposals in differential quantum sensing.
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Detecting and characterizing decoherence-inducing noise sources is critical for developing robust quantum technologies and deploying quantum sensors operating at molecular scales. However, current noise spectroscopies rely on severe approximations that sacrifice accuracy and precision. We propose a novel approach to overcome these limitations. It self-consistently extracts noise spectra that characterize the interactions between a quantum sensor and its environment from commonly performed dynamical decoupling-based coherence measurements. Our approach adopts minimal assumptions and is resilient to measurement errors. We quantify confidence intervals and sensitivity measures to identify experiments that improve spectral reconstruction. We employ our method to reconstruct the noise spectrum of a nitrogen-vacancy sensor in diamond, resolving previously undetected nuclear species at the diamond surface and revealing that previous measurements had overestimated the strength of low-frequency noise by an order of magnitude. Our method uncovers previously hidden structure with unprecedented accuracy, setting the stage for precision noise spectroscopy-based quantum metrology.
In the field of quantum sensing, quantum entangled states have the potential to beat the standard quantum limit (SQL) and to approach the Heisenberg limit (HL)1. Since the nitrogen-vacancy (NV) center is a qubit at room temperature, the entangled state among an NV array will offer new possibilities for quantum sensing and computing. However, considering decoherence, it is not clear whether entangled sensing can achieve sensitivity beyond the SQL under ambient conditions2,3. We have previously evaluated the decoherence of a shallow NV-NV pair. At Quantum Innovation (QI) 2024, we characterized the decoherence using noise spectroscopy and observed two types of noise with autocorrelation times on the ~μs and ~ns scales. Our results are consistent with previous studies, which attributed these noise sources to the surface electron spin bath and the surface-modified phonons4. As demonstrated by Y. Matsuzaki et al.3, the autocorrelation time is required to be comparable to the evolution time (~μs) for the entangled state. Therefore, we showed that the ratio of the coupling constants to the two types of noise determines whether the entangled state between NV-NV pair beats the SQL. Compared to the temperature-dependent phonon effects, the electron spin density is more readily controlled by surfacetermination techniques. Surface electron spins are a promising target for designing the decoherence environment surrounding NV-NV entangled sensors. In this study, to determine the optimal surface electron spin density for NV-NV entangled sensing, we calculated the flip-flop rate among surface electron spins, as well as the coupling constant to the NV center.
Noise spectroscopy with quantum sensors is a powerful tool for characterising the properties of the sensor environment and detecting critical magnetic phenomena. While replacing single sensors with large ensembles promises substantial gains in measurement sensitivity and field of view, the output becomes difficult to interpret when there is a variable coupling to targets across the sensing ensemble. In this work we present an analysis procedure for accessing the true source noise spectrum using ensemble coherence from dynamical decoupling measurements. We show that sequence timing plays a dual role in ensemble noise spectroscopy, setting both the frequency selectivity and the weighted collection of signal across the ensemble, and demonstrate how incorporation of the coupling distribution allows accurate parameter extraction of the noise. We apply this procedure to a model system, shallow nitrogen-vacancy centres in diamond, and show that consistent information about the spectral character of MHz-range surface noise can be obtained from two sensing ensembles featuring distinct depth distributions. Our results pave the way for using large quantum sensor ensembles for quantitative, broadband noise spectroscopy, with straightforward extension to other solid-state and molecular sensing platforms.
Quantum algorithms such as dynamical decoupling can be used to improve the sensitivity of a quantum sensor to a signal while suppressing sensitivity to noise. Atomic clocks are among the most sensitive quantum sensors, with recent improvements in clock technology allowing for unprecedented precision and accuracy. These clocks are highly sensitive to variations in fundamental constants, making them ideal probes for local ultralight scalar dark matter. Further improvements to the sensitivity are expected in proposed nuclear clocks based on a nuclear transition in the thorium-229 isotope. We investigate the use of various quantum metrology algorithms in the search for dark matter using quantum clocks. We propose a broadband dynamical decoupling algorithm and compare it with quantum metrology protocols that have been previously proposed and demonstrated, namely, differential spectroscopy and narrowband dynamical decoupling. We conduct numerical simulations of scalar dark matter searches with realistic noise sources and accounting for dark matter decoherence. Finally, we propose an alternative thorium nuclear transition excitation method that bypasses the technical challenges associated with vacuum ultraviolet lasers.
Quantum sensors take advantage of the inherent sensitivity of quantum systems to external environment perturbations to precisely measure target signals. The same interaction with the environment, however, limits the device sensitivity by reducing the coherence of the quantum states. Quantum control can play a crucial role in improving the sensor performance. We explore quantum control tools to improve the performance of a NitrogenVacancy (NV) center as a single-qubit sensor of ultra-weak magnetic fields in noisy environments. We present a method to obtain a precise spectroscopic characterization of the NV environment, instrumental to design robust sensing strategies with improved noise protection. Then, we exploit optimal quantum control based on a set of numerical methods to optimize the temporal dependence of the sensor driving field adapted to quantum sensing purposes, and prove its advantage to achieve best compromises between signal acquisition and noise cancellation.