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arXiv:2302.12956 · Physical Review A

Quantum metrology algorithms for dark matter searches with clocks

Muhammad H. Zaheer, Naleli Jubert Matjelo, David B. Hume, Marianna S. Safronova, David R. Leibrandt

Published Jan 2, 2025• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.111.012601

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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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Atom interferometers with long baselines are envisioned to complement the ongoing search for dark matter. They rely on atomic manipulation based on internal (clock) transitions or state-preserving atomic diffraction. Principally, dark matter can act on the internal as well as the external degrees of freedom to both of which atom interferometers are susceptible. We, therefore, study in this contribution the effects of dark matter on the internal atomic structure and the atom’s motion. In particular, we show that the atomic transition frequency depends on the mean coupling and the differential coupling of the involved states to dark matter, scaling with the unperturbed atomic transition frequency and the Compton frequency, respectively. The differential coupling is only of relevance when internal states change, which makes detectors, e.g., based on single-photon transitions sensitive to both coupling parameters. For sensors generated by state-preserving diffraction mechanisms like Bragg diffraction, the mean coupling modifies only the motion of the atom as the dominant contribution. Finally, we compare both effects observed in terrestrial dark-matter detectors.