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arXiv:2103.06284 · Quantum Science and Technology

Quantum sensitivity limits of nuclear magnetic resonance experiments searching for new fundamental physics

Deniz Aybas, Hendrik Bekker, John W. Blanchard, Dmitry Budker, Gary P Centers, Nataniel L. Figueroa, A. V. Gramolin, Derek F. Jackson Kimball, Arne Wickenbrock, Alexander O. Sushkov

Published Apr 26, 2021• 27 citations
arXivHTMLPDF

Abstract

Abstract Nuclear magnetic resonance is a promising experimental approach to search for ultra-light axion-like dark matter. Searches such as the cosmic axion spin-precession experiments (CASPEr) are ultimately limited by quantum-mechanical noise sources, in particular, spin-projection noise. We discuss how such fundamental limits can potentially be reached. We consider a circuit model of a magnetic resonance experiment and quantify three noise sources: spin-projection noise, thermal noise, and amplifier noise. Calculation of the total noise spectrum takes into account the modification of the circuit impedance by the presence of nuclear spins, as well as the circuit back-action on the spin ensemble. Suppression of the circuit back-action is especially important in order for the spin-projection noise limits of searches for axion-like dark matter to reach the quantum chromodynamic axion sensitivity.

DOI
10.1088/2058-9565/abfbbc

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quant-pharXiv:2605.17457•Physical review. D/Physical review. D.•May 19, 2026•1 citation
Abstract Nuclear magnetic resonance is a promising experimental approach to search for ultra-light axion-like dark matter. Searches such as the cosmic axion spin-precession experiments (CASPEr) are ultimately limited by quantum-mechanical noise sources, in particular, spin-projection noise. We discuss how such fundamental limits can potentially be reached. We consider a circuit model of a magnetic resonance experiment and quantify three noise sources: spin-projection noise, thermal noise, and amplifier noise. Calculation of the total noise spectrum takes into account the modification of the circuit impedance by the presence of nuclear spins, as well as the circuit back-action on the spin ensemble. Suppression of the circuit back-action is especially important in order for the spin-projection noise limits of searches for axion-like dark matter to reach the quantum chromodynamic axion sensitivity.
Direct detection of dark matter remains an important outstanding problem since abundant astrophysical evidence points towards its existence, but no experiment has succeeded in detecting it. Axions and axion-like-particles are some of the most compelling candidates for dark matter given their appearance in many theories of physics beyond the Standard Model and their relatively unexplored parameter space compared to other candidates. Recently, the Cosmic Axion Spin Precession Experiment-Electric (CASPEr-e) has used nuclear magnetic resonance (NMR) to search for effective magnetic fields created by axionic dark matter. By decreasing technical noise sources, CASPEr-e is projected to reach the standard quantum limit where spin projection noise is the dominant noise source limiting sensitivity. However, some axion models predict axion couplings to normal matter that would be too small for even a quantum limited CASPEr-e experiment to detect. This creates a need for surpassing the spin projection noise limit in NMR dark matter searches. In this thesis, I explore the prospects for surpassing the quantum limit in NMR by using spin squeezed states, entangled states with variance in one projection reduced below the standard quantum limit. First, I propose an experimental scheme for generating squeezed states by coupling the spins to an off-resonant circuit to create a One-Axis-Twist Hamiltonian. Then, using exact results and numerical simulations, I determine the amount of squeezing that can be achieved given decoherence and noise. Next, I perform modeling to show that squeezing can accelerate dark matter searches despite earlier results that argued squeezing cannot improve experimental sensitivity when subject to decoherence. Finally, I apply these results to the CASPEr-e experiment and show that at axion frequencies near 100MHz, squeezing can speed up the experiment by a factor of up to 30, corresponding to a sensitivity improvement by a factor of over 5.
The detection of axion dark matter poses a significant challenge due to its exceptionally weak coupling to standard-model particles. Here we develop a noise-tolerant quantum-metrology scheme based on coupled 129^{129}129Xe spin ensembles to search for such weakly interacting particles. Within an experimentally accessible parameter regime, our scheme achieves an ideal exclusion limit on the axion coupling constant that is several orders of magnitude more stringent than that of conventional detection methods. We further investigate the performance of our scheme under dissipative noise and find that its robustness is fundamentally governed by the energy-spectrum structure of the composite spin-environment system. Remarkably, when a bound state emerges in the spectrum, the exclusion limit asymptotically recovers its ideal value in the non-Markovian dynamics, whereas under the Markovian approximation the limit deteriorates significantly due to noise. Our results establish a universal mechanism for noise-resilient exploration of beyond-standard-model physics, which can be practically implemented by engineering bound-state formation via tuning the Larmor frequency of the spin ensembles.
Spin squeezing has been explored in atomic systems as a tool for quantum sensing, improving experimental sensitivity beyond the spin standard quantum limit for certain measurements. To optimize absolute metrological sensitivity, it is beneficial to consider macroscopic spin ensembles, such as nuclear spins in solids and liquids. Coupling a macroscopic spin ensemble to a parametrically-modulated resonant circuit can create collective spin squeezing by generating spin correlations mediated by the circuit. We analyze the squeezing dynamics in the presence of decoherence and finite spin polarization, showing that achieving 7 dB spin squeezing is feasible in several nuclear spin systems. The metrological benefit of squeezing a macroscopic spin ensemble lies in the suppression of technical noise sources in the spin detection system relative to the spin projection noise. This expands the experimental sensitivity bandwidth when searching for signals of unknown frequency and can improve the resonant signal-to-noise ratio. Squeezing macroscopic spin ensembles may prove to be a useful technique for fundamental physics experiments aimed at detecting spin interactions with oscillating background fields, such as ultralight dark matter.
One of the areas of research of the Superconducting Quantum Systems and Materials (SQMS) center is the application of quantum sensing to fundamental physics searches, demonstrating that quantum sensors can greatly improve the sensitivity of experiments searching for Beyond the Standard Model (BSM) physics, or performing high-precision measurements. Theorists have developed many ideas for BSM physics that would result in interactions that can in principle be detected, but with signals small enough that they haven t been observed yet. In this field, the capability to lower the detector s thermal noise to few or dozens of mK, and to use QIS technologies such as Josephson Parametric Amplifiers and photon counters (in-situ or itinerant) enable us to reach unprecedented sensitivities and faster scan rates. Here is presented an overview of the quantum sensing efforts at SQMS [1], focusing on theoretical advancements and experimental searches for Dark Sector particles (as dark matter candidates and not), gravitational waves, and precision measurements. The experiments conducted, or under preparation, include axion dark matter (DM) [2, 3], dark photon DM searches [4,5], light-shining-through-wall experiments [6], cavity-based searches for high frequency gravitational waves [7], and measurements of the electron magnetic moment [8]. [1] Berlin, A., et al. "Searches for new particles, dark matter, and gravitational waves with SRF cavities." arXiv preprint arXiv:2203.12714 (2022). [2] Giaccone, B., et al. "Design of axion and axion dark matter searches based on ultra high Q SRF cavities." arXiv preprint arXiv:2207.11346 (2022). [3] Braggio, C., et al. "Quantum-enhanced sensing of axion dark matter with a transmon-based single microwave photon counter." arXiv preprint arXiv:2403.02321 (2024). [4] Fan, X., et al. "One-electron quantum cyclotron as a milli-eV dark-photon detector." Physical review letters 129.26 (2022): 261801. [5] Cervantes, R., et al. "Deepest sensitivity to wavelike dark photon dark matter with superconducting radio frequency cavities." Physical Review D 110.4 (2024): 043022. [6] Romanenko, A., et al. "Search for dark photons with superconducting radio frequency cavities." Physical review letters 130.26 (2023): 261801. [7] Berlin, A., et al. "Electromagnetic cavities as mechanical bars for gravitational waves." Physical Review D 108.8 (2023): 084058. [8] Fan, X., et al. "Measurement of the electron magnetic moment." Physical review letters 130.7 (2023): 071801.
The enhancement of weak signals and the detection of hypothetical particles, facilitated by quantum amplification, are crucial for advancing fundamental physics and its practical applications. Recently, it was experimentally observed that magnetic field can be amplified by using nuclear spins under Markovian noise, [H. Su, et al., Phys. Rev. Lett. 133, 191801 (2024)]. Here, we theoretically propose amplifying the magnetic-field signal by using nuclear spins by the quantum Zeno effect (QZE). Under identical conditions, we demonstrate that compared to the Markovian case the amplification of the weak magnetic field can be enhanced by a factor about e1/2e^{1/2}e1/2 under a Gaussian noise. Moreover, through numerical simulations we determine the optimal experimental parameters for amplification conditions. This work shows that the combination of the QZE and spin amplification effectively enhances the amplification of the weak magnetic field. Our findings may provide valuable guidance for the design of experiments on establishing new constraints of dark matter and exotic interactions in the near future.
Searches for axion and axionlike dark matter based on solid-state spin qubits are fundamentally limited by strong longitudinal dephasing, which rapidly suppresses the sensitivity gains offered by entanglement. Here we show that quantum error correction (QEC) can substantially enhance axion search sensitivity in realistic semiconductor spin qubit platforms by mitigating this dominant noise source. By integrating an optimally chosen repetition code QEC with logical GHZ block entanglement, we derive closed-form expressions for the quantum Fisher information that explicitly incorporate the finite coherence time of the axion field. Our analysis demonstrates that modest QEC cycle frequencies are sufficient to significantly reduce the effective dephasing rate, thereby restoring a broad parameter regime in which entanglement-enhanced sensing surpasses the standard quantum limit. Projecting these results onto CMOS-compatible device parameters, we find that QEC-protected entangled sensing can revive otherwise inaccessible quantum advantages, yielding up to order-of-magnitude improvements in sensitivity to the axion-electron coupling gaeg_{ae}gae​. These results establish a practical and theoretically controlled pathway for using QEC to improve qubit array searches for physics beyond the Standard Model.