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Prospects for spin squeezing in nuclear magnetic resonance dark matter searches

Eric Boyers

Published Jan 1, 2022• 0 citations

Abstract

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.

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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.

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.

We recently showed that macroscopic nuclear spin ensembles prepared in coherent spin states can dramatically enhance the interaction rates of weakly interacting cosmic relics-such as dark matter and the cosmic neutrino background-through collective quantum effects analogous to Dicke superradiance, where the de-excitation and excitation rates scale as the square of the number of spins,

N^2

. We thus coined these processes superradiant interactions. In this paper, we propose a protocol to realize this enhancement and boost the discovery potential for such relics. We show how concepts from quantum optics can be adapted to nuclear spins coupled to superconducting circuits, enabling high-sensitivity systems. The spins are first initialized into a coherent spin state via a

π/2

Rabi pulse from the ground state. When the circuit is sufficiently detuned from resonance, the spin-circuit interaction implements a squeezing Hamiltonian. Because squeezing must outpace spin relaxation and dephasing, the protocol favors macroscopic ensembles and high-quality superconducting circuits. During this squeezing phase, the standard quantum variance is reduced by up to 4.8 orders of magnitude-equivalent to 48 dB of squeezing-for circuits with quality factors

Q \sim 10^8

-

10^9

. The signal imprinted on the spins during the squeezing protocol can be magnified by further utilizing the squeezing interactions, easing the requirement for shot-noise-limited readout. This protocol has the potential to significantly accelerate axion and dark photon dark matter searches and extend the reach of existing axion experiments to probe QCD axion-nuclear spin couplings. More broadly, it paves the way for detecting coherent inelastic interactions from other cosmic relics-most notably the cosmic neutrino background-and establishes nuclear-spin-based systems as a new class of quantum, ultra-low-threshold detectors.

We propose a magnetic resonance force microscopy (MRFM) search for axion dark matter around 1 GHz. The experiment leverages the axion's derivative coupling to electrons, which induces an effective A.C. magnetic field on a sample of electron spins polarized by a D.C. magnetic field and a micromagnet. A second pump field at a nearby frequency enhances the signal, with the detuning matched to the resonant frequency of a magnet-loaded mechanical oscillator. The resulting spin-dependent force is detected with hih sensitivity via optical interferometry. Accounting for the relevant noise sources, we show that current technology can be used to put constraints competitive with those from laboratory experiments with just a minute of integration time. Furthermore, varying the pump field frequency and D.C. magnetic field allows one to scan the axion mass. Finally, we explore this setup's capability to put constraints on other dark matter - Standard Model couplings.

Axions are a compelling dark matter candidate suggested by theories beyond the Standard Model. The predicted axion-electron coupling and the resulting pseudomagnetic field allow for laboratory axion searches. Here we report an experimental axion search via a superconductor-spin hybrid magnetometer. A state-of-the-art broadband magnetometer with a sensitivity of sub-100 aT/Hz

^{1/2}

at tens of kHz has been realized by coupling a ferrite spin sensor to a readout system based on a superconducting quantum interference device. The most stringent terrestrial constraints on the axion-electron coupling have been established in the frequency range 5$\sim$60 kHz. In the future, an improvement on the constraints of more than 4 orders of magnitude is foreseeable through arrays of superconductor-spin hybrid magnetometers with optimized designs. This work demonstrates the potential of superconductor-spin hybrid magnetometers in high-precision magnetic field sensing and the study of fundamental physics.

The hypothetical axion particle (of unknown mass) is a leading candidate for dark matter (DM).Many experiments search for axions with microwave cavities, where an axion may convert into a cavity photon, leading to a feeble excess in the output power of the cavity.Recent work [Backes et al., Nature 590, 238 (2021)] has demonstrated that injecting squeezed vacuum into the cavity can substantially accelerate the axion search.Here, we go beyond and provide a theoretical framework to leverage the benefits of quantum squeezing in a network setting consisting of many sensor cavities.By forming a local sensor network, the signals among the cavities can be combined coherently to boost the axion search.Furthermore, injecting multipartite entanglement across the cavities-generated by splitting a squeezed vacuum-enables a global noise reduction.We explore the performance advantage of such a local, entangled sensor network, which enjoys both coherence between the axion signals and entanglement between the sensors.Our analyses are pertinent to next-generation DM-axion searches aiming to leverage a network of sensors and quantum resources in an optimal way.Finally, we assess the possibility of using a more exotic quantum state, the Gottesman-Kitaev-Preskill (GKP) state.Despite a constant-factor improvement in the scan time relative to a single-mode squeezed state in the ideal case, the advantage of employing a GKP state disappears when a practical measurement scheme is considered.

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

g_{ae}

. These results establish a practical and theoretically controlled pathway for using QEC to improve qubit array searches for physics beyond the Standard Model.