Refined ultralight scalar dark matter searches with compact atom gradiometers

Leonardo Badurina, Diego Blas, and Christopher McCabe

Phys. Rev. D 105, 023006 – Published 6 January 2022

Abstract

Atom interferometry is a powerful experimental technique that can be employed to search for the oscillation of atomic transition energies induced by ultralight scalar dark matter (ULDM). Previous studies have focused on the sensitivity to ULDM of km-length atom gradiometers, where atom interferometers are located at the ends of very long baselines. In this work, we generalize the treatment of the time-dependent signal induced by a linearly-coupled scalar ULDM candidate for vertical atom gradiometers of any length and find correction factors that especially impact the ULDM signal in short-baseline gradiometer configurations. Using these results, we refine the sensitivity estimates in the limit where shot noise dominates for AION-10, a compact 10 m gradiometer that will be operated in Oxford, and discuss optimal experimental parameters that enhance the reach of searches for linearly-coupled scalar ULDM. After comparing the reach of devices operating in broadband and resonant modes, we show that well-designed compact atom gradiometers are able to explore regions of dark matter parameter space that are not yet constrained.

Received 1 October 2021
Accepted 22 December 2021

DOI:https://doi.org/10.1103/PhysRevD.105.023006

Physics Subject Headings (PhySH)

Atom interferometry Dark matter

Dark matter detectors

Gravitation, Cosmology & AstrophysicsAtomic, Molecular & OpticalParticles & Fields

Authors & Affiliations

Leonardo Badurina^1,*, Diego Blas^2,3,1, and Christopher McCabe ¹

¹Theoretical Particle Physics and Cosmology Group, Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
²Grup de Física Teòrica, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
³Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain

^*leonardo.badurina@kcl.ac.uk

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Vol. 105, Iss. 2 — 15 January 2022

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Images

Figure 1
Schematic spacetime diagram of the atom gradiometer concept with $n = 2$ LMT kicks. The experiment consists of a pair of cold-atom interferometers performing single-photon transitions between a ground state (blue) and an excited state (red). Height, or radial position, is shown on the vertical axis, and the time axis is horizontal. The laser pulses (wavy lines) traveling across the baseline from opposite sides are used to divide, redirect, and recombine the atomic states, yielding interference patterns that are sensitive to the modulation of the atomic transition frequency caused by couplings to DM. Beam-splitter ( $π / 2$ ) pulses, which begin and end the sequence, are shown in black, while $π$ -pulses are shown in light gray. Atom-light interactions with $π / 2$ -pulses are shown as black squares, while atom-light interactions with $π$ -pulses are shown with gray circles. The gradiometer length $Δ r$ is also shown.
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Figure 2
Estimated reach in the shot noise limit of searches for scalar DM interactions with electrons within the $0.1 Hz \leq f_{ϕ} \leq 4 Hz$ signal window. We plot curves assuming $SNR = 1$ and an integration time of $T_{int} = 10^{8} s$ for a 10 m atom gradiometer with $n = 1000$ , $S_{n} = 10^{- 8} {Hz}^{- 1}$ , and: fixed gradiometer length $Δ r = 4.86 m$ for different interrogation times $T$ (left panel); optimal gradiometer length $Δ r$ for different interrogation times $T$ (right panel). As $T$ increases, the curves move to higher values of $m_{ϕ}$ and $d_{m_{e}}$ . The loss in sensitivity can be mitigated somewhat by increasing $Δ r$ . The orange regions show parameter space that has already been excluded through searches for violations of the equivalence principle via terrestrial torsion balance experiments [48] and MICROSCOPE [49].
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Figure 3
Estimated reach in the shot noise limit of searches for scalar DM interactions with electrons using a 10 m atom gradiometer. We assume $T_{int} = 10^{8} s$ , $S_{n} = 10^{- 8} {Hz}^{- 1}$ and $SNR = 1$ . In purple, ‘AION-10 (this work)’, we plot the result from the refined AION-10 calculation. The bold lines show the power-averaged envelope, while the fainter curves show the full estimated projection. Left panel: the experimental parameters are $n = 1000$ , $Δ r = 4.86 m$ , $r_{1, i} = 0 m$ , and $v_{i} = 4.04 m / s$ resulting in $T = 0.74 s$ , which is the maximum value of $T$ in a 10 m gradiometer. Right panel: the parameters are $n = 1000$ , $Δ r = 7.8 m$ , $r_{1, i} = 0 m$ , $v_{i} = 1.5 m / s$ and $T = 0.3 s$ , which are chosen to maximize the sensitivity at $2 π f_{ϕ} = 10 Hz$ . The orange regions show parameter space that has already been excluded through searches for violations of the equivalence principle via terrestrial torsion balance experiments [48] and MICROSCOPE [49]. In green, ‘AION-10 (JCAP’20)’, we plot the ‘goal’ estimate from Ref. [21]. The insets in each plot depict the spacetime diagram of the interferometric sequence for the aforementioned set of experimental parameters.
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Figure 4
Estimated reach in the shot noise limit of searches for scalar DM interactions with photons using a 10 m atom gradiometer after an integration time of $T_{int} = 10^{8} s$ , assuming $S_{n} = 10^{- 8} {Hz}^{- 1}$ and $SNR = 1$ . In purple, ‘AION-10 (this work)’, we plot the refined projection for AION-10 for the maximum $T$ parameters $n = 1000$ , $Δ r = 4.86 m$ , $r_{1, i} = 0 m$ and $v_{i} = 4.04 m / s$ resulting in $T = 0.74 s$ . In green, ‘AION-10 (JCAP’20)’, we plot the AION-10 ‘goal’ estimate from Ref. [21]. The bold lines show the power-averaged sensitivity, while the fainter curves show the full expected sensitivity. The orange regions show parameter space that has already been excluded through searches for violations of the equivalence principle via terrestrial torsion balance experiments [48] and MICROSCOPE [49]. The inset depicts the spacetime diagram of the interferometric sequence.
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Figure 5
Comparison of the estimated reach in the shot noise limit of searches for scalar DM interactions with electrons between broadband and resonant modes after $T_{int} = 10^{8} s$ and assuming $S_{n} = 10^{- 8} {Hz}^{- 1}$ and $SNR = 1$ . The green curve shows the broadband mode estimate, previously shown as the ‘AION-10 (this work)’ curve in the right panel of Fig. 3. The purple curves shows the resonant mode projection for $Q = 2$ , $T = 0.3 s$ , $n = 500$ , $Δ r = 8.0 m$ , $r_{1, i} = 0.0 m$ and $v_{i} = 4.25 m / s$ . The blue curve shows the resonant mode projection for $Q = 20$ , $T = 0.03 s$ , $n = 50$ , $Δ r = 8.0 m$ , $r_{1, i} = 0.0 m$ and $v_{i} = 5.7 m / s$ . The insets depict the spacetime diagrams for each resonant mode sequence. The orange regions show the excluded parameter space from torsion balance experiments [48] and MICROSCOPE [49].
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