Searching for screened scalar forces with long-baseline atom interferometers

TL;DR

This work targets screened scalar fifth forces, notably chameleon and symmetron models, using a 10 m-scale long-baseline atom interferometer with an internal annular source mass. The authors introduce a Q-flip protocol to convert a static fifth-force into a time-modulated signal and an in situ gravity calibration to disentangle Newtonian gravity from the scalar signal, enabling shot-noise-limited sensitivity. Numerical field calculations coupled to a detailed measurement strategy yield projections that improve existing bounds by about 1–1.5 orders of magnitude, especially near the dark-energy scale for chameleons and in the μ ~ 10^{-2}–10^{-1} meV range for symmetrons. The approach is compatible with forthcoming facilities (AION-10, VLBAI) and adaptable to broader models and longer baselines, offering a practical pathway to probing screened scalar theories in laboratory settings.

Abstract

Screened scalars are ubiquitous in many dark-sector models. They give rise to non-trivial fifth forces whilst evading experimental constraints through density-dependent screening mechanisms. We propose equipping a 10\,m-scale long-baseline atom interferometer with an annular planar source mass inside the vacuum chamber to search for such screened fifth forces. Two key challenges arise: distinguishing the static fifth force from backgrounds, and isolating it from the plate's Newtonian gravity. We introduce the `$Q$-flip protocol', which alternates between interferometry sequences to induce controllable time-dependence, aiding signal extraction and de-trending of transient noise. We further develop an \emph{in situ} calibration procedure to characterise the plate's Newtonian gravity and reach shot-noise-limited sensitivity. We show that our proposal could test theoretically motivated parameter space, advancing existing bounds in chameleon and symmetron screened scalar models by $1$ to $1.5$ orders of magnitude. Our proposal is directly applicable to forthcoming experiments, such as AION-10 or VLBAI, and is readily extensible to broader theoretical models and longer baselines.

Figures (7)

• Figure 1: Schematic of the top of the proposed experimental setup (not to scale) showing the upper interferometer of the gradiometer. A $1\,\mathrm{cm}$ thick planar source mass is positioned at the top of the vacuum chamber with a central hole of radius 40% of that of the chamber to allow for laser transmission. An atom cloud superposition is shown with the upper state having a closest approach to the plate of $1$ cm. The scalar force drops off exponentially in strength with distance such that it barely acts on the lower state. These atoms are launched from approximately $5$ m below the source mass. A second identical interferometer, with atom source at 0 m, is operated simultaneously using common laser pulses (depicted by the red line). Magnetic shielding surrounds the vacuum chamber, protecting from stray fields.
• Figure 2: Numerically modelled scalar fields in a vacuum chamber, sourced by a $1$ cm thick plate at the top with a hole satisfying $R_{\mathrm{H}}=0.4 R_{\rm vac}$. Top: Chameleon field with $M=M_{\rm Pl}$ and $\Lambda=10$ meV. Bottom: Symmetron field, normalised by its VEV ($v=\mu / \sqrt \lambda$), with $M=1$ GeV, $\lambda=1$, and $\mu=1.5\times10^{-2}$ meV.
• Figure 3: Spacetime diagrams of atom gradiometer sequences in the presence of a plate at $10.01$ m. The acceleration sourced by a chameleon field with $M=M_{\rm Pl}$ and $\Lambda=\mathrm{meV}$ is shown by the blue contours in the right panels. Top: Spacetime diagram of a resonant $Q=2$ sequence. The left panel shows the full sequence with pulses at times $0$, $T/2$, $T$, $3T/2$, and $2T$. The right panel shows the atom trajectories in the vicinity of the plate. Bottom: Spacetime diagram for the butterfly sequence, which is insensitive to scalar forces due to the symmetry of the sequence. The right panel shows the atom trajectories in the vicinity of the plate. The resonant and butter sequences differ by the omission of the central laser pulses at time $T$.
• Figure 4: Top: Time series of gradiometer phases using the $Q$-flip protocol. Measurements are first made using the resonant $Q=2$ sequence, which is sensitive to the scalar and gravitational fields sourced by the plate. The sequence then switches to the butterfly sequence, which is insensitive to these effects. Stochastic shot noise is present in each measurement. Repeating the resonant--butterfly cycle produces an oscillating phase readout with period $1/f_0$. Bottom: Square-root of the PSD of the above time series. Spikes appear at odd multiples of the fundamental frequency $f_0$ with amplitudes proportional to $\sqrt{T_{\rm int}}\Delta\Phi_p$.
• Figure 5: Gradiometer phase as a function of minimum atom-plate separation $d_c$, achieved by varying the atom launch velocity. Upper panel: plate gravity (green) and chameleon (purple) with $\Lambda=10^{-1.7}$ meV, $M=10^{-4}\,M_\mathrm{Pl}$ contributions to the phase. Lower panel: relative phase with respect to the gravitational contribution. The blue dashed line shows $d_c = R_{\rm vac}$. Gravitational effects dominate the total phase, with the scalar force detectable only at $d_c \lesssim R_{\rm vac}$ due to exponential suppression at larger separations. By measuring the phase at multiple separations $d_c > R_{\rm vac}$, the gravitational contribution can be characterised and subtracted from measurements at $d_c = 1\,{\rm cm}$.