Magnetic Levitation as a New Probe of Non-Newtonian Gravity

Abstract

We present MORRIS (Magnetic Oscillatory Resonator for Rare-Interaction Studies) and propose the first tabletop search for non-Newtonian gravity due to a Yukawa-like fifth force using a magnetically levitated particle. Our experiment comprises a levitated sub-millimeter magnet in a superconducting trap that is driven by a time-periodic source. Featuring short-, medium-, and long-term stages, MORRIS will admit increasing sensitivities to the force coupling strength $α$, optimally probing screening lengths of $λ\sim 1\,\mathrm{mm}$. Our short-term setup provides a proof-of-principle study, with our medium- and long-term stages respectively constraining $α\lesssim 10^{-4}$ and $α\lesssim 10^{-5}$, leading over existing bounds. Our projections are readily recastable to concrete models predicting the existence of fifth forces, and our statistical analysis is generally applicable to well-characterized sinusoidal driving forces. By leveraging ultralow dissipation and heavy test masses, MORRIS opens a new window onto tests of small-scale gravity and searches for physics beyond the Standard Model.

Figures (6)

• Figure 1: A: Top view of the proposed short- and medium-term experimental setups for MORRIS, showing the mass-wheel and the trapped particle. We include the separation between the driving and test masses at closest approach $a$, the distance modulation $R$, the frequency of the drive $\omega_d$, and the total force experienced by the particle $F_\mathrm{tot}(t)$. B: Side view of the proposed long-term setup, consisting of two traps. In the driving trap, an AC electromagnetic drive excites the trapped particle. C: The force experienced by the sensing particle with signal period $T_s$. The dependence of this force to $a$ and $R$ is explained in Ref. supp_mat.
• Figure 2: The force power spectral density of our levitated particle taken at the resonance frequency of the particle, $\mathcal{P}(\omega_s)$, with varying closest approach distance $a$. We assume our short-term configuration (c.f. \ref{['tab:configs']}). Shown is the expected gravitational signal ($\alpha = 0)$ with five equally spaced data points (red markers). The fifth-force signals from three benchmark points are also shown, labeled according to $(\alpha, \lambda)$. The noise floor is assumed to be thermal, $S_{FF}^{\mathrm{noise}}(\omega_s) = S_{FF}^\mathrm{therm}$ (c.f. \ref{['eq:thermal_noise']}).
• Figure 3: The $95\%$ confidence level projected limits on positive values of $\alpha$ with scale $\lambda$ from MORRIS. Shown are the limits from our short-, medium-, and long-term configurations, summarized in \ref{['tab:configs']}. The bands around each limit illustrate their $1\sigma$ range. The solid regions indicate the existing fifth-force limits from laboratory Hoskins:1985tnKapner:2006siYang:2012zzbTan:2020vpf and geophysical Adelberger:2003zx experiments. The transparent regions show the preferred regions for light moduli arising from supersymmetric string theory Dimopoulos:1996kpDimopoulos:2003mw.
• Figure 4: Comparisons between the gravitational signal ($\alpha=0$) from the full calculation and our approximation, \ref{['eq:force_approx']}. This is shown in the time domain (top) and in the power spectral density (bottom) using \ref{['eq:periodogram-dft']}. The oscillation amplitude $\mathcal{F}_\mathrm{osc}$ is given by the difference between the total force at the closest separation $a$ and farthest separation $a + 2R$ for a single source mass. The approximation accurately captures the resonant peak, occurring at the signal frequency $f = f_s$ and which we use in our inferencing. The noise floor is assumed to be thermal and is computed in the main text. We use our short-term setup, taking $r_0 \approx 1.95\,\mathrm{cm}$.
• Figure 5: The $95\%$ confidence level projected limits on absolute values of $\alpha$ with screening length $\lambda$. We show the limits from our short-, medium-, and long-term configurations. The dashed lines above unity $|\alpha|$ are thin, closed contours where negative values of $\alpha$ are allowed. The existing constraints and theoretical regions are discussed in the main text.