Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios

We report on precision resonance spectroscopy measurements of quantum states of ultracold neutrons confined above the surface of a horizontal mirror by the gravity potential of Earth. Resonant transitions between several of the lowest quantum states are observed for the first time. These measurements demonstrate that Newton’s inverse square law of gravity is understood at micron distances on an energy scale of $10^{-14}\mathrm{eV}$. At this level of precision, we are able to provide constraints on any possible gravitylike interaction. In particular, a dark energy chameleon field is excluded for values of the coupling constant $\beta >5.8\times 10^8$ at 95% confidence level (C.L.), and an attractive (repulsive) dark matter axionlike spin-mass coupling is excluded for the coupling strength $g_s{g}_p>3.7\times 10^{-16}$ ($5.3\times 10^{-16}$) at a Yukawa length of $\lambda =20\mu \mathrm{m}$ (95% C.L.).

Figure 1

Setup and results for the employed gravity resonance spectroscopy. Left: The lowest eigenstates and eigenenergies with confining mirrors at bottom and top separated by $30.1\mu \mathrm{m}$. The observed transitions are marked by arrows. Center: The transmission curve determined from the neutron count rate behind the mirrors as a function of oscillation frequency showing dips corresponding to the transitions shown on the left. Right: Upon resonance at 280 Hz, the transmission decreases with the oscillation amplitude in contrast to the detuned 160 Hz. Because of the damping, no revival occurs. All plotted errors correspond to a standard deviation around the statistical mean.

Figure 2

Spatial probability density of UCN in Earth’s gravitational field times the number of counted neutrons measured with a track detector [19] behind the mirrors. A fit to the data (solid red line) gives the relative abundances of state $|1⟩$ (dashed gray line) and $|2⟩$ (dot-dashed green line). No higher states are found.

Figure 3

Exclusion plot for chameleon fields (95% confidence level). Our newly derived limits (solid line) are 5 orders of magnitude lower than the upper bound from precision tests of atomic spectra (dot-dashed line) [27]. Pendulum experiments [28] provide a lower bound (dashed line).

Figure 4

Limits on the pseudoscalar coupling of axions (95% confidence level). Our limit for a repulsive (attractive) coupling is shown in a solid (dashed) line marked with $\mathrm{A}+(\mathrm{A}-)$. The limits are a factor of 30 more precise than the previous ones derived from a direct measurement at the micron length scale [29] derived from our previous experiment with UCN marked B [13, 14].