Cryogenic test of gravitational inverse square law below 100-micrometer length scales

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The inverse-square law is a hallmark of theories of gravity, impressively demonstrated from astronomical scales to sub-millimeter scales, yet we do not have a complete quantized theory of gravity applicable at the shortest distance scale. Problems within modern physics such as the hierarchy problem, the cosmological constant problem, and the strong CP problem in the Standard Model motivate a search for new physics. Theories such as large extra dimensions, ‘fat gravitons,’ and the axion, proposed to solve these problems, can result in a deviation from the gravitational inverse-square law below 100 μm and are thus testable in the laboratory.

We have conducted a sub-millimeter test of the inverse-square law at 4.2 K. To minimize Newtonian errors, the experiment employed a near-null source, a disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, were positioned on the two sides of the source mass at a nominal distance of 280 μm. As the source was driven sinusoidally, the response of the test masses was sensed through a superconducting differential accelerometer. Any deviations from the inverse-square law would appear as a violation signal at the second harmonic of the source frequency, due to symmetry.

We improved the design of the experiment significantly over an earlier version, by separating the source mass suspension from the detector housing and making the detector a true differential accelerometer. We identified the residual gas pressure as an error source, and developed ways to overcome the problem. During the experiment we further identified the two dominant sources of error - magnetic cross-talk and electrostatic coupling. Using cross-talk cancellation and residual balance, these were reduced to the level of the limiting random noise.

No deviations from the inverse-square law were found within the experimental error (2σ) down to a length scale λ = 100 μm at the level of coupling constant |α|≤2. Extra dimensions were searched down to a length scale of 78 μm (|α|≤4). We have also proposed modifications to the current experimental design in the form of new tantalum source mass and installing additional accelerometers, to achieve an amplifier noise limited sensitivity.