Search for Screened Interactions Associated with Dark Energy below the $100\mu \mathrm{m}$ Length Scale

We present the results of a search for unknown interactions that couple to mass between an optically levitated microsphere and a gold-coated silicon cantilever. The scale and geometry of the apparatus enable a search for new forces that appear at distances below $100\mu \mathrm{m}$ and which would have evaded previous searches due to screening mechanisms. The data are consistent with electrostatic backgrounds and place upper limits on the strength of new interactions at $<0.1\mathrm{fN}$ in the geometry tested. For the specific example of a chameleon interaction with an inverse power law potential, these results exclude matter couplings $\beta >5.6\times 10^4$ in the region of parameter space where the self-coupling $\mathrm{\Lambda }\gtrsim 5\mathrm{meV}$ and the microspheres are not fully screened.

Figure 1

(Left) Schematic of the optical trap and shielding electrodes. The electrode in the foreground is removed to show the inside of the trap. (Right) Enlargement of the region near the trap. A $5\mu \mathrm{m}$ diameter microsphere is suspended at the focus of an upward-propagating laser beam. The $10\mu \mathrm{m}$ thick Au-coated Si cantilever is positioned at $\sim 20–200\mu \mathrm{m}$ separations from the microsphere and oscillated in the $z$ direction using a nanopositioning stage.

Figure 2

Measured response of microsphere 1 versus the distance from the cantilever face as the cantilever is swept in $z$ with a constant bias of 1, 2, 3, 4, and 5 V. The data points are shown as dots and the best fit model as solid lines. (Inset) Amplitude of the fit component $\propto {\partial }_z{E}_z$ (top) and the fit component $\propto E_z{\partial }_z{E}_z$ (bottom). Fits to the expected linear and quadratic dependence on the voltage are also shown (solid lines).

Figure 3

Measured response for microspheres 1 (top), 2 (middle), and 3 (bottom) versus the distance from the cantilever face as the cantilever is swept in $z$ with a nominal bias of 0 V. The best fit electrostatic background-only model (dashed line) and the amplitude of a chameleon force at the 95% C.L. upper limit for $\mathrm{\Lambda }=10\mathrm{meV}$ (solid line) are also shown.

Figure 4

Limits on $\mathrm{\Lambda }$ versus $1/\beta =M/M_{\mathrm{Pl}}$ for the chameleon model discussed in the text. The 95% C.L. exclusion limits from this search are denoted by the dark (gray) region. Recent constraints from atom interferometry are shown by the light (blue) region [16, 17]. The horizontal line indicates $\mathrm{\Lambda }=2.4\mathrm{meV}$. Limits from neutron interferometry [18, 19, 20] and from the Eöt-Wash torsion balance experiment [8, 14, 44] are denoted by the hatched regions. These limits are shown only in the restricted regions of parameter space considered in Refs. [14, 18].