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Measuring Gravity at Small Distances

T.J. Bay
Aharon Kapitulnik

Recent experiments have verified Newtonian gravity at length scales under 100 μm. This experiment tests for variations at smaller scales using a rotating drive mass and a test mass-bearing cantilever at a separation of ~30 μm. The drive mass consists of a TeCu disc with one hundred radial trenches cut into the surface which are filled with a thermal-expansion matched epoxy(figure 1, left). The trenches are then covered by a deposition of gold to create a smooth equipotential surface to eliminate electrostatic forces along with a gold pattern near the edge of the drive mass to allow for spin speed detection (figure 1, right). The mass is then actuated by a helium gas quartz rotor (figure 2).

Figure 1

Figure 2

Test Mass and Cantilever

The cantilever design considers factors of spring constant, quality factor, the droop in earth′s gravity and resonance frequency. A small number of ~5 g gold prism test masses (figure 3) are epoxied onto the cantilevers. The cantilever spring constant and test mass give a resonance frequency of about 350 Hz. The frequency of the AC gravitational signal is matched to the cantilever/test-mass resonance by feedback-controlling the spin of the rotor (figure 4). Radiation pressure damping is used to lower the effective quality factor of the cantilever with out reducing sensitivity.


Force Detection

Force measurement sensitivity of the cantilever is ultimately limited by thermal noise. To minimize the cantilever thermal noise we operate the experiment at 4.2 K. Other sources of noise are mitigated by operating the cantilevers in a vacuum and vibrationally isolating the experiment from the floor and vacuum pumps.

Fabry-Pérot Interferometer

Cantilever position readout is achieved through use of an interferometer (figure 5) whose cavity is formed from the cleaved end of an optical fiber and the top surface of the test mass on the cantilever. Reflected optical power is then a simple a function of the cantilever position.

Figure 3

Figure 4

Figure 5

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