Abatement of Thermal Noise due to Internal Damping in 2D Oscillators with Rapidly Rotating Test Masses

Abstract

Mechanical oscillators can be sensitive to very small forces. Low frequency effects are up-converted to higher frequency by rotating the oscillator. We show that for 2-dimensional oscillators rotating at frequency much higher than the signal the thermal noise force due to internal losses and competing with it is abated as the square root of the rotation frequency. We also show that rotation at frequency much higher than the natural one is possible if the oscillator has 2 degrees of freedom, and describe how this property applies also to torsion balances. In addition, in the 2D oscillator the signal is up-converted above resonance without being attenuated as in the 1D case, thus relaxing requirements on the read out. This work indicates that proof masses weakly coupled in 2D and rapidly rotating can play a major role in very small force physics experiments.

Testing the weak equivalence principle with macroscopic proof masses on ground and in space: A brief review

“…Weak coupling ensures high sensitivity to differential accelerations; fast rotation up-converts the signal from the orbital frequency (1.7 · 10 −4 Hz) to the much higher spin frequency (1 Hz) where not only 1/f electronics noise but also thermal noise from internal damping is much lower. 13 Once all known sources of thermal noise are taken into account, the integration time required to perform a UFF/WEP test to 10 −17 with a signal to noise ratio of 2 is of about 3 hours. 14 As a result, a reliable 10 −17 test can be performed in 1 day (corresponding to 15 revolutions around the Earth and to 8 measurement cycles).…”

Testing the equivalence principle in space after the MICROSCOPE mission

“…Limitations to the spin rate of RTB come from concerns about rotation noise (on ground it includes motor and bearings noise) and the attenuation of the signal strength at frequencies above the natural oscillation mode (the system being in essence a forced oscillator [14]). With a natural torsional frequency ν tor = 1 798 Hz, the highest spin rate so far is ν spinRT B = 2 3 ν tor 0.84 mHz [3].…”

“…Mechanical suspensions are very versatile and allow the concentric test cylinders to be arranged in such a way that they co-rotate with the spacecraft around the symmetry axis, being sensitive in the plane perpendicular to it. In this plane the relative displacements caused by tiny low frequency differential accelerations between the test cylinders -such as a violation signal-can be detected, upconverted by rotation to a much higher frequency where thermal noise is much lower [14]. After initial spin up, spacecraft stabilitazion is maintained passively by conservation of angular momentum, which ensures extremely low rotation noise and does not need propellant -to be left for drag-free control and occasional manoeuvres [17].…”

“…Thermal noise due to internal damping in the suspensions decreases with the frequency as 1/ √ ν [13,14]. A signal of WEP violation with the Earth as source would be DC on ground and at orbital frequency in space.…”

“…If care is taken in flying an experiment somewhat more sensitive than ground balances, the improvement achievable in space can be impressive. Rapid rotation of the spacecraft and consequent up-conversion of the signal to high frequency, at which thermal noise is low and integration time is short, are the main drivers of the "Galileo Galilei" (GG) space experiment to test the equivalence principle to 10 −17 without invoking cryogen-ics ( [14][15][16][17], [4]).…”