Demonstration of Displacement Sensing of a mg-Scale Pendulum for mm- and mg-Scale Gravity Measurements

Gravity generated by large masses has been observed using a variety of probes from atomic interferometers to torsional balances. However, gravitational coupling between small masses has never been observed so far. Here, we demonstrate sensitive displacement sensing of the Brownian motion of an optically trapped 7 mg pendulum motion whose natural quality factor is increased to $10^8$ through dissipation dilution. The sensitivity for an integration time of one second corresponds to the displacement generated in a millimeter-scale gravitational experiment between the probe and a 100 mg source mass, whose position is modulated at the pendulum mechanical resonant frequency. Development of such a sensitive displacement sensor using a milligram-scale device will pave the way for a new class of experiments where gravitational coupling between small masses in quantum regimes can be achieved.

Figure 1

(a) Experimental setup. Outside the vacuum system, a phase modulator and an intensity modulator are inserted between the optical fiber and the laser source for laser stabilization. Inside the vacuum chamber, a five-stage vibration isolation setup is installed with the monitor for laser stabilization and the ring cavity being fixed to the maximally isolated stage. (b) Vibration isolation system. Inside the vacuum chamber, we install the five-stage vibration isolation stage. On the main platform, the laser intensity monitor, the reference cavity, and the ring cavity are installed. (c),(d) Mechanical oscillator. The pictures show the 7 mg movable mirror of 3 mm diameter and 0.5 mm thickness, which is photographed before setting it on the main plate as shown in Fig. 1.

Figure 2

(a) The measured spectra with the bandwidth of 1 Hz and the noise budget from 10 Hz to 100 kHz. The suspension thermal noise is calculated using the result in [29] and the frequency noise modified by the optical spring effect is calculated using the result in [26]. (b) The spectra from 100 to 400 Hz. By combining the thermal noise and the frequency noise due to the optical spring, the width of the spectral peak at the resonant frequency of 280 Hz is broadened.