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The preparation of a mechanical oscillator driven by quantum back-action is afundamental requirement to reach the standard quantum limit (SQL) for forcemeasurement, in optomechanical systems. However, thermal fluctuating forcegenerally dominates a disturbance on the oscillator. In the macroscopic scale,an optical linear cavity including a suspended mirror has been used for theweak force measurement, such as gravitational-wave detectors. Thisconfiguration has the advantages of reducing the dissipation of the pendulum(i.e., suspension thermal noise) due to a gravitational dilution by using athin wire, and of increasing the circulating laser power. However, the use ofthe thin wire is weak for an optical torsional anti-spring effect in thecavity, due to the low mechanical restoring force of the wire. Thus, there isthe trade-off between the stability of the system and the sensitivity. Here, wedescribe using a triangular optical cavity to overcome this limitation forreaching the SQL. The triangular cavity can provide a sensitive and stablesystem, because it can optically trap the mirror's motion of the yaw, throughan optical positive torsional spring effect. To show this, we demonstrate ameasurement of the torsional spring effect caused by radiation pressure forces.

An optically trapped mirror for reaching the standard quantum limit