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