  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 mirror's 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.
