  Most studies for postselected weak measurement in optomechanical system focus
on using a single photon as a measured system. However, we find that using weak
coherent light instead of a single photon can also amplify the mirror's
position displacement of one photon. In the WVA regime (Weak Value
Amplification regime), the weak value of one photon can lie outside the
eigenvalue spectrum, proportional to the difference of the mirror's position
displacement between the successful and failed postselection and its successful
postselection probability is dependent of the mean photon number of the
coherent light and improved by adjusting it accordingly. Outside the WVA
regime, the amplification limit can reach the level of the vacuum fluctuations,
and when the mean photon number and the optomechanical coupling parameter are
selected appropriately, its successful postselection probability becomes
higher, which is beneficial to observe the maximum amplification value under
the current experimental conditions. This result breaks the constraint that it
is difficult to detect outside the WVA regime. This opens up a new regime for
the study of a single photon nonlinearity in optomechanical system.
