Implementation of weak measurement amplification with the weak coherent light and optomechanical system

TL;DR

This paper demonstrates that weak coherent light can be used in optomechanical systems to amplify mirror displacement, expanding the applicability of weak value amplification beyond single-photon regimes and enabling new experimental possibilities.

Contribution

It introduces the use of weak coherent light for amplification in optomechanical systems, surpassing previous single-photon limitations and exploring regimes outside traditional WVA constraints.

Findings

Amplification of mirror displacement with weak coherent light is feasible.

Successful postselection probability depends on mean photon number and can be optimized.

Amplification can reach vacuum fluctuation levels outside the WVA regime.

Abstract

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.