Weak value amplification in optomechanical system with Mach-Zehnder interferometer

Abstract

In this work an optomechanical system inside a Mach-Zehnder interferometer is studied from the perspective of the weak value amplification effect. The optomechanical system consists of a Fabry-Pérot cavity with a moving mirror in the middle. Single photons are post-selected in the detector located in one of the output ports of the interferometer (dark port), which allows to enlarge the displacement caused by a single photon over the moving mirror of the cavity.

Since the interaction between a single photon and the mirror is weak, the amplification factor of the displacement corresponds to a weak value. By making the initial and final states of the photon quasi-orthogonal, the weak value becomes large and the radiation pressure force exerted by the photon is increased, making a single photon behave as ``many photons'' will do.

However, the amplification effect comes at the cost of the lost of data. The usefulness of weak values for parameter estimation in our setup is analyzed from the perspective of the Fisher information. Although the maximum precision of the estimation does not change either by using weak values or by implementing weak measurements without post-selection, in the first scenario all the information can be put in a small amount of post-selected events, which allows to construct an estimator of optomechanical parameters at a lower cost (fewer observations of the measurement device are needed). The scenarios in which the weak measurement is affected by white and time-correlated classical noise were also analyzed; in the first case, the maximum precision is the same in both measurement strategies (with or without post-selection), while in the second case the maximum precision is increased when weak values are employed.