Weak value amplification in an optomechanical system with mach-zehnder interferometer

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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-Perot cavity with a moving mirror in the middle. Single photons are post-selected in the detector 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. The amplification effect comes, however, at the cost of the lost of data. The usefulness of weak values for parameter estimation in our setup is analysed from the perspective of the Fisher information. Although the precision of the estimation does not change either by using weak values or by implementing measurements that do not rely on post-selection, in the first scenario all the information can be put in a small amount of post-selected events, which is a verification of a well known general result in the existing literature on the subject.
Tesis (Ph.D. in Physics)--Pontificia Universidad Católica de Chile, 2021