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In this paper, we explore the possibilities of realizing weak value amplification (WVA) using purely atomic degrees of freedom. Our scheme identifies the internal electronic states and external motional states of a single trapped $^{40}$Ca$^+$ ion as the system degree and pointer degree respectively, and their controllable weak coupling is provided by a bichromatic light field. In our experimental demonstration, by performing appropriate postselection on the internal states, a position displacement of 4 angstroms (in phase space) of the trapped ion is amplified to 10 nanometers. The sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated. The high operational flexibility of this procedure allows fully exploration of the peculiarities of WVA.
Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak value require
We study the possibility of varying the measured lifetime of a decaying particle based on the technique of weak value amplification in which an additional filtering process called postselection is performed. Our analysis made in a direct measurement
In a quantum-noise limited system, weak-value amplification using post-selection normally does not produce more sensitive measurements than standard methods for ideal detectors: the increased weak value is compensated by the reduced power due to the
An experimental proposal is presented in which dark port post-selection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-Perot cavity and i
In a weak measurement with post-selection, a measurement value, called the weak value, can be amplified beyond the eigenvalues of the observable. However, there are some controversies whether the weak value amplification is practically useful or not