In this Letter, we experimentally demonstrate the first realization of weak value amplification (WVA) using purely atomic degrees of freedom. Our measurement model identifies the internal electronic states and external motional states of a single trapped
40Ca
+ ion as the system degree and pointer degree respectively, and their controllable weak coupling is provided by a bichromatic light field. By performing appropriate postselection on the internal states, a tiny position displacement of 4 angstroms of the trapped ion is amplified to 10 nanometers in our experiment. The extreme sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated, which may have relation to the phase estimation applications. This work has potential to advance the abundant metrological applications related to the atomic interferometric process, and allows fully exploration of the peculiarities of WVA owing to the high operational flexibility of this procedure .
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
40Ca+ 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 $\ensuremath{\sim}4\AA{}$ (in phase space) of the trapped ion is amplified to $\ensuremath{\sim}10$ nm. 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.