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 ${}^{40}\mathrm{Ca}^{+}$ 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 $\sim 4\AA$ (in phase space) of the trapped ion is amplified to $\sim 10$ 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.

• Received 8 January 2019
• Revised 19 June 2019

DOI:https://doi.org/10.1103/PhysRevA.100.062111