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In this paper, we explore the possibilities of realizing weak valueamplification (WVA) using purely atomic degrees of freedom. Our schemeidentifies the internal electronic states and external motional states of asingle trapped $^{40}$Ca$^+$ ion as the system degree and pointer degreerespectively, and their controllable weak coupling is provided by a bichromaticlight field. In our experimental demonstration, by performing appropriatepostselection on the internal states, a position displacement of 4 angstroms(in phase space) of the trapped ion is amplified to 10 nanometers. Thesensitivity of the amplification effect to the relative phase of the quantumstate is also demonstrated. The high operational flexibility of this procedureallows fully exploration of the peculiarities of WVA.

Scheme and Experimental Demonstration of Fully Atomic Weak Value Amplification