Quantum Simulation of Quantum Field Theory with a Trapped Ion System

We report on the experimental quantum simulation of interacting bosonic and fermionic quantum field modes with a trapped ion system [1]. We consider a basic model of only one fermion and one anti-fermion interacting through a bosonic field mode, which reveals interesting features such as self-interactions, particle creation and annihilation and non-perturbative regimes. We experimentally study these phenomena by manipulating the internal degrees of freedom of a multi-level single $^{171}\mathrm{Yb}^+$ ion and its motional state, based on the proposal of Ref. [1]. Our experimental scheme is a scalable approach and can be extended beyond the limit of classical computation of quantum field theory when more fermions and bosons are included. \\[4pt] [1] J. Casanova, et al., Phys. Rev. Lett, 107, 260501 (2011)