Fig. 17: Wannier-Stark confinement of a pair of \({{\mathbb{Z}}}_{2}\) charges in the chain.
From: Synthetic \({{\mathbb{Z}}}_{2}\) gauge theories based on parametric excitations of trapped ions
a Two bosonic particles (filled red circles), with an attached electric-field string connecting them. b Contour plots for the dynamics of the boson distribution \({\overline{n}}_{i}(t)=\langle {a}_{i}^{{{{\dagger}}} }{a}_{i}(t)\rangle\), the electric field on the links \({\overline{s}}_{i}^{x}(t)=\langle {\sigma }_{i,{{{{{{{{\bf{e}}}}}}}}}_{1}}^{x}(t)\rangle\), as well as the block entanglement entropy \(S({\rho }_{A})=-{{{{{{{\rm{Tr}}}}}}}}\{{\rho }_{A}\log {\rho }_{A}\}\). We consider a chain of 32 sites, and set the electric field to \(h=1.2{t}_{1,{{{{{{{{\bf{e}}}}}}}}}_{1}}\) (upper row), and \(h=0.3{t}_{1,{{{{{{{{\bf{e}}}}}}}}}_{1}}\) (lower row). The initial state is \({\vert}_{i}\bullet \sim \!\! \sim {\bullet }_{j}\rangle\) in the notation of Eq. (65), which corresponds to a product state for the bosons being localized at sites i. j, and a domain wall of the gauge qubits for the links in between.
