Fig. 1: Synthetic \({{\mathbb{Z}}}_{2}\) gauge links and Gauss’ law.
From: Synthetic \({{\mathbb{Z}}}_{2}\) gauge theories based on parametric excitations of trapped ions
a Schematic representation of the effective Hamiltonian in Eq. (5). The two modes labeled by 1,2, which play the role of matter fields, are coupled by a synthetic tunneling of strength \({t}_{1,{{{{{{{{\bf{e}}}}}}}}}_{1}}\)(6) that is mediated by a qubit that plays the role of the gauge field, and effectively sits on the synthetic link. In addition to the tunneling, the electric-field term of strength h(6) drives transitions in the qubit (inset). b For a single particle, Gauss' law (8) for a distribution of background charges q1 = 0, q2 = 1, is fulfilled by the two states \(\vert {1}_{1},{-}_{1,{{{{{{{{\bf{e}}}}}}}}}_{1}},{0}_{2}\rangle ,\vert {0}_{1},{+}_{1,{{{{{{{{\bf{e}}}}}}}}}_{1}},{1}_{2}\rangle\), characterized by the absence or presence of an electric field attached to the matter particle sitting on the leftmost or rightmost site. These electric-field states are represented by arrows parallel (anti-parallel) to the external field h, and the presence (absence) of the corresponding electric-field line is represented by a thicker (shaded) golden link.
