Fig. 12: ’t Hooft loop entanglement in the gauge qubits.
From: Synthetic \({{\mathbb{Z}}}_{2}\) gauge theories based on parametric excitations of trapped ions
We represent a scheme for the second-order virtual tunneling of a boson, which initially occupies the left site (upper state) and aims to tunnel to right, which is penalized energetically by the on-site energy \({\Delta }_{2}\,\gg \,{t}_{1,{{{{{{{{\bf{e}}}}}}}}}_{n}}\). After the virtual tunneling and the accompanying stretching of the electric-field line (intermediate states), the second tunneling process back to the left site can either compress the string, or stretch it further until it winds around the plaquette. The superposition of these possible transitions (lower state) leads to an entangled state. We use thick and thin yellow lines to represent the presence and absence of an electric field, respectively.
