Fig. 11: ♢-scheme for \({{\mathbb{Z}}}_{2}\) tunneling in a plaquette.
From: Synthetic \({{\mathbb{Z}}}_{2}\) gauge theories based on parametric excitations of trapped ions
On the left, we represent schematically the four possible gauge-invariant states in the sector with background charges q1 = 1, q2 = 0, which correspond to Eq. (45). We use thick and thin yellow lines to represent the presence and absence of an electric field, respectively. Likewise, dark and bright red circles represent the presence and absence of a matter particle, respectively. We see that, when the matter particle resides on the left or right site, a 't Hooft electric field line that winds around the plaquette can be present or absent, doubling the number of possible states. On the right, we depict an effective ♢-scheme in quantum optics, in which the gauge-invariant tunneling induces two copies of the Λ-scheme of Fig. 4, which appeared for a single link and two bosons that lead to bright and dark states, and mode entanglement.
