Observation of Emergent $\mathbb{Z}_2$ Gauge Invariance in a Superconducting Circuit.

Lattice gauge theory (LGT) is one of the most fundamental subjects in modern quantum many-body physics, and has recently attracted many research interests in quantum simulations. Here we experimentally investigate the emergent $\mathbb{Z}_2$ gauge invariance in a 1D superconducting circuit with 10 transmon qubits. By precisely adjusting the staggered longitude and transverse fields to each qubit, we construct an effective Hamiltonian containing a LGT and gauge-broken terms. The corresponding matter sector can exhibit localization, and there also exist a 3-qubit operator, of which the expectation value can retain nonzero for long time in a low-energy regime. The above localization can be regarded as confinement of the matter field, and the 3-body operator is the $\mathbb{Z}_2$ gauge generator. Thus, these experimental results demonstrate that, despite the absent of gauge structure in the effective Hamiltonian, $\mathbb{Z}_2$ gauge invariance can still emerge in the low-energy regime. Our work paves the way for both theoretically and experimentally studying the rich physics in quantum many-body system with an emergent gauge invariance.