Quantum simulation of $(1+1)$-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases

We present a theoretical study of quantum simulations of $(1+1)$-dimensional U(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and a Higgs matter field, by using ultra-cold bosonic gases on a one-dimensional optical lattice. Starting from the extended Bose-Hubbard model with on-site and nearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model as a low-energy effective theory. The derived gauge-Higgs model exhibits nontrivial phase transitions between confinement and Higgs phases, and we discuss the relation with the phase transition in the extended Bose-Hubbard model. Finally, we study real-time dynamics of an electric flux by the Gross-Pitaevskii equations and the truncated Wigner approximation. The dynamics is governed by a bosonic analog of the Schwinger mechanism, i.e., shielding of an electric flux by a condensation of Higgs fields, which occurs differently in the Higgs and the confinement phase. These results, together with the obtained phase diagrams, shall guide experimentalists in designing quantum simulations of the gauge-Higgs models by cold gases.