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We present a theoretical study of quantum simulations of $(1+1)$-dimensionalU(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and aHiggs matter field, by using ultra-cold bosonic gases on a one-dimensionaloptical lattice. Starting from the extended Bose-Hubbard model with on-site andnearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model asa low-energy effective theory. The derived gauge-Higgs model exhibitsnontrivial phase transitions between confinement and Higgs phases, and wediscuss the relation with the phase transition in the extended Bose-Hubbardmodel. Finally, we study real-time dynamics of an electric flux by theGross-Pitaevskii equations and the truncated Wigner approximation. The dynamicsis governed by a bosonic analog of the Schwinger mechanism, i.e., shielding ofan electric flux by a condensation of Higgs fields, which occurs differently inthe Higgs and the confinement phase. These results, together with the obtainedphase diagrams, shall guide experimentalists in designing quantum simulationsof the gauge-Higgs models by cold gases.

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