Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

TL;DR

This paper proposes a theoretical framework for simulating a 3D U(1) gauge-Higgs model using atomic quantum simulation with an extended Bose-Hubbard model on optical lattices, exploring phase diagrams and dynamical phenomena.

Contribution

It introduces a novel approach to simulate a non-standard gauge-Higgs model with asymmetric couplings using cold atoms, and analyzes its phases and dynamics.

Findings

Identified confinement and Higgs phases via Monte-Carlo simulations.

Simulated real-time electric flux evolution and calculated string tension.

Proposed an experimental setup for atomic quantum simulation of the model.

Abstract

In this paper, we study theoretically atomic quantum simulations of a U(1) gauge-Higgs model on a three-dimensional (3D) spatial lattice by using an extended Bose-Hubbard model with intersite repulsions on a 3D optical lattice. Here, the phase and density fluctuations of the boson variable on each site of the optical lattice describe the vector potential and the electric field on each link of the gauge-model lattice, respectively. The target gauge model is different from the standard Wilson-type U(1) gauge-Higgs model because it has plaquette and Higgs interactions with asymmetric couplings in the space-time directions. Nevertheless, the corresponding quantum simulation is still important as it provides us with a platform to study unexplored time-dependent phenomena characteristic of each phase in the general gauge-Higgs models. To determine the phase diagram of the gauge-Higgs model at zero temperature, we perform Monte-Carlo simulations of the corresponding 3+1-dimensional U(1) gauge-Higgs model, and obtain the confinement and Higgs phases. To investigate the dynamical properties of the gauge-Higgs model, we apply the Gross-Pitaevskii equations to the extended Bose-Hubbard model. We simulate the time-evolution of an electric flux that initially is put on a straight line connecting two external point charges. We also calculate the potential energy between this pair of charges and obtain the string tension in the confinement phase. Finally, we propose a feasible experimental setup for the atomic simulations of this quantum gauge-Higgs model on the 3D optical lattice. These results may serve as theoretical guides for future experiments.