Physics Colloquium

hile non-perturbative approaches such as lattice gauge theory led to significant advances in understanding the physics of strong interactions, many problems remain out of reach for classical computation, in particular, real-time dynamics or properties of QCD at finite baryon density that are being explored in heavy-ion collision experiments. Recent advances in the technology of engineering custom interactions for ultra-cold atomic gases in optical lattices opened a possibility for quantum simulations as was envisioned by R. Feynman in the 1980s. The main idea is that the degrees of freedom of the original system are mapped onto a quantum Hamiltonian whose dynamics can be realized in a laboratory. Many condensed matter Hamiltonians, such as Bose-Hubbard model, have been recently studied in this way. Quantum simulation of gauge theories is however challenging since the gauge symmetry is not naturally present in the ultra-cold atomic systems. I will review the current status of theoretical proposals for quantum simulation of field theories and then focus on our recent work on an explicitly gauge-invariant formulation of the Abelian-Higgs model for simulation on optical lattices.