Quantum simulation of the (1+1)-dimensionalU(1)Lattice QED with Rydberg atoms

Gauge Theories like Quantum chromodynamics (QCD) display non perturbative effects which mostlyprevent their study via analytical tools. A possible approach to study and simulate these theoriesis the Lattice Gauge Theory formulation, i.e., a space-time discretization through a lattice. Inthe quantum link formulation of lattice gauge theories every field state on the link of the latticeis identified with a quantum spin state. This allows to simulate the theory via quantum systemslike a chain of cold neutral atoms characterized by highly excited Rydberg states. In this thesisa brief introduction to the Lattice Quantum electrodynamics (Lattice QED) is given, focusing onits Hamiltonian formulation and on the Gauss’ law constraint. An example of a Rydberg atomsquantum simulator for the quantum link formulation of a(1 + 1)-dimensionalU(1)lattice gaugeQED is presented. Finally, we will numerical simulate the time-evolution of a small-scale systemwith exact diagonalization techniques.