Systems with quantized real and synthetic gauge fields: dynamics and applications

We study systems with quantized real and synthetic gauge fields, with quantization meaning that the magnetic (gauge) field can be in a quantum superposition. We discuss various platforms to realize this quantization. We show how the quantized gauge field can mediate interaction between initially non-interacting particles which can be used to facilitate, i.e., photon-photon interaction and simulate various models of interacting particles. The energy spectrum of particles on a lattice with magnetic field is highly sensitive to the magnetic flux as illustrated by the Hofstadter butterfly. Its quantized version is discussed. Engineered synthetic gauge fields can reach high magnitude and enable operation at elevated temperatures.