Quantum simulation of Dynamical gauge field for ultra-cold atoms in a cavity

Quantum simulation of synthetic gauge field in ultra-cold atoms provides opportunity to realize the analogues of Landau levels of electrons and Quantum Hall Physics, Hofstadter-Harper Hamiltonian, and topological phases in a much more controlled environment. Where the initial studies were mostly on synthetic gauge fields that do not have dynamics of their own, a number of current studies aimed to create dynamical gauge field for neutral ultra -cold atoms to extend the scope of such analogue quantum simulations for condensed matter and high-energy physics related phenomena.
In this work, we propose that ultra cold atoms in high finesse ring cavity of suitable geometry to create a non-uniform dynamical gauge field for neutral ultracold atom. The resulting energy spectrum is similar to the energy dispersion for an electron in a similar magnetic modulation that can effectively create one dimensional flow of such ultra-cold atoms. Starting with single atoms dynamics in such synthetically created dynamical non-uniform gauge field we extend this idea to the ultra-cold atomic Bose-Einstein condensates and study the corresponding dynamics.