Ultracold gases are ideal platforms to perform quantum simulations, because they are fully quantum by essence and their environment and some of the key parameters are well under controlled. In addition, quantum electrodynamic, which governs light-matter interaction, is a U(1) symmetry gauge theory, it is also possible to mimic higher symmetry gauge theory by dressing the atom with laser fields to simulate problems ranging from quantum information, condensed-matter, to high-energy physics. In this talk, I will explain how artificial non-Abelian gauge fields can be generated in an ultracold gas using atom-light interactions. I will then give several examples where we emphasize on specific properties of these non-Abelian gauge fields. As a first example, I will discuss close-loop transformations, which depend on the initial point in sharp contrast with the classical Gauss-Bonnet theorem [1].  I will follow on the wave-packet non-inertial dynamic in homogenous non-Abelian gauge [2]. Finally, I will present recent experiments where we realized an atomtronics spin field effect transistor [3].
 

[1] F. Leroux, K. Pandey, R. Rehbi, F. Chevy, C. Miniatura, B. Grémaud, and D. Wilkowski, Non-Abelian Adiabatic Geometric Transformations in a Cold Strontium Gas, Nat. Commun. 9, 3580 (2018).
[2] M. Hasan, C. S. Madasu, K. D. Rathod, C. C. Kwong, C. Miniatura, F. Chevy, and D. Wilkowski, Wave Packet Dynamics in Synthetic Non-Abelian Gauge Fields, Phys. Rev. Lett. 129, 130402 (2022).
[3] C. S. Madasu, M. Hasan, K. D. Rathod, C. C. Kwong, and D. Wilkowski, Datta-Das Transistor for Atomtronic Circuits Using Artificial Gauge Fields, Phys. Rev. Res. 4, 033180 (2022).