Gauge fields are ubiquitous in Physics. For example, in the context of high energy physics, they are the fundamental carrier of forces; while in condensed matter systems the associated physical fields (electrical and magnetic) are essential in creating and understanding many-body phenomena. Here I present our experimental work synthesizing static gauge fields for ultracold neutral atoms (bosonic and fermionic alkali atoms), analogous to applied fields in condensed matter systems. I will discuss these static gauge fields in the language of spin-orbit coupling where it consists of an equal sum of Rashba and Dresselhaus couplings. In experiment, we couple two internal states of our alkali atoms with a pair of ``Raman'' lasers and load our degenerate quantum gas into the resulting adiabatic eigenstates. For a Bose gas, a function of the Raman laser strength, a new exchange-driven interaction between the two dressed spins develops, which drives a (quantum) phase transition from a state where the two dressed spin states spatially mix, to one where they phase separate. Going beyond this simple modification to the spin-dependent interaction, we show that in the limit of large laser intensity, the particles act as free atoms, but interact with contributions from higher even partial waves.

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