In this Letter, we report the first experimental realization and investigation of a spin-orbit coupled Fermi gas. Both spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state are observed as hallmarks of spin-orbit coupling in a Fermi gas. The single particle dispersion is mapped out by using momentum-resolved radio-frequency spectroscopy. From momentum distribution and momentum-resolved radio-frequency spectroscopy, we observe the change of fermion population in different helicity branches consistent with a finite temperature calculation, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system.

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Using two crossed 1064-nm optical-dipole-trap lasers to be the Raman beams, an effective vector gauge potential for Bose-Einstein condensed 87 Rb in the F = 2 hyperfine ground state is experimentally created. The moderate strength of the Raman coupling still can be achieved when the detuning from atomic resonance is larger than the excited-state fine structure, since rubidium has 15 nm energy-level spitting. The atoms at the far detuning of the Raman coupling are loaded adiabatically into the dressed states by ramping the homogeneous bias magnetic field with different paths and the dressed states with different energies are studied experimentally. The experimental scheme can be easily extended to produce the synthetic magnetic or electric field by means of a spatial or time dependence of the effective vector potential.

Polar molecules in an optical lattice provide a versatile platform to study quantum many-body dynamics. Here we use such a system to prepare a density distribution where lattice sites are either empty or occupied by a doublon composed of an interacting Bose-Fermi pair. By letting this out-of-equilibrium system evolve from a well-defined, but disordered, initial condition, we observe clear effects on pairing that arise from inter-species interactions, a higher partial-wave Feshbach resonance and excited Bloch-band population. These observations facilitate a detailed understanding of molecule formation in the lattice. Moreover, the interplay of tunnelling and interaction of fermions and bosons provides a controllable platform to study Bose-Fermi Hubbard dynamics. Additionally, we can probe the distribution of the atomic gases in the lattice by measuring the inelastic loss of doublons. These techniques realize tools that are generically applicable to studying the complex dynamics of atomic mixtures in optical lattices.