Strongly Interacting And Two-dimensional Spin-Orbit Coupled Ultracold Fermi Gases

In recent years, the spin-orbit coupling ultracold atomic gases attracted people great interest. Using spin orbit coupling effect in ultracold atoms in a very easy-to-control system can easily simulate many physical behavior of charged particles in electromagnetic field associated with interesting physical phenomena of quantum effects, such as quantum Hall systems, spin Hall effect, topological insulators, p-wave superconductor and Majorana fermions like.This PhD thesis introduce our recent work based on ultracold Bose-Fermi Mixture gases lab, including study about the radio-frequency's effect on Feshbach resonance, dissociation of Feshbach molecules in ultracold Fermi gases with spin-orbit (SO) coupling, and report the experimental realization of a two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases. Moreover, we design a simple scheme to generate 2D SOC in ultracold Fermi gases, and produce a perpendicular Zeeman field to open the band gap at the Dirac point.We study the one-diemensional spin-orbit coupling, which is equal weight of Rashba and Dresselhaus SOC, and make a simple introduction about the Rashba and Dresselhaus SOC. Also, we make a throretical description of the Raman coupling strength in datail, and study the effect about wavelength of Raman laser and external magnetic field on Raman coupling strength to select a suitable parameters for our experment.We demonstrate experimentlly to control magnetic Feshbach resonance in ultracold 40K Fermi Gases using radio-frequency (RF) field. We present spectroscopic measurement of three ground deeply bound molecular levels by the RF radiation in ultracold 40K Fermi gases. Modifying the scattering properties by RF field in shown by measuring the loss profile in experiment. This work provides the high accuracy location of ground molecular states near s-wave Feshbach resonance, which enable further improvement to determine the s-wave scattering length of 40K and can be used to study the crossover regime from a Bose-Einstein condensate to a Bardeen-cooper-Schrieffer superfluid in presence of RF field.We study the dissociation of Feshbach molecules in ultracold Fermi gases with spin-orbit (SO) coupling. Since SO coupling can induce a quantum transition between Feshbach molecules and the fully polarized Fermi gas, the Feshbach molecules can be dissociated by the SO coupling. We experimentally realize this type of dissociation in ultracold gases of 40K atoms with SO coupling created by Raman beams and observe that the dissociation rate is highly nonmonotonic on both the positive and negative Raman-detuning sides. Our results show that the dissociation of Feshbach molecules can be controlled by different degrees of freedoms, i.e., the SO-coupling intensity or the momenta of the Raman beams, as well as the detuning of the Raman beams.In experiment, we firstly realized two-dimensional synthetic spin-orbit coupled ultracold Fermi gases, get energy-momentum dispersion of the dressed atoms, and get highly controllable and stable Dirac point for ultracold fermionic atoms. Finally, we plot the trajectory of the Dirac point in momentum space.Through changing the polarization of the Raman laser we design a simple scheme to generate a perpendicular Zeeman field to open the band gap at the Dirac point in the realized 2D spin-orbit coupled ultracold Fermi gases. The band gap can be controlled precisely by the effective perpendicular Zeeman field in our experiment.