Orbital Feshbach Resonance Of Ultracold Fermi Gases In An Optical Lattice

In last more than two decades,researches on ultracold atoms have attracted a great deal of atten-tion and ultracold atoms have been developed as useful experimental carriers for studying many body physics in recent years.The interaction between atoms can be precisely regulated,and atoms them-selves are relatively easy to be controlled.The scattering length between two atoms can be accurately adjusted by many types of Feshbach resonance to any value.Due to the general development of the synthesis gauge fields technology,many new controlling methods for ultracold atoms has developed rapidly.Most recently,some theoretical and experimental works on the spin-orbit coupling and spin correlation systems have been carried out in simulating quantum many body systems.Realization of these research opens a broad avenue in ultracold atoms to study quantum phases,including superfluid.In this thesis,we first study the orbital Feshbach resonance of ultracold two-electron¹⁷³Yb Fermi gas in a one-dimensional optical lattice.We consider a two-band model under the assumptions of a local-density approximation for the optical lattice potential and a mean-field approximation for the intraband Cooper pairings.We get three crucially important properties for the system,the superfluid-Landau-Fermi-liquid?LFL?crossover corresponding to the tunneling energy,the particle condensation in momentum space,and the superfluid-LFL phase transition corresponding to the temperature.We explain how to realize and manipulate these properties.Then by adding a Raman coupling between two different nuclear spin states in a two-channel model,an open channel and a closed channel,we find that the Raman coupling strength can prevent formation of Cooper pairs and compress the system,compromising its superfluidity.While in the presence of a synthetic magnetic flux,the Raman laser can promote superfluidity by adjusting the in-teraction between Cooper pairs,especially for a large orbital Feshbach resonance detuning.Further,we show the significant consequences of the chiral edge current by introducing a synthetic two dimen-sional lattice.We find that the chiral edge currents vary periodically with the flux.We find that the chiral edge currents in the open channel case may change their directions versus the orbital Feshbach resonance detuning.In contrast,for a closed channel,the detuning merely supports the chiral edge current and the directions of the chiral currents do not change with the variation of the detuning,which means the chirality remains unchanged.Meanwhile,we also present a theoretical study of Bose-Einstein condensate?BEC?atoms in a cav-ity with a periodic optical potential.We use a two-mode approximation where the Bogoliubov mode can be filled by a large number of atoms in comparison with the condensate mode.We show that the superradiant phase transition can be controlled by the two external pump lasers and the interaction be-tween atoms.By considering a suitable damping rate of the cavity for an adiabatic approximation,the system behaves as an effective two-mode model in which two atomic modes are coupled to each other through the mediation of the optical field by an effective coupling parameter.This leads to effective frequency shifts of two modes,which can be effectively controlled by the detuning of the cavity field.We show that in the effective two-mode model,the phase noise appears as a classical stochastic pump term which drives the amplitude quadratures of the condensate and the Bogoliubov modes.Mean-while,the effect of the coupling between the phase noise and the two modes of BEC can be eliminated by manipulating the detuning of the cavity even for a dense optical field.