Efects Of Atomic Interaction On Tunneling Dynamics Of Condensate In Optical Lattice

In recent years, the study of superfluid Fermi gases in optical lattices has openednew frontiers of research in the physics of ultracold atomic gases, especially since thesuperfluidity of ultracold fermions in optical lattices has been stablished. In such a low-density quantum system, people have made many theoretical eforts in the crossover fromthe Bose-Einstein condensation(BEC) to the Bardeen-Cooper-Schriefer (BCS)state, suchas Bloch oscillations. The first part presented the nonlinear Landau-Zener tunnelingand the nonlinear Rabi oscillations of superfluid Fermi gases between Bloch bands in anaccelerating optical lattice. Within the hydrodynamic theory and a two-level model, thetunneling probability of superfluid Fermi gases between Bloch bands is obtained. Wefind that, as the system crosses from the Bose-Einstein condensation (BEC) side to theBCS side, the tunneling rate is closely related to the particle density: when the density issmaller (larger) than a critical value, the tunneling rate at unitarity is larger (smaller) thanthat in the BEC limit. This is well explained in terms of an efective interaction and anefective potential. Furthermore, the nonlinear Rabi oscillations of superfluid Fermi gasesbetween the bands are discussed by imposing a periodic modulation on the level bias andthe strength of the lattice. Analytical expressions of the critical density for suppressing orenhancing the Rabi oscillations are obtained. It is shown that, as the system crosses fromthe BEC side to the BCS side, the critical density strongly depends on the modulationparameters (i.e., the modulation amplitude and the modulation frequency). For a fixeddensity, a high-frequency or low-frequency modulation can suppress or enhance the Rabioscillations both at unitarity and in the BEC limit. For an intermediate modulationfrequency, the Rabi oscillations are chaotic along the entire BEC-BCS crossover, especially,on the BCS side. Interestingly, we find that the modulation of the lattice strength onlywith an intermediate modulation frequency has significant efect on the Rabi oscillationsboth in the BEC limit and at unitarity; that is, an intermediate-frequency modulationcan enhance the Rabi oscillations, especially on the BCS side.In second section the nonlinear Landau Zener tunneling and nonlinear Rabi oscilla-tions of Bose Einstein condensate (BEC) with higher-order atomic interaction betweenthe Bloch bands in an accelerating optical lattice are discussed. Within the two-levelmodel, the tunneling probability of BEC with higher-order atomic interaction betweenBloch bands is ob-tained. We finds that the tunneling rate is closely related to thehigher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BECwith higher-order atomic interaction between the bands are discussed by impos-ing aperiodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It isshown that the critical value strongly depends on the modulation parameters (i.e., themodulation amplitude and frequency) and the strength of periodic potential.The third part the anisotropy of dipole-dipole interaction is revealed by energy band,tunneling dynamics and stabilities of a dipolar condensate in one-dimensional opticallattices. It is demonstrated that the Bloch band structure, the tunneling rate betweenBloch bands and the stabilities of Bloch states can be controlled by adjusting the efectiveaspect ratio of the condensate and the dipolar orientation.Finally, in the fifth chapter of this paper, we summarize the main results and givean outlook of the future in this field.