We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and honeycomb lattice. The many body physics of cold atom in harmonic potential is investigated in the frame of mean-field Gross-Pitaevskii equation. Then the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice, are investigated by using cluster dynamical mean-field theory and continuous time quantum Monte Carlo method. We also study the quantum spin Hall effect in the kagome optical lattice.
We investigate the nonlinear dynamics of a system composed of a cigar-shaped Bose-Einstein condensate and an optical cavity with the two sides coupled dispersively.By adopting discrete-mode approximation for the condensate,taking atom loss as a necessary part of the model to analyze the evolution of the system,while using trial and error method to find out steady states of the system as a reference,numerical simulation demonstrates that with a constant pump,atom loss will trigger a quantum optical bi-stability switch,which predicts a new interesting phenomenon for experiments to verify.
We consider two coupled Gross Pitaevskii equations describing a two-component Bose Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential, and investigate the dynamics of vector solitons. By using a direct method, we construct a novel family of vector soliton solutions, which are the linear combination between dark and bright solitons in each component. Our results show that due to the superposition between dark and bright solitons, such vector solitons possess many novel and interesting properties. The dynamics of vector solitons can be controlled by the Feshbach resonance technique, and the vector solitons can keep the dynamic stability against the variation of the scattering length.
By using a unified theory of the formation of various types of vector-solitons in two-component Bose-Einstein condensates with tunable interactions, we obtain a family of exact vector-soliton solutions for the coupled nonlinear Schrodinger equations. Moreover, the Bogoliubov equation shows that there exists stable dark soliton in specific situa- tions. Our results open up new ways in considerable experimental interest for the quantum control of multi-component Bose Einstein condensates.
We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitaevskii equations are developed to study the nonlinear dynamics of BoseEinstein condensates. Analytically, we present the integrable conditions for the Gross Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose Einstein condensates.
