Theoretical studies of BEC/BCS states in quantum atomic gases

在本研究项目中，我们对BEC/BCS状态进行了研究，得到了以下结果：1) BCS/BEC交叉中的单粒子激发及相关现象：我们发现，在被困于谐波势中的费米气体中，单粒子激发的能隙由凝结物表面附近的安德里夫模决定。rf隧穿电流谱在弱耦合区Andreev模式处有一个峰值，在势中心由阶参量决定的能量处有一个峰值。3)涡旋状态和涡旋成核过程。：通过求解BdG方程，研究了BCS/BEC交叉区粒子激发的涡旋态和能谱。随着相互作用强度的增大，粒子在涡旋中心的分布减小，形成离散的核层。我们还证明了该耦合区域的涡旋状态可以用双分量GL方程来描述。4)非平衡过程：对GP方程进行了数值模拟，研究了超流体涡旋状态的形成过程。我们发现，在涡旋形成的早期状态下，由于开尔文波的作用，形成了湍流状态，然后系统稳定到三角晶格状态。

In this research project, we investigated the BEC/BCS states, and obtained the following results.1) Single-particle excitations and related phenomena in BCS/BEC crossover : We find that, in the Fermi gas trapped in a harmonic potential, the energy gap of the single-particle excitation is determined by the Andereev mode localized near the surface of the condensate. The rf-tunneling current spectral has a peak at the position of the Andreev mode in the weak coupling region, while it has a peak at the energy determined by the order parameter at the cencer of the potential.3) Vortex states and process of vortex nucleation. : We investigated vortex states and energy spectrum of particle excitations in the BCS/BEC crossover region, by solving the BdG equation. With increasing the strength of the interaction, the particle distribution at the vortex center is reduced and descrete core levels are formed. We also showed that the vortex state in this coupling region is described by use of two components GL equation.4) Nonequilibrium processes : We performed numerical simulation of the GP equation and investigated the formation processes of superfuild vortex states. We find that, in an early state of vortex formation, turbulent states are formed as results of the Kelvin waves, and then the system settles down to the state of the triangular lattice.