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Theoretical studies of BEC/BCS states in quantum atomic gases

量子原子气体中BEC/BCS态的理论研究

基本信息

批准号：
17540368
负责人：
MATSUMOTO Hideki
金额：
$ 2.24万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540368/
关键词：
quantum atomic gas Bose-Einstein condensation BCS BEC crossover insulator-superfluid transiton optical lattice Feshbach resonance superfluid vortex state Hubbard model

项目摘要

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.

在本研究项目中，我们研究了BEC/BCS态，并得到了以下结果：1）BCS/BEC交叉中的单粒子激发和相关现象：我们发现，在陷于谐波势中的费米气体中，单粒子激发的能隙由局域于凝聚体表面附近的Andereev模式决定。射频隧道电流谱在弱耦合区Andreev模位置有一个峰值，而在势中心由序参量决定的能量处有一个峰值。3)涡旋态和涡旋成核过程。：我们通过求解 BdG 方程，研究了 BCS/BEC 交叉区域中粒子激发的涡旋态和能谱。随着相互作用强度的增加，涡中心的颗粒分布减少，并形成离散的核心水平。我们还表明，该耦合区域中的涡旋态是用两分量GL方程来描述的。4）非平衡过程：我们对GP方程进行了数值模拟，并研究了超流体涡旋态的形成过程。我们发现，在涡旋形成的早期状态，由于开尔文波而形成湍流状态，然后系统稳定到三角晶格状态。