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中国科学通报:英文版

Quantum information and many body physics with cold atoms

Zhang, Xiaofei, Chen, Yao-Hua, Liu, Guo-cai, Wu, Wei, Wen Wen, Lin Lin, Wu-Ming

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

我们在各种各样的外部潜力与冷原子在量信息和许多身体物理考察我们的最近的理论进展,例如泛音潜力, kagome 光格子,三角形的光格子,和蜂房格子。在泛音潜力的冷原子的许多身体物理在吝啬地的 Gross-Pitaevskii 方程的框架被调查。然后量阶段转变和在三角形的光格子的冷原子的强烈相关的效果,和蜂房格子上的交往的迪拉克费米子,被使用簇调查动态吝啬地的理论和连续时间量蒙特卡罗方法。我们也在 kagome 学习量旋转霍尔效果光格子。

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我们在各种各样的外部潜力与冷原子在量信息和许多身体物理考察我们的最近的理论进展,例如泛音潜力, kagome 光格子,三角形的光格子,和蜂房格子。在泛音潜力的冷原子的许多身体物理在吝啬地的 Gross-Pitaevskii 方程的框架被调查。然后量阶段转变和在三角形的光格子的冷原子的强烈相关的效果,和蜂房格子上的交往的迪拉克费米子,被使用簇调查动态吝啬地的理论和连续时间量蒙特卡罗方法。我们也在 kagome 学习量旋转霍尔效果光格子。
Nonlinear effects lie amongst the most interesting phenomena in physical, chemical and biological systems. In quantum physics nonlinearity is provided by inter-particle interactions. A theoretical many-body description can be made in the framework of the mean field approximation, which yields the Hartree-Fock equations for a system of interacting fermions and the Gross-Pitaevskii equation for interacting bosons. The latter is widely applied to Bose-Einstein condensates (BECs) of cold atoms and satisfactorily describes a variety of nonlinear phenomena, such as the superfluid transition, formation of single vortices and vortex lattices. From the mathematical point of view the Gross-Pitaevskii equation is equivalent to the nonlinear Schrödinger equation, used in nonlinear optics for the description of self-focusing and soliton propagation.
Above-barrier reflection of cold alkali atoms by resonant laser light was considered analytically within the Gross-Pitaevskii approximation. Correction for the reflection coefficient because of a weak nonlinearity of the stationary Schrödinger equation has been derived using multiscale analysis as a form of perturbation theory. The nonlinearity adds spatial harmonics to linear incident and reflecting waves. It was shown that the role of nonlinearity increases when the kinetic energy of an atom is nearly to the height of the potential barrier. Results are compared to the known numerical derivations for wave functions of the Gross-Pitaevskii equation with the step potential.