原子光纤中物质波演化的唯象描述

The Phenomenological Description of Time Evolutionof Matter Waves inside an Atom Fiber

最近,Luo等人在实验上实现了所谓的原子光纤技术(原子物质波沿着一个25μm长的螺旋型波导走完了完整的两圈路径)。本文替该弯曲原子光纤中物质波的时间演化量子力学过程提供了一个唯象描述,主要讨论了三个相关问题:(i)原子物质波与弯曲波导相互作用的有效哈密顿量的构造;(ii)获得描述弯曲原子光纤中物质波的波函数;(iii)证明该物质波波函数恰好是原子动量算符的本征态,表明该唯象描述是自洽的。我们认为本文的唯象模型对于所谓的"原子光学"(atomoptics)的研究是有一定意义的。

More recently, Luo et al. reported a novel experiment of the so-called "atom fiber", i.e., an atomic guide that can control the matter waves (such as cold neutral atoms and ideally Bose-Einstein condensates) on a two dimensional surface of the atom chip. A phenomenological description of time evolution of atomic matter waves inside a spiral shaped atomic-wave guide is presented in this paper. We study three related topics: (i) the effective Hamiltonian and the time-development equation governing the matter waves; (ii) the wavefunctions describing the matter waves in the noncoplanar atom guide; (iii) showing that such wavefunctions obtained is just the eigenstates of the atomic momentum operator. It is believed that both the idea and the results presented here may have relevance to some fundamental problems of atom optics.