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Physical Review A

Cloaking spin- 12 matter waves

De‐Hone Lin

Published Jun 28, 2010• 23 citations
Publisher

Abstract

A physical construct for the cloaking of relativistic spin-$\frac{1}{2}$ matter waves is proposed. It is shown that when the effective energy and mass of relativistic spin-$\frac{1}{2}$ particles moving in an effective vector field in a spherical shell are controlled, their matter waves can be perfectly guided through the shell without any distortion or loss; that is, the construct provides a three-dimensional cloaking shell for relativistic spin-$\frac{1}{2}$ matter waves. The proposal serves as the basis for some interesting applications such as providing a method to guide the matter waves of spin particles and an ideal setup to exhibit spin-spin interactions as well as perfect quantum interferences of some global effects in spin-$\frac{1}{2}$ matter waves.

DOI
10.1103/physreva.81.063640

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To understand the propagation behavior of an oblique incident matter wave in a three-dimensional non-spherical quantum cloak, we perform the transformation design for the prolate spheroidal coordinate system and obtain a quantum cloak with an ellipsoidal shape. The mass parameters and effective potential for the creation of a perfect prolate spheroidal invisibility region are given. The analytic representations of the cloaked matter wave and probability current in the cloaking shell are presented. Special attention is paid to the discussions of the probability current in the cloaking shell for only that current can manifestly exhibit how the wave vector of the matter wave is curved, rotated, and guided in the cloaking shell to flow around the non-spherically invisible region. With the current analysis, one shows that the presented cloak can perfectly guide the matter wave in the situation of any oblique incidence. The proposed prolate spheroidal cloak for matter waves provides the first non-spherically three-dimensional setup for quantum cloaking.
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