Abstract
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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