Multidimensional transformation design method for matter waves

Abstract

A multidimensional transformation design method that allows us to design a cloaking shell of multivariables for matter waves is proposed. As applications, cloaking shells for an elliptical invisible region, a region specified by the radial and angular variables, and an invisible region specified by the polar angle for the Coulomb scattering wave have been designed. It is shown that the mass parameters required for a perfect cloaking of a matter wave in the elliptical coordinate system are constant.

Controlling matter waves in momentum space

“…As pointed out in [9][10][11], the essence of the TDM is to look for a coordinate transformationp i =p i (p) such that the quantum wave is transformed from (p i ) into (p i ) and keeps form invariance.…”

“…In contrast to the transformation design in position space [7][8][9][10][11], where the particle mass itself has to be modulated by the cloak to reach the cloaking effect or get to a new transformed state [10], the presented momentum cloak is independent of the particle mass itself, and the cloak can be created by only constructing an anisotropic trap and offering the effective potential U in the p space. This could probably point out an alternative application of the transformation design in the quantum world.…”

“…Several methods have been suggested to approach this goal. They are based on the inverse scattering theory [3], the cancellation of scattering phase shifts [4][5][6], and the transformation design manner [7][8][9][10][11] . The first approach needs to construct infinite ring-shaped potentials to invisibly block a matter wave from a spherical concealing space, while the rest have to provide an effective potential and control the particle mass in a specific guiding region such that the matter wave flows around, or passes through, a concealed region and, undisturbed, returns to its initial incident position, achieving the effect of invisibility.…”

A mass-independent conformal quantum cloak

“…Several schemes developed from the inverse scattering theory [1], the cancellation of scattering phase shifts [2], and the transformation design method (TDM) [3,4] have been proposed for the construction of an invisibility cloak. The first and second schemes approach the device with a finite number of ring-shaped potentials [1] and the zero phase shift conditions of the lowest two partial waves [5][6][7], while the TDM carries out the device by way of reinterpreting a transformation structure as the mass parameters of the quantum particle and an effective potential in a specific shell, which leads the matter wave to flow around the internal region of the cloak [8][9][10][11]. Among these three proposals, the steering with the cloak generated by the TDM is exact.…”

Detecting the existence of an invisibility cloak using temporal steering

“…Invisibility cloak based on the transformation design method (TDM) has attracted great attentions in the past decade 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 . The main idea of the TDM is to perform the coordinate transformation on the wave equation of the corresponding cloaking wave to create the hiding region ( Fig.…”