Cloaking of matter waves under the global Aharonov-Bohm effect

Multidimensional transformation design method for matter waves

“…As an illustration, the solution of a two-dimensional (2D) cylindrically symmetric quantum cloak is given by (f (ρ),ϕ) instead of by the original (ρ,ϕ), where f (ρ) is a function of the radial variable ρ = x 2 + y 2 that performs a scaling transformation and creates an invisible region around the origin. The effective coordinate-related mass parameters and potential in the cylindrical cloaking shell can be found as M ij = diag(ρf (ρ)/f (ρ),f (ρ)/ρf (ρ))M and U = (1 − ff /ρ)E [6]. However, a coordinate transformation obtained by the direct replacement of variables in Eq.…”

“…Motivated by the concept of the transformation design developed in transformation optics [1][2][3], controlling matter waves to create an invisible region has recently been of much interest [4][5][6][7]. It has been shown that matter waves could be controlled to propagate along a spherical shell without suffering any scattering, leaving an invisible region, by using a transformation design method (TDM) that reinterprets the transformation structure of coordinates as the effective coordinate-dependent factor of mass and potential in the original untransformed system [4,6].…”

“…It has been shown that matter waves could be controlled to propagate along a spherical shell without suffering any scattering, leaving an invisible region, by using a transformation design method (TDM) that reinterprets the transformation structure of coordinates as the effective coordinate-dependent factor of mass and potential in the original untransformed system [4,6]. Differing from TDM, an alternative approach that controls the distribution of matter waves to form a spherically invisible region is given by inverse scattering theory.…”

“…It nevertheless needs to provide infinite many ring-shaped different potentials to approach perfect cloaking [5]. Recently, it was shown that invisible cloaks for a matter wave under the global effect of a magnetic flux, and interacting with the field of a Dirac monopole, could be designed [6,7]. The TDM of matter waves is thus applicable to controlling an interacting matter wave, producing an invisible region.…”

Aharonov-Bohm detection of two-dimensional magnetostatic cloaks

“…Recent papers have looked at solutions to neutralize the magnetic flux through certain regions of space in order to realize two-dimensional quantum cloaks, which may improve quantum experimental setups or bias measurements related to the paths of matter waves 23 . Similarly, transformation optics has been applied 24 on the quantum mechanics platform to design a cloak for quantum particles under A-B effect.…”