Approximate quantum cloaking and almost trapped states

Abstract

We describe families of potentials which act as approximate cloaks for matter waves, i.e., for solutions of the time-independent Schrödinger equation at energy $E$, with applications to the design of ion traps. These are derived from perfect cloaks for the conductivity and Helmholtz equations, by a procedure we refer to as isotropic transformation optics. If $W$ is a potential which is surrounded by a sequence $\{V_n^E{\}}_{n=1}^{\infty }$ of approximate cloaks, then for generic $E$, asymptotically in $n$ (i) $W$ is both undetectable and unaltered by matter waves originating externally to the cloak; and (ii) the combined potential $W+V_n^E$ does not perturb waves outside the cloak. On the other hand, for $E$ near a discrete set of energies, cloaking {\it per se} fails and the approximate cloaks support wave functions concentrated, or {\it almost trapped}, inside the cloaked region and negligible outside. Applications include ion traps, almost invisible to matter waves or customizable to support almost trapped states of arbitrary multiplicity. Possible uses include simulation of abstract quantum systems, magnetically tunable quantum beam switches, and illusions of singular magnetic fields.

Revised, with new figures. Single column format

References in corpus (7)

• General Relativity in Electrical Engineering
• Confirmation of Cylindrical Perfect Invisibility Cloak Using Fourier-Bessel Analysis
• Cloaking of Matter Waves
• Electromagnetic cloaking by layered structure of homogeneous isotropic materials
• Full-wave invisibility of active devices at all frequencies
• Effectiveness and improvement of cylindrical cloaking with the SHS lining
• Ambiguities in the scattering tomography for central potentials

Cited by in corpus (3)

• Invisibility and Inverse Problems
• The scattering of a cylindrical invisibility cloak: reduced parameters and optimization
• Approximate quantum and acoustic cloaking