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arXiv:0806.0368 · Physical Review Letters

Approximate Quantum Cloaking and Almost-Trapped States

Allan Greenleaf, Yaroslav Kurylev, Matti J. Lassas, Gunther A. Uhlmann

Published Nov 26, 2008• 93 citations
arXivHTMLPDF

Abstract

We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies E, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak. For certain E, however, the approximate cloaks are resonant, supporting wave functions almost trapped inside the cloaked region and negligible outside. Applications include dc or magnetically tunable ion traps and beam switches.

DOI
10.1103/physrevlett.101.220404

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We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies E, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak. For certain E, however, the approximate cloaks are resonant, supporting wave functions almost trapped inside the cloaked region and negligible outside. Applications include dc or magnetically tunable ion traps and beam switches.
As the modern development of electronic device smaller and smaller, quantum effect would become significant. Thus extending the concept of quantum mechanics into design of new electronic devices becomes more important. Controlling the movement of these electrons plays the central role in this issue. In this work, we propose a new quantum cloaking mechanism which has completely different to the previous work of Liao et al [1]. This mechanism is based on the scattering cancellation and the interplay among the nodal points of partial waves, that one can simultaneously guide the probability flux outside the interior and keep the total scattering cross section negligible. Moreover, we can put any electric devices inside quantum cloaking without affecting outside probability of matter wave. With the analogy between quantum matter waves and classical waves, the concept of our method can be applied in other fields, such as electromagnetic and acoustic systems, etc.
A physical construct for the cloaking of relativistic spin-12\frac{1}{2}21​ matter waves is proposed. It is shown that when the effective energy and mass of relativistic spin-12\frac{1}{2}21​ 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-12\frac{1}{2}21​ 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-12\frac{1}{2}21​ matter waves.
A cornerstone in the operation of numerous detecting and sensing quantum setups is the sharp change in the response once a condition ceases to be effective; this regime is typically realized by perfectly cloaking a nanoinclusion from the propagating matter waves. Such a purpose is found well-served by optimally sized nanocylinders, embedded into a suitable quantum texture, that efficiently hide themselves from obliquely impinging electron beams. The optimal designs exhibit high selectivity for particle energies while being wideband with respect to incidence angles; these features render them deployable in various quantum devices from furtive sensors and detectors to quantum switches and matter-wave filters.
Parabolic quantum cloaks with unbounded and bounded invisible regions are presented with the method of transformation design. The mass parameters of particles for perfect cloaking are shown to be constant along the parabolic coordinate axes of the cloaking shells. The invisibility performance of the cloaks is inspected from the viewpoints of waves and probability currents. The latter shows the controllable characteristic of a probability current by a quantum cloak. It also provides us with a simpler and more efficient way of exhibiting the performance of a quantum cloak without the solutions of the transformed wave equation. Through quantitative analysis of streamline structures in the cloaking shell, one defines the efficiency of the presented quantum cloak in the situation of oblique incidence. The cloaking models presented here give us more choices for testing and applying quantum cloaking.
We introduce the concept of furtive quantum sensing, demonstrating the possibility of concealing quantum objects from matter waves while maintaining their ability to interact and to get excited by the impinging particles. This is obtained by cloaking, with tailored homogeneous metamaterial layers, quantum systems having internal degrees of freedom. The effect is a low-observable quantum sensor with drastically reduced elastic scattering and optimized absorption levels, a concept that opens interesting venues in particle detection, high-efficiency electrical pumping, and quantum information processing.