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Physics Letters A

Comment on “Relative phase between quantum transmission and reflection amplitudes in one dimension” by Y. Fu

Massimiliano Sassoli de Bianchi

Published Aug 1, 1996• 0 citations
Publisher
DOI
10.1016/0375-9601(96)00509-9

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arXiv:1709.07027•Europhysics Letters (EPL)•Jan 2, 2018•20 citations
Abstract When a light wave is reflected at the interface between two semi-infinite media, the relative phase between the reflected and incident amplitudes is a fundamental optical effect. Another fundamental phase relation arises in a symmetric beam splitter between its reflection and transmission amplitudes. Both effects originate from the phase structure of wave scattering, although their underlying connection is not always clearly understood. As a pedagogical investigation, this paper systematically analyzes these phase relations using simple one-dimensional potential models in quantum mechanics and provides intuitive physical explanations. For a symmetric square barrier, the reflected and transmitted amplitudes necessarily differ in phase by ±π/2, with the reflection phase referenced at the interface on the incident side and the transmission phase referenced at the interface on the exit side. The result is further extended to general symmetric barriers, for which the detailed form of the barrier determines only whether the phase difference is +π/2 or -π/2. The role of this phase structure in the second-order interference of two identical particles is then examined. Through this sequence of analysis, half-wave loss at a reflecting interface, the phase relation in a symmetric beam splitter, and multiparticle quantum interference are incorporated into a unified wave-scattering framework. This treatment provides a useful pedagogical reference for related topics in quantum mechanics and optics courses.
The scattering of quantum particles by non-Hermitian (generally non-local) potentials in one dimension may result in asymmetric transmission and/or reflection from left and right incidence. After extending the concept of symmetry for non-Hermitian potentials, eight generalized symmetries based on the discrete Klein's four-group (formed by parity, time reversal, their product, and unity) are found. Together with generalized unitarity relations they determine selection rules for the possible and/or forbidden scattering asymmetries. Six basic device types are identified when the scattering coefficients (squared moduli of scattering amplitudes) adopt zero/one values, and transmission and/or reflection are asymmetric. They can pictorically be described as a one-way mirror, a one-way barrier (a Maxwell pressure demon), one-way (transmission or reflection) filters, a mirror with unidirectional transmission, and a transparent, one-way reflector. We design potentials for these devices and also demonstrate that the behavior of the scattering coefficients can be extended to a broad range of incident momenta.