Superoscillatory PT-symmetric potentials

Yaniv Eliezer*, Alon Bahabad, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the one-dimensional PT-symmetric Schrödinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatorylike potential always generates an entirely real eigenvalue spectrum, its counterpart based on the superoscillatory wave function gives rise to an intricate pattern of PT-symmetry-breaking transitions, controlled by the parameters of the superoscillatory function. One scenario of the transitions proceeds smoothly via a set of threshold values, while another one exhibits a sudden jump to the broken PT symmetry. Another noteworthy finding is the possibility of restoration of the PT symmetry, following its original loss, in the course of the variation of the parameters.

Original languageEnglish
Article number043830
JournalPhysical Review A
Volume98
Issue number4
DOIs
StatePublished - 15 Oct 2018

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