Imaginary Gauge Transformation in Momentum Space and Dirac Exceptional Point

Jose H. D. Rivero, Liang Feng, and Li Ge

Phys. Rev. Lett. 129, 243901 – Published 7 December 2022

Abstract

An imaginary gauge transformation is at the core of the non-Hermitian skin effect. Here, we show that such a transformation can be performed in momentum space as well, which reveals that certain gain- and loss-modulated systems in their parity-time ( $P T$ ) symmetric phases are equivalent to Hermitian systems with real potentials. Our analysis in momentum space also distinguishes two types of exceptional points (EPs) in the same system. Besides the conventional type that leads to a $P T$ transition upon the continuous increase of gain and loss, we find real-valued energy bands connected at a Dirac EP in hybrid dimensions, consisting of a spatial dimension and a synthetic dimension for the gain and loss strength.

Received 23 September 2022
Accepted 22 November 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.243901

Physics Subject Headings (PhySH)

Microcavity & microdisk lasers Non-Hermitian systems Waveguides

PT-symmetry

General Physics

Authors & Affiliations

Jose H. D. Rivero^1,2, Liang Feng³, and Li Ge ^1,2,*

¹Department of Physics and Astronomy, College of Staten Island, CUNY, Staten Island, New York 10314, USA
²The Graduate Center, CUNY, New York, New York 10016, USA
³Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA