Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems

TL;DR

This paper demonstrates how non-Hermitian photonic waveguide systems with pseudo PT symmetry can simulate relativistic Zitterbewegung, revealing controllable oscillations and energy localization with potential applications in optical systems.

Contribution

It introduces a novel approach to observe and control relativistic Zitterbewegung in non-Hermitian optical waveguides using pseudo PT symmetry, expanding understanding of relativistic quantum phenomena in photonics.

Findings

Periodic suppression of ZB trembling observed

Spatial energy localization achieved

Hermitian-like ZB oscillations demonstrated

Abstract

Zitterbewegung (ZB) is a phenomenon in relativistic quantum systems where the electron wave packet exhibits a trembling or oscillating behavior during its motion, caused by its interaction or coupling with the negative energy state. To directly observe ZB in electronic systems is difficult, due to the challenges associated with the atomic scale wavelength of the electron. Photonic systems offer an alternative paradigm. We exploit the concept of pseudo parity-time (pseudo PT ) symmetry to study ZB in non-Hermitian quantum systems implemented as an experimentally feasible optical waveguide array. In particular, the non-Hermitian Hamiltonian is realized through evanescent coupling among the waveguides to form a one-dimensional lattice with periodic modulations in gain and loss along the guiding direction. As the modulation frequency is changed, we obtain a number of phenomena including periodically suppressed ZB trembling, spatial energy localization, and Hermitian-like ZB oscillations. We calculate phase diagrams indicating the emergence of different types of dynamical behaviors of the relativistic non-Hermitian quantum system in an experimentally justified parameter space. We provide numerical results and a physical analysis to explain the distinct dynamical behaviors revealed by the phase diagrams. Our findings provide a deeper understanding of both the relativistic ZB phenomenon and non-Hermitian pseudo-PT systems, with potential applications in controlling/harnessing light propagation in waveguide-based optical systems.