Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{PT}$-symmetric quantum rotator

TL;DR

This paper explores wave transport in a $ ext{PT}$-symmetric kicked quantum rotator, revealing how localization and resonances influence symmetry breaking and induce ratchet acceleration, with an optical setup proposed for visualization.

Contribution

It introduces a $ ext{PT}$-symmetric extension of the kicked quantum rotator, analyzing localization effects, symmetry breaking, and ratchet acceleration, along with an optical implementation proposal.

Findings

Dynamical localization supports the unbroken $ ext{PT}$ phase.

In the resonance regime, $ ext{PT}$ symmetry is broken and ratchet acceleration occurs.

Optical implementation can visualize acceleration modes in fractional Talbot cavities.

Abstract

We consider wave transport phenomena in a $\mathcal{PT}$-symmetric extension of the periodically-kicked quantum rotator model and reveal that dynamical localization assists the unbroken $\mathcal{PT}$ phase. In the delocalized (quantum resonance) regime, $\mathcal{PT}$ symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically-kicked $\mathcal{PT}$-symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.