Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain

TL;DR

This paper investigates a bosonic chain with phase-dependent chiral photon transport and boundary-sensitive stability, revealing a connection to non-Hermitian models despite a Hermitian Hamiltonian.

Contribution

It introduces a bosonic Kitaev-Majorana chain model exhibiting phase-dependent chirality and boundary condition sensitivity, linking Hermitian dynamics to non-Hermitian phenomena.

Findings

Photon propagation is phase-dependent and can be amplified directionally.

Boundary conditions drastically affect mode localization and stability.

The Hermitian model shows a surprising connection to non-Hermitian asymmetric-hopping models.

Abstract

We study a 1D chain of non-interacting bosonic cavities which are subject to nearest-neighbour parametric driving. With a suitable choice of drive phases, this model is strongly analogous to the celebrated Kitaev chain model of a 1D p-wave superconductor. The system exhibits phase-dependent chirality: photons propagate and are amplified in a direction that is determined by the phase of the initial drive or excitation. Further, we find a drastic sensitivity to boundary conditions: for a range of parameters, the boundary-less system has only delocalized, dynamically unstable modes, while a finite open chain is described by localized, dynamically stable modes. While our model is described by a Hermitian Hamiltonian, we show that it has a surprising connection to non-Hermitian asymmetric-hopping models.