Phase-Dependent Chiral Transport and Effective Non-Hermitian Dynamics in a Bosonic Kitaev-Majorana Chain

Abstract

We study a 1D chain of noninteracting bosonic cavities which are subject to nearest-neighbor parametric driving, thus realizing a bosonic Hamiltonian whose form is reminiscent of the celebrated Kitaev model of a 1D p-wave superconductor. For a suitable choice of drive phases, the model exhibits a number of remarkable properties. This includes phase-dependent chirality: Photons propagate and are amplified in a direction determined by the phase of the initial drive or excitation. It also exhibits a drastic sensitivity to boundary conditions: For a range of parameters, the boundaryless 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. In addition to being of fundamental interest as a new kind of topological bosonic system, our system also has potential practical utility as a quantum amplifier and a source of multimode entangled photons.