Chiral current circulation and $\mathcal{PT}$ symmetry in a trimer of oscillators

TL;DR

This paper develops a quantum theory for a bosonic trimer with complex couplings, revealing how tuning phases induces chiral currents and unidirectional circulation, especially near $ ext{PT}$ symmetry breaking points, with implications for nanoscale nonreciprocal devices.

Contribution

It introduces a novel quantum model of a bosonic trimer with complex couplings that enables control of chiral currents and circulation, highlighting the role of $ ext{PT}$ symmetry and exceptional points.

Findings

Chiral currents can be induced by tuning complex phases.

Unidirectional circulation occurs under specific coupling conditions.

Population dynamics show notable features near $ ext{PT}$ symmetry breaking points.

Abstract

We present a simple quantum theory of a bosonic trimer in a triangular configuration, subject to gain and loss in an open quantum systems approach. Importantly, the coupling constants between each oscillator are augmented by complex arguments, which give rise to various asymmetries. In particular, one may tune the complex phases to induce chiral currents, including the special case of completely unidirectional (or one-way) circulation when certain conditions are met regarding the coherent and incoherent couplings. When our general theory is recast into a specific non-Hermitian Hamiltonian, we find interesting features in the trimer population dynamics close to the exceptional points between phases of broken and unbroken $\mathcal{PT}$ symmetry. Our theoretical work provides perspectives for the experimental realization of chiral transport at the nanoscale in a variety of accessible nanophotonic and nanoplasmonic systems, and paves the way for the potential actualization of nonreciprocal devices.