Observing complementary Lucas sequences using non-Hermitian zero modes

TL;DR

This paper demonstrates how complementary Lucas sequences, including Fibonacci numbers, can be observed in a non-Hermitian physical system with gain and loss modulation, revealing their manifestation in localized edge states and a constant-intensity mode.

Contribution

It introduces a physical platform that exhibits complementary Lucas sequences through non-Hermitian zero modes in a gain-loss modulated system.

Findings

Lucas sequences appear in localized edge states

Constant-intensity mode also exhibits Lucas sequence properties

Physical realization of Lucas sequences in non-Hermitian systems

Abstract

The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, defined by the same recurrence relation, are less well-known. In this work, we show that a special case of such complementary Lucas sequences can be observed on the same physical platform. It consists of a gain-and-loss-modulated non-Hermitian reservoir bridging two mirror-symmetric systems, which manifests the Lucas sequences in linearly localized edge states and a constant-intensity mode, respectively.