Supersymmetric reshaping and higher-dimensional rearrangement of photonic lattices

TL;DR

This paper introduces a supersymmetric approach to design 2D photonic lattices with spectra matching 1D Jx lattices, enabling scalable, robust quantum imaging and state transfer applications.

Contribution

It presents a novel supersymmetry-based method to create higher-dimensional photonic systems with identical spectra to 1D lattices, improving scalability and robustness.

Findings

2D systems retain key imaging and state transfer properties

Method extends to other separable-spectrum systems

Facilitates experimental fabrication and robustness

Abstract

Integrated Jx photonic lattices, inspired by the quantum harmonic oscillator and due to their equidistant eigenvalue spectrum, have been proven extremely useful for various applications, such as perfect imaging and coherent transfer of quantum states. However, to date their large-scale implementation remains challenging. We apply concepts from supersymmetry to construct two-dimensional (2D) systems with spectra identical to that of one-dimensional (1D) Jx lattices. While exhibiting different dynamics, these 2D systems retain the key imaging and state transfer properties of the 1D Jx lattice. Our method extends to other systems with separable spectra, facilitates experimental fabrication, and may increase robustness to fabrication imperfections in large-scale photonic circuits.