# Topological edge states of interacting photon pairs emulated in a topolectrical circuit

## TL;DR

This paper demonstrates a classical topolectrical circuit that simulates topological states of interacting photon pairs, enabling the study of quantum topological phenomena through accessible measurements.

## Contribution

The authors design a topolectrical circuit that emulates a quantum system with topological two-photon states, providing a new platform for exploring quantum topological physics.

## Key findings

- Successfully simulated two-photon topological states in a circuit
- Measured bulk and edge state frequencies and topological invariants
- Reconstructed two-photon probability distribution from circuit data

## Abstract

Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities can be achieved by realizing topological states of quantum light. This area, however, remains largely uncharted due to the number of experimental challenges. Here, we take an alternative route and design a classical structure based on topolectrical circuits which serves as a simulator of a quantum-optical one-dimensional system featuring the topological state of two photons induced by the effective photon-photon interaction. Employing the correspondence between the eigenstates of the original problem and circuit modes, we use the designed simulator to extract the frequencies of bulk and edge two-photon bound states and evaluate the topological invariant directly from the measurements. Furthermore, we perform a reconstruction of the two-photon probability distribution for the topological state associated with one of the circuit eigenmodes.