Topological States of Interacting Photon Pairs Emulated in a Topolectrical Circuit

In the present work, we study the formation of topological edge states of bound photon pairs, doublons. We consider a one-dimensional array of optical microresonators with tunneling nearest-neighbor couplings, with two photons traveling along the array. Considering the interaction between photons that share the same resonator and taking into account two-photon tunneling processes, we construct a system that supports topological edge states of doublons and does not support any edge states in the single-photon regime. Thus, we provide an example of interaction-induced topological states of quantum light. To illustrate our findings, we perform an analog emulation of the proposed system applying topolectrical circuit platform. We demonstrate that the eigenstates of the Hamiltonian describing initial two-particle quantum problem can be exactly mapped to the eigenmodes of a two-dimensional classical electric circuit composed of inductors and capacitors. We realize such a circuit working at kHz frequencies and study it experimentally. After obtaining the signatures of the two-photon edge state in the resonance spectrum of the circuit, we perform a reconstruction of the corresponding eigenmode and thus provide the direct evidence of the edge state formation. To demonstrate the topological origin of this doublon edge state, we extract the associated topological invariant directly from the experimental data. Obtained experimental results fully support our theoretical predictions and provide valuable insights into topological protection in interacting quantum systems and its emulation with classical setups.