Uncontrolled disorder effects in fabricating photonic quantum simulators on a kagome geometry: A projected-entangled-pair-state versus exact-diagonalization analysis

Abstract

We propose a flexible numerical framework for extracting the energy spectra and photon transfer dynamics of a unit kagome cell with disordered cavity-cavity couplings under realistic experimental conditions. A projected-entangled pair state (PEPS) ansatz to the many-photon wavefunction allows to gain a detailed understanding of the effects of undesirable disorder in fabricating well-controlled and scalable photonic quantum simulators. The correlation functions associated with the propagation of two-photon excitations reveal intriguing interference patterns peculiar to the kagome geometry and promise at the same time a highly tunable quantum interferometry device with a signature for the formation of resonant or Fabry-Pe\'rot-like transmission of photons. Our results justify the use of the proposed PEPS technique for addressing the role of disorder in such quantum simulators in the microwave regime and promises a sophisticated numerical machinery for yet further explorations of the scalability of the resulting kagome arrays. The introduced methodology and the physical results may also pave the way for unraveling exotic phases of correlated light on a kagome geometry.