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Algebraic Variational Framework for Robust Entanglement in Driven-dissipative Kerr Resonators: Foundations for Integrated Photonic Quantum Technologies

Isamu Ohnishi

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.6820521

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Networks of nonlinear resonators offer intriguing perspectives as quantum simulators for nonequilibrium many-body phases of driven-dissipative systems. Here, we employ photon correlation measurements to study the radiation fields emitted from a system of two superconducting resonators in a driven-dissipative regime, coupled nonlinearly by a superconducting quantum interference device, with cross-Kerr interactions dominating over on-site Kerr interactions. We apply a parametrically modulated magnetic flux to control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate, we observe a crossover from an ordered to a delocalized state of photons. The presented coupling scheme is intrinsically robust to frequency disorder and may therefore prove useful for realizing larger-scale resonator arrays.
The framework of Keldysh path integral concisely describes quantum systems driven away from thermal equilibrium, such as the two-photon driven Kerr oscillator. Within the thermodynamic limit of diverging photon number, we map it to a Martin-Siggia-Rose-Janssen-de Dominicis path integral and obtain a purely classical, stochastic equivalent where photon self-interaction plays the role of temperature. This perspective sheds light on the difficulties encountered in the search for an effective thermodynamic potential to describe the bistability of the model. It allows us to estimate the bistable tunneling rates using a real-time instanton technique leading to an analytical expression of the phase boundary, the first to our knowledge. It opens the way to powerful semianalytical techniques to be applied to various quantum optics models displaying bistability.