Abstract
<title>Abstract</title> <p>The seminal phenomenon of the Bose-Einstein condensation has been observed on a large variety of physical platforms, e.g., superfluid helium, fermions with attractive interactions, quasiparticles in solids, and ultracold atomic gases. Recently, the Bose–Einstein condensation of non-interacting photons in an optical microcavity has been confirmed experimentally. Here, we report the experimental observation of Bose-Einstein like condensation and collective Bogoliubov excitations in a low dissipative microwave resonator with embedded superconducting quantum network composed of multiple flux qubits. Under strong coherent pumping the resonator mode becomes macroscopically populated, giving rise to hybridized photon–qubit collective modes. The Bogoliubov-like collective excitations appearing in a response to a nearby-frequency probe tone, accompanied by pronounced bistability and hysteresis in the measured transmission coefficient, provide the first experimental evidence of a Bose–Einstein–like condensate of microwave photons on a superconducting circuit platform. A theoretical framework based on Gross-Pitaevskii formalism and taking into account the ac Stark effect inducing the effective interaction between photons, quantitatively reproduces the experimental observations and identifies the regime of appearance of microwave Bogoliubov excitations. These results establish a proof of principle for exploiting driven collective states in superconducting circuits as a platform for quantum-limited microwave detection and engineered many-body photonic systems for quantum information processing.</p>