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Under nonequilibrium conditions, quantum optical systems reveal unusualproperties that might be distinct from those in condensed matter. Thefundamental reason is that photonic eigenstates can have arbitrary occupationnumbers, whereas in electronic systems these are limited by the Pauliprinciple. Here, we address the steady-state transport of pseudothermal photonsbetween two waveguides connected through a cavity with Bose-Hubbard interactionbetween photons. One of the waveguides is subjected to a broadband incoherentpumping. We predict a continuous transition between the regimes of Lorentzianand Gaussian chaotic light emitted by the cavity. The rich variety ofnonequilibrium transport regimes is revealed by the zero-frequency noise. Thereare three limiting cases, in which the noise-current relation is characterizedby a power-law, $S\propto J^\gamma$. The Lorentzian light corresponds toBreit-Wigner-like transmission and $\gamma=2$. The Gaussian regime correspondsto many-body transport with the shot noise ($\gamma=1$) at large currents; atlow currents, however, we find an unconventional exponent $\gamma=3/2$indicating a nontrivial interplay between multi-photon transitions andincoherent pumping. The nonperturbative solution for photon dephasing isobtained in the framework of the Keldysh field theory and Caldeira-Leggetteffective action. These findings might be relevant for experiments on photonblockade in superconducting qubits, thermal states transfer, and photonstatistics probing.

Transport of pseudothermal photons through an anharmonic cavity