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## Transport of pseudothermal photons through an anharmonic cavity

Under nonequilibrium conditions, quantum optical systems reveal unusual properties that might

be distinct from those in condensed matter. The fundamental reason is that photonic eigenstates

can have arbitrary occupation numbers, whereas in electronic systems these are limited by the Pauli principle. Here, we address the steady-state transport of pseudothermal photons between two waveguides connected through a cavity with Bose–Hubbard interaction between photons. One of

the waveguides is subjected to a broadband incoherent pumping. We predict a continuous transition between the regimes of Lorentzian and Gaussian chaotic light emitted by the cavity. The rich variety of nonequilibrium transport regimes is revealed by the zero-frequency noise. There are three limiting cases, in which the noise-current relation is characterized by a power-law, S ∝ J^γ . The Lorentzian light corresponds to Breit-Wigner-like transmission and γ = 2. The Gaussian regime corresponds to many- body transport with the shot noise (γ = 1) at large currents; at low currents, however, we find an unconventional exponent γ = 3/2 indicating a nontrivial interplay between multi-photon transitions and incoherent pumping. The nonperturbative solution for photon dephasing is obtained in the framework of the Keldysh field theory and Caldeira-Leggett effective action. These findings might be relevant for experiments on photon blockade in superconducting qubits, thermal states transfer, and photon statistics probing.